Along with monocrystalline and liquid scintillation materials the polymer scintillation compositions – plastic scintillators which have a diversity of advantages (technology of preparation, work surface etc.), are widely used. Plastic scintillators represent a complex system composed of a polymer (polymer base) and an organic luminescent compound (luminescent additive). The important mechanism in scintillators operation is nonradiative transfer of electrons excitation energy from base matrix to luminescent additives. In this study we have investigated composition composed of polymethylmethacrylate with naphthalene and 1,4-bis(5-phenyloxazol-2-yl)benzene (POPOP) which were used as luminescent additives. The donor of energy is naphthalene and the acceptor is POPOP molecule. The calculations were carried out by using Gaussian 98 program package. Geometry optimizations of the single molecules were carried out with the use of Becke’s three-parameter hybrid method with Lee, Yang and Parr (B3LYP) gradient-corrected correlation functional and the standard 6-31G(d) basis set. The theoretical UV-vis spectra were obtained by ZINDO/S methods where discrete spectra of excitation energies and corresponding their oscillator strengths were estimated from several tens lowest-energy singlet and triplet transitions. The following sequence of calculations was used: • Optimization of molecules naphthalene and POPOP separately; • UV-vis spectra calculations for each of these molecules; • Construction of different space configurations of complex composed of naphthalene and POPOP located in parallel planes; • Configuration interactions and energy levels for different space configurations of complexes naphthalene-POPOP. Analyses of theoretical data indicated that excited energy levels of naphthalene are located higher than the lowest singlet states of POPOP and this is the key condition for intermolecular energy transfer. Calculated UV-vis spectra (energy of π→π* transitions and their oscillator strengths) of POPOP, naphthalene and their various complexes are in good agreement with experimental data. The oscillator strength of POPOP’s π→π* transition increases as the number of molecules in complex increases. These results are confirmed by experimental data on POPOP luminescence dependence on concentration of naphthalene in composition. The space configuration of POPOP-naphthalene which provides the best agreement of estimated and experimental results was determined.
This work is a theoretical study of supramolecular host-guest systems comprising a macrocycle cucurbit[8]uril (CB[8]) and copper(II) complexes. As guest complexes, Cu(en)2, Cu(cyclen) and Cu(cyclam) were considered (en – ethylenediamine, cyclen – 1,4,7,10-tetraazacyclododecane, cyclam – 1,4,8,11-tetraazacyclotetradecane).
Quantum-chemical calculations were performed in the framework of the density functional theory using the PBE exchange-correlation functional [1] and a specially optimized double-zeta basis set implemented into the PRIRODA program package [2,3].
As a result of this work, optimal structures of isolated copper(II) complexes as well as their host-guest complexes with cucurbit[8]uril were determined. The structural parameters obtained quantum-chemically are in a good agreement with some available experimental X-ray data [4,5]. At the next step the maximum number of water molecules in the innner cavity of CB[8] was estimated. It was found that this number equal 13. Additionally, thermodynamic parameters of inclusion reactions of the complexes under study into cucurbit[8]uril taking into account effects of water molecules desorption from the CB[8] cavity were estimated. The calculated Gibbs free energy gains ΔG0298 for these reactions are –47.2, -47.4 and 2.6 kcal/mol for ethylenediamine, cyclen and cyclam copper(II) complexes, correspondingly. It was shown, that the thermodynamic probability of the reaction with the cyclam copper(II) complex increases remarkably as the temperature increases.
The authors are indebted to the Russian Foundation for Basic Research (Grant No 08-03-00861-а).
References
Кукурбит[n]урилы (CB[n]) представляют собой макроциклические кавитанды, обладающие рядом уникальных химических свойств и нашедшие широкое практическое применение.
В данной работе представлены результаты квантово-химического исследования структурных и термодинамических особенностей формирования CB[n], выполненного на уровне теории функционала плотности (версия РВЕ) c использованием DZ базисного набора. Для полностью оптимизированных структур проводился расчет частот нормальных колебаний. Отсутствие в спектре мнимых значений частот служило подтверждением того, что оптимизированные структуры отвечают минимумам на поверхности потенциальной энергии. Из термохимического анализа рассчитывались термодинамические характеристики систем: полная энтропия, энтальпия и свободная энергия Гиббса.
На основе имеющихся экспериментальных данных предложен механизм формирования кукурбит[n]урилов в процессе синтеза. В результате детального квантово-химического анализа этого механизма впервые удалось обосновать экспериментально установленный факт наибольшего выхода CB[6] в условиях синтеза по сравнению с другими гомологами семейства CB[n].
Для водных растворов CB[6] и CB[8] исследовано структурирование молекул воды в полости кавитанда, а именно, определены состав и строение водно-молекулярных кластеров, формирующегося внутри этих кавитандов.
Проведено детальное исследование структуры супрамолекулярных соединений включения с участием CB[8] и бис-этилендиаминового, цикленового и цикламового комплексов Cu(II). Полученные структурные параметры находятся в хорошем согласии с некоторыми имеющимися рентгеноструктурными данными. Оценены термодинамические параметры реакций включения, протекающие по механизму гость-хозяин с учетом конкурентного замещения воды в полости кавитанда.
Авторы благодарят Российский фонд фундаментальных исследований за финансовую поддержку (грант 08-03-00861-а)
A new approach to static and dynamic first and second hyperpolarizabilities and two-photon absorption transition moments based on the algebraic diagrammatic construction (ADC) scheme for polarization propagator [1] and intermediate state representation concept (ISR) [2] was formulated and implemented. The approach comprises approximation schemes ADC/ISR(n) treating linear, quadratic and cubic response properties consistently up to second order (n=2) of many-body perturbation theory. Several useful extensions of the ADC/ISR schemes beyond second order were also introduced, including the so-called ADC/ISR(2)-E scheme treating consistently double excitations through first order and the ADC/ISR(3/2) scheme treating excitation energies and transition moments respectively through third and second order.
In the ADC/ISR approach, the quantum mechanical sum-over-state (SOS) expressions for liner and non-linear response functions can be transformed to equations operating with matrix quantities representing transition operators and shifted Hamiltonian within the basis of intermediate states [3]. Evaluation of the resulting matrix equations can be efficiently accomplished using the block-Lanczos algorithm in order to cope with the resolvent matrices entering the ADC/ISR response equations.
The ADC/ISR methods were tested in the first applications to series of prototype molecules including H2O, HF, CO, H2CO, HCN, NH3. For these molecules the static first and second hyperpolarizabilities were calculated. As an example of frequency dependent properties, the second harmonic generation (SHG), optical rectification (OR) and electric-field-induced second harmonic generation (ESHG) effects were considered. The resonant two-photon absorption (r TPA) characteristics were calculated for selected transitions of the above molecules. The present results of the ADC(1), ADC(2), ADC(2)-E and ADC(3/2) schemes are in good agreement with the data of the linear response coupled cluster schemes CCS, CC2 and CCSD. At the ADC(3/2) level our results are only slightly inferior to the results of the CC3 scheme, known for its high accuracy reaching the accuracy of the full configuration interaction (FCI) method. Very favorable scaling and convergence properties of the ADC/ISR methods were found with respect to the number of Lanczos iterations, level of the electron correlation account and size of the one-particle basis set. These allow us to conclude that the developed ADC/ISR approach and implemented approximation schemes appear to be highly promising for ab initio calculations of various molecular response properties.
[1] J. Schirmer, Phys. Rev. A.– 1982.– Vol. 26.– P. 2395.
[2] J. Schirmer, A. B. Trofimov, J. Chem. Phys.– 2004.– Vol. 120.– P. 11449.
[3] A. B. Trofimov, I. L. Krivdina, J. Weller, J. Schirmer, Chem. Phys.– 2006.– Vol. 329.– P. 1.
Regularities of gas-phase adsorption of formaldehyde on Cu, Ag, Au, Pd and Pt surfaces attract attention due to the rapid development of heterogeneous catalysis on transition metals. It is known that H2CO is the main product originated in the industrial partial oxidation of methanol on silver surfaces and it is an important intermediate in the industrial synthesis of methanol on supported copper surfaces [1,2]. In this work the quantum chemical modeling of the gas-phase adsorption of formaldehyde and ionic forms of methylene glycol on (111) face of Cu, Ag, Au, Pd and Pt is carried out in the framework of density functional theory. Adsorption surface was modeled with the Me31(19,12) cluster. Results indicate weak interaction of formaldehyde with all considered metals. The internal geometric parameters of the adsorbed formaldehyde molecule are identical to those computed for the gas-phase molecule. Obtained results permit to conclude that formaldehyde adsorbs physically on (111) surface of all considered metals. Cationic form of methylene glycol chemisorbs on Cu, Ag, Au, Pd and Pt surfaces with high energetic effect. Adsorption energy of CH3O+ decreases in a series: Pd > Pt > Cu > Ag > Au. Cationic form of methylene glycol is bonded to metal through carbon atom situated on top position relative to surface. During optimization of methylene glycol anionic form position on metal surface two possible adsorption states were found. The less stable adsorption state was established only for Cu, Ag and Au surface. For favorable adsorption state adsorption energy decreases in a series: Pt > Pd > Au > Cu > Ag and thus isn't correlate with the row obtained for CH3O+. The adsorption bond CH3O2-/Me is more strong than CH3O+/Me for all considered metals. In favorable adsorption state anionic form of methylene glycol is bonded to metal through oxygen atom situated near on top position relative to surface. It is known that CH3O2- adsorbs on IB-metals and platinum group metals in water solutions with dissociation and formation of atomic hydrogen. In this work the possibility of dissociative gas-phase adsorption of anionic form of methylene glycol was examined. It was shown that CH3O2- dissociates on (111) face of all considered metals with formation of formic acid anion and two atoms of hydrogen. [1] J.F. Walker, Formaldehyde, Reinhold, New York, NY, 1964. [2] K. Klier, Adv. Catal. 11 (1982) 243.
In classical theory of molecular structure the intramolecular phenomena are explained on base of the molecule presentation in the form of system of “effective atoms”, as well as of “valent interaction” and “nonviolent interaction”. From the viewpoint of quantum mechanics the molecule is system of nuclei and electrons. Therefore mapping of classical concepts onto quantum mechanics should be realized by means of exploration of electronic density distribution (&rho). The quantitative measures, characterizing “effective atoms” (Ω) and interatomic interactions, are introduced in “quantum mechanics of atoms in molecules” (QTAIM). Among these are: charge q(Ω), energy E(Ω) and volume V(Ω). We studied such concepts as “inductive effect” and “steric effect” in n-alkanes, isopropylalkanes and tretbutylalkanes proceeding from q(Ω), E(Ω) and V(Ω). The optimized structures of n-alkanes (from CH3CH3 to CH3(CH2)6CH3), isopropylalkanes (from (CH3)2CHCH3 to (CH3)2CH(CH2)6CH3), tretbutylalkanes (from (CH3)3CCH3 to (CH3)3C(CH2)6CH3) were obtained with help G98W [1]. The accuracy of iterative procedures convergence for all molecules was no more than: 1.6×10 –10 a.u. in energy, 5.6×10 –6 a.u./bor in forces (gradients), 8.8×10 –-9 in density matrix. The properties of atoms (Ω) (charge q(Ω), energy E(Ω), volume V(Ω)) were found by means of AimAll [2]. The properties of groups q(R), E(R), V(R), R = (CH3)2CH, (CH3)3C, CH2 и CH3 were computed by summing up of corresponding q(Ω), E(Ω), V(Ω). The maximal total error makes up 1.0×10 –3 a.u. in summary charge, 8.9×10 –4 a.u. in total energy. V(Ω) were defined by integration within bounds of 0.001 a.u. and corresponding atomic surfaces. In these limits V(Ω) encompass more than 99.3% of &rho molecules under consideration. The intramolecular interactions in classical theory are divided into electrostatic and mechanical ones. In framework of QTAIM it has appeared possible to link concepts “inductive effect” and “steric effect” with &rho distribution, to give them the quantitative measures (q(R), E(R), V(R)) and to define range of propagation along molecular chain. It is found from q(R) analysis that inductive effect of CH3-, (CH3)2CH-, (CH3)3C- spreads to one adjacent group. At that the group electronegativity (&chi(R)) is represented by inequality &chi(СН3) > &chi((СН3)3С >&chi((CH3)2CH) > &chi(-CH2-) > &chi(>CH-)> &chi(>C<). Steric interaction of functional groups are embodied in topology of &rho distribution as internuclear boundaries deformation and path lines curvature in comparison with stressless groups. Steric effect is defined by E(R), V(R), R = (CH3)2CH-, (CH3)3C- and spreads to two adjacent groups. 1. Frisch M.J., Trucks G.W., Schlegel H. B., et. al., Gaussian 98W (Revision A.11), Gaussian Inc., Pittsburgh PA, 2001. 2. AIMAll (Version 08.11.29), Todd A. Keith, 2008 (aim.tkgristmill.com).
A short excursion to the world of DNA structure and dynamics is presented. The most attention is paid to specific interaction between complementary nucleic acid bases, in which adenine forms two hydrogen bonds with thymine and guanine forms three hydrogen bonds with cytosine. This interaction is very important because it stabilizes the double helical DNA structure, and because the form of the potential of the interaction determines the dynamics of the complementary base pairs [1]. To obtain the form of the potential, investigators use many different methods including the most accurate ab initio quantum-chemical calculations [2], approximate method of atom-atom potential functions [3], approximate mathematical formulas like the potential of Morze [4] or empirical potential [5]. In this paper we propose a new mathematical formula to imitate the form of the potential. The formula is well grounded and advantageously differs from others due to its simplicity and convenience in practice. To derive it, we use a simple mechanical analog that consists of two coupled pendulums oscillating in the horizontal plane. We illustrate applications of the formula to study oscillations of complementary bases. In the frameworks of the model proposed we obtain the dynamical equations, find their solutions, calculate the main dynamical characteristics of the model system and compare the results obtained for two cases: for adenine – thymine base pair and for guanine – cytosine base pair. 1. Saenger W. Principles of Nucleic Acid Structure. Springer-Verlag, Berlin, 1984. 2. Sponer J, Leszczynski J, Hobza P. Hydrogen bonding and stacking of DNA bases: a review of quantum-chemical ab initio studies. J Biomol Struct Dyn. 14, 117-35, 1996. 3. Khutorskii V.E., Poltev V.I. The influence of complementary base pair interactions on secondary structure formation and conformational transitions in polynucleotides. Mol. Biol. (Mosk), 9, 747-51, 1975. 4. Peyrard M. and Bishop A.R. Statistical mechanics of a nonlinear model for DNA denaturation. Phys. Rev. Lett. 62, 2755-2758, 1989. 5. Yakushevich L.V. Savin A.V., Manevitch L.I. On the Internal dynamics of topological solitons in DNA. Phys. Rev. E-66, 016614, 2002.
Efficient block-Lanczos iterative procedure was employed to solve the eigenstate problem of the third-order algebraic-diagrammatic construction [ADC(3)] method for electron propagator (one-particle Green's function) [1]. The new approach allows for the fast generation of convergent photoelectron profiles suitable for reliable interpretation of the experimental data, prior to the full convergence of the individual states. The latter feature is especially useful in description of the inner-valence regions of photoelectron spectra dominated by dense structure of weak satellite transitions, "correlation bands", acquiring their intensities from the main photoelectron lines due to the strong configuration interaction and electron correlation effects, also known as "breaking down of the molecular orbital picture of ionization" [2]. The specific choice of the block-Lanczos starting vectors in form of the n unit vectors defined within the space of selected 1h- (one-hole) configurations describing electron detachment from the outermost molecular orbitals enables convergence to states with non-zero intensities and provides means for their assignment in terms of the projections onto the 1h-configurations. The algorithm is formulated so that only first n rows of eigenvectors need to be evaluated and stored what substantially decreases computational costs (efforts).
The block-Lanczos ADC(3) method was used to study the full valence-shell ionization spectrum of 1,3,5-trichlorobenzene and m-chlorobromobenzene. The energies and relative intensities of the vertical outer-valence ionization transitions were calculated until full convergence which was checked against the results of the standard Davidson diagonalization based approach. For these and the higher-lying transitions, theoretical spectral envelope extending up to 40 eV was generated and compared to the results of the recent synchrotron photoelectron measurements. The present theoretical results are in good agreement with the experimental spectra, providing unambiguous assignments of most observed structures. The basis set effect on the lowest ionization energies was studied at the level of the outer-valence Green's function (OVGF) approximation scheme. Some comparisons of the present results to the spectra of benzene, thiophene and halothiophenes [3] were made. Possible influence of the Jahn-Teller and pseudo Jahn-Teller effects on the shape of the observed photoelectron bands in 1,3,5-trichlorobenzene was discussed.
This work was partially supported by RFBR grant 08-03-00523.
[1] J. Schirmer, L. S. Cederbaum, O. Walter, Phys. Rev. A.- 1983.- Vol. 28.- P. 1237.
[2] L. S. Cederbaum, W. Domcke, J. Schirmer, W. von Niessen, Adv. Chem. Phys.- 1986.- Vol. 65.- P. 115.
[3] A. B. Trofimov, J. Schirmer, D. M. P. Holland et al., Chem. Phys.- 2001.- Vol. 263.- P. 167.
The core level ionization and excitation spectra and the valence shell ionization spectra of guanine and cytosine were studied theoretically using the algebraic-diagrammatic construction (ADC) ab initio Green's function approach. The fourth and third order ADC schemes for electron propagator [1] were employed in the core and valence shell ionization studies, respectively. The second order polarization propagator ADC method [2] was employed to study the core excitations.
The calculations were used to interpret the results of recent gas-phase synchrotron radiation experiments which for the first time allowed for clear observation of signals due to various tautomer in the XPS, NEXAFS and valence-shell photoelectron spectra of the molecules under study. The Boltzmann population ratios (BPRs) of guanine and cytosine tautomers at the experimental temperatures (T = 600 K and 450 K, respectively) were established from the results of accurate ab initio thermochemical calculations which included CCSD / cc-pVTZ level of theory. The calculated BPRs were used in modeling of the ionization and excitation spectra.
The theoretical spectra obtained are in good agreement with the experimental results, allowing for unambiguous assignment of the observed structures in terms of signals from the individual atoms and tautomers. In guanine, as well as in cytosine, essentially three tautomers, one of which consists of two rotamers, contribute significantly to the resulting spectra. The tautomerism is most pronounced in core photoemission spectra, enabling determination of ratios of oxo and hydroxy tautomer forms from the experimental data [3]. The experimental tautomer ratios agree well with the present theoretical estimates. The valence shell photoelectron spectra of guanine and cytosine [4] also demonstrate important signatures of tautomerism, but most of the bands here are more complex and formed by numerous overlapping transitions of different final states and tautomers, so that the observed features are less tautomer specific.
This work was supported by RFBR grant 08-03-00523.
[1] J. Schirmer, L. S. Cederbaum, O. Walter, Phys. Rev. A.- 1983.- Vol. 28.- P. 1237.
[2] J. Schirmer, Phys. Rev. A.- 1982.- Vol. 26.- P. 2395.
[3] V. Feyer, O. Plekan, R. Richter, M. Coreno, G. Vall-llosera, K. C. Prince, A. B. Trofimov, I. L. Zaytseva, T. E. Moskovskaya, E. V. Gromov, J. Schirmer, J. Phys. Chem. A.- 2009.- Vol. 113.- P. 5736.
[4] A. B. Trofimov, J. Schirmer, V. B. Kobychev, A. W. Potts, D. M. P. Holland, L.Karlsson, J. Phys. B: At. Mol. Opt. Phys.- 2006.- Vol. 39.- P. 305.
Local hybrid functionals [1] provide a very promising new generation of exchange-correlation functionals for the simultaneous accurate description of various properties (atomization energies, reaction barrier heights [2-5], NMR chemical shifts [6], EPR g tensors, etc.) within Kohn-Sham density functional theory. Intrinsically, compared to the traditional (global) hybrids (e.g., B3LYP, PBE0PBE, TPSSh) local hybrids exhibit larger flexibility, due to going from a constant exact-exchange admixture to a position-dependent one. The latter is governed by a so-called local mixing function (LMF), and this is the crucial quantity which controls the overall performance of local hybrids.
The most successful LMFs have been derived partially in a semiempirical way, based on a physically justified balance between the elimination of Coulomb self-interaction and efficient simulation of nondynamical correlation. As basic variables such LMFs may employ the dimensionless density gradient [4], the ratio of von Weizsäcker kinetic energy density to local kinetic energy density [1,2], spin polarization [5], etc. On the other hand, LMFs can be derived within a purely ab initio approach based, for instance, on the adiabatic connection (AC) formalism [7]. While this has so far been less successful from a practical point of view, it provides valuable insights into the performance and limits of various local hybrids. Also, a number of striking qualitative similarities between the LMFs derived within these different approaches suggest some underlying common principles. Here we briefly review the abovementioned methodological aspects, present new LMFs, discuss selected computational results, and provide an outlook on the further improvement of local hybrid functionals and their extension to computation of other properties.References:
[1] J. Jaramillo, G. E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118 (2003) 1068.
[2] H. Bahmann, A. Rodenberg, A. V. Arbuznikov, M. Kaupp J. Chem. Phys. 126 (2007) 011103.
[3] M. Kaupp, H. Bahmann, A. V. Arbuznikov, J. Chem. Phys. 127 (2007) 194102.
[4] A. V. Arbuznikov, M. Kaupp, Chem. Phys. Lett. 440 (2007) 160.
[5] A. V. Arbuznikov, H. Bahmann, M. Kaupp, J. Phys. Chem. A, doi: 10.1021/jp903233q.
[6] A. V. Arbuznikov, M. Kaupp, Chem. Phys. Lett. 442 (2007) 496.
[7] A. V. Arbuznikov, M. Kaupp, J. Chem. Phys. 128 (2008) 214107.
Обнаружено, что корреляция электронов в атоме гелия, молекуле водорода и других простых молекулах имеет динамическую природу, то есть, обусловлена тем, что электроны посещают одну и ту же точку в различные моменты времени, и не может быть учтена посредством стационарных функций. Задача об атоме гелия в основном состоянии сводится к вычислению эффективного заряда ядра по известному первому потенциалу ионизации. Пространственная часть стационарной волновой функции атома не может быть чем-либо иным кроме простого произведения волновых водородоподобных функций электронов, потому что она (или плотность вероятности или парная плотность вероятности)не может в принципе учесть корреляцию движения электронов во времени. Эффективный заряд ядра атома гелия оказывается меньше (1.3444) чем предписывается минимумом в стандартной процедуре минимизации энергии (1.375). Причиной этому служит, на наш взгляд, инерция движения электронов. Ее и необходимо учитывать вместо введения корреляций в расчетах потенциальных энергий притяжения и отталкивания, как это имеет место в методе Гиллерааса. Возможно ли достичь решения проблемы электронной корреляции с помощью функций, зависящих от относительных координат и импульсов электронов или с помощью интегрирования по траекториям, автору неизвестно. Минимизация полной энергии атома с помощью единственной функции неправомерна, несмотря на возможность достижения наиболее глубокого минимума. Вместо этого следует получать функцию для каждого электрона. В случае гелия следует рассматривать два состояния с соответствующими волновыми функциями, энергиями ионизации и минимумами, одно для каждого из идентичных электронов в собственно атоме гелия, другое для единственного электрона в ионе гелия. Получаемые по такому правилу волновые функции внешних nl электронов являются водородоподобными. Они могут быть построены путем линейной комбинации 1s и nl орбиталей, но должны быть выражены в виде водородной nl функции с соответствующим эффективным зарядом. С такими функциями выполняется очевидное правило: радиусы атомов изменяются медленно у элементов слева направо в рядах Таблицы Менделеева. Более того, обнаруживается строгая зависимость между величинами энергии диссоциации гомоатомных молекул и глубинами (или объемами) области перекрывания атомов.
В данном сообщении представлены результаты исследования электронного строения гексаядерного комплекса [Cu6(μ3-O)2(μ-4-Br-pz)6(μ-3,5-Ph2-4-Br-pz)3]- с использованием теоретических (квантово-химическое моделирование) и экспериментальных (магнетохимические измерения) методов.1
В рамках UB3LYP-BS вычислительной процедуры оценены параметры изотропного обмена (Jij) между всеми возможными парами парамагнитных центров. На основании полученных данных предложена наиболее простая модель изотропного обмена (с минимальным числом параметров), которая была использована для описания магнитных свойств комплекса и нахождения оптимальных значений параметров по данным магнетохимических измерений.
Установлено, что в рассматриваемом комплексе преобладают антиферромагнитные взаимодействия. Показано, что обмен внутри треугольных фрагментов чрезвычайно чувствителен к положению кислородного центра относительно плоскости Cu3. Энергетический спектр спиновых уровней комплекса имеет блочную структуру, которую можно объяснить, рассматривая Cu6(μ3-O)2 остов как систему двух слабовзаимодействующих треугольных фрагментов Cu3(μ3-O). Вычисленные значения Jij были использованы в качестве начальных при нахождении оптимальных значений параметров, наилучшим образом описывающих экспериментальные данные. Показано, что процедура оптимизации воспроизводит выявленные в ходе квантово-химических расчетов закономерности в значениях Jij только в том случае, если в спин-гамильтониан добавлен антисимметричный вклад. Использование такого спин-гамильтониана позволяет описать весь массив экспериментальных данных. В рамках простой изотропной модели экспериментальные значения Jij определяются с погрешностью, обусловленной необходимостью описать низкотемпературное поведение, которое в большей степени контролируется антисимметричным обменом.
Liquid-crystalline lanthanide complexes (lanthanidomesogens) are a class of molecular materials that have intensively been studied during the last decade[1-3]. The rationale for the research interest in lanthanidomesogens is that, by incorporation of rare-earth ions in liquid crystals, it is possible to obtain magnetic or luminescent liquid crystals. The information about a lanthanidomesogens structure is extremely necessary for a prediction of their liquid crystal behavior and an estimation of magnetic and photophysical characteristics. However, presence in structure of liquid-crystalline complexes a great number of long alkyl chains cumbers an obtaining of a mono-crystal for X-Ray analysis. Therefore, calculation of lanthanidomesogen structure by quantum chemical methods is now the important and actual problem.
The objects of studying were series of polymorphic thermotropic low-viscose tris(β-diketonates) adducts of Ln(III) with 5,5`-diheptadecyl-2,2`-bipyridine, where Ln(III) – La ÷ Lu.
On purpose to definition of the basic energy conditions of molecules of complexes the optimization of coordination polyhedron geometry for all of lanthanide ions in various spin conditions was calculated by PBE method within the limits of DFT.
On the basis of the calculations the anisometry of molecules is defined. Its value decreases at increasing of the terminal substituting group length in β-diketones. This parameter makes direct impact on width of a molecule of a complex. The value of the anisotropy of geometry changes not essentially in the lanthanide row. Geometrical parameters of a coordination polyhedron correlate with data X-RAY for not LC complexes with a similar nearest environment of a lanthanide ion.
Calculations were made on the supercomputer of the collective using centre RAS.
This work was supported by the Russian Foundation for Basic Researches project 08-03-00900-a and BRHE post-doctoral fellowship program Y5-C07-05 (REC 007).
Reference:
The properties of ferroactive oxocarbons H2C4O4 and
D2C4O4 (squaric acids, (H/D)2SQ [1]) are studied by
quantum-chemical approach [2] to microscopic theory of H-bonded order-disorder materials. The pseudospin
formalism in the frames of Ising-type model Hamiltonian with tunneling terms [3] is used. The set of
this model Hamiltonian parameters including tunneling integral &Omega and Ising parameters
Jij for both materials treated was obtained by means of RHF,MP2-MP4 and DFT/B3LYP
calculations for different types of model clusters, that simulate the character fragments of
(H/D)2SQ layered crystalline structure. Several basis sets of 6-31G type up to
6-311++G(2d,2p) were utilized. The proton/deuteron transfer barriers and the total energy of the
necessary clusters (as a function of proton/deuteron distribution) needed to obtain &Omega and
Jij parameters respectively are calculated. The resulting &Omega and Jij values
were used in the limits of mean field approximation to handle single-layer and double-layer models of
(H/D)2SQ crystals. For both cases the light nuclei ordering within the layer responded to the
ferroelectric state but in the double-layer model the layers were polarized in the opposite directions.
Then according to calculations performed the low-temperature structural phase transitions (SPT) in the
(H/D)2SQ materials exhibits 2d-ferroelectric (inside single layer) and 3d-antiferroelectric
nature in full agreement with experiment. The role of interlayer proton (deuteron) coupling as well as
the dependence of the observed for SPT thermodynamic H/D-isotope effect on the geometric isotope effect
are discussed. It is found that proton/deuteron coupling between the neighboring layers is about an
order weaker than within the layer. The observed thermodynamic isotope effect (&Delta Tc
&asymp 140K) is mostly caused by the H/D geometrical isotope effect, while the difference in the
tunneling parameters &Omega(H) and &Omega(D) plays a modest role.
This work is supported by the RFBR project 08-03-00195.
The search of molecules with photoswitchable magnetic properties was actual goal of current coordination chemistry [1]. It is well known that spiropyrans, spirooxazines, and chromenes undergo reversible rearrangement of the spirocyclic and merocyanine isomers upon UV-irradiation of its solutions or polymer films. On the other hand, some four-coordinated Ni(II) complexes exist in an equilibrium of diamagnetic square-planar and paramagnetic tetrahedral forms [2-4].
For these purposes quantum chemistry calculations of substituted chromenes with annulated five 1, six 2, and seven 3 membered nitrogen containing heterocyclic ring as bidentate ligands were performed with using density functional theory (B3LYP/6-311+G**).
Our calculations predict stable structures both in closed and open forms of bis-chelate complexes with photochromic ligands. In all cases systems with open form of the ligands is more favorable that structure with closed form of the substituted chromenes. Relative stability of the two forms depends on spatial structure of the ligands. It was shown that in the open form low spin diamagnetic complex is more stable but in the closed form high spin paramagnetic structure is favorable. For systems 1-3 intramolecular spin-forbidden reaction was investigated. The energy barrier to the rearrangement between the two isomers was evaluated as the height of the MECP where the change in the spin state of a molecule (crossover) occurs at the intersection of the minimal energy reaction paths located on singlet and triplet PESs. According to computation for the open form of complex 3 biradical state was predicted.
This work financially has been supported by Russian Foundation for Basic Research (project 09-03-00684) and Ministry of Education and Science RNP 2.2.1.1.2348.
Metal complexes with redox-active ligands possessing valence tautomeric are characterized by the existence of two isomers with different charge distributions, and consequently, different optical, electric and magnetic properties [1]. The interconversion between different electronic states of isomers is accomplished by a reversible intramolecular electron transfer.
The reaction of interconversion between high spin Co(II) and low spin Co(III) forms of complex (3,5-Di-t-butyl-1,2-semiquinone-N-(2-hydroxy-3,5-di-t-butylphenyl)imine-O,N,O')-(3,5-di-t-butyl-1,2-quinone-N-(2-hydroxy-3,5-di-t-butylphenyl)imine-O,N,O')-cobalt [2] with using model structure, in which i-Pr groups were replaced by hydrogen, were investigated by method of density functional theory [B3LYP*/6-311++G(d,p)].
The computed geometric parameters well agree with those obtained by X-ray determination [3]. Performed calculations showed that relative energy of the two isomers is in good agreement with experimental data, which indicated that the low spin form (Co(III)) is more stable (10.2 kcal/mol) than the high spin (Co(II)). With using modified algorithm of finding minimum energy crossing point [4], the MECP structure in which occurs interconversion between doublet and quartet PES was located. It was shown that gradient descent from MECP on the doublet PES can lead to two minima. The first corresponds to thermodynamic more stable low spin isomer Co(III), the second leads to low spin isomer Co(II). The energy difference between these structures is 9.2 kcal/mol. Distribution of spin density and occupancy of orbitals of computed stationary points on the PES were discussed.
This work financially has been supported by Russian Foundation for Basic Research (project 09-03-00684) and Ministry of Education and Science RNP 2.2.1.1.2348.
В данном сообщении представлены результаты квантово-химического моделирования электронной структуры четырехъядерных комплексов железа(II) с общей формулой [Fe4(μ-CN)4(L)4(L/)4]4+ [1, 2]. Эти соединения содержат квадратный фрагмент Fe4(μ-CN)4. Металлические центры 1 и 3 (2 и 4), находящиеся на диагоналях, имеют одинаковое лигандное окружение: L2Fe(СN)2 (1 и 3) и L/Fe(NC)2 (2 и 4). Характер наблюдаемых зависимостей χ(T) зависит от природы бидентантного (L) и тетрадентантного (L/) лигандов [1, 2]. Например, комплекс с L = bpy и L/ = tpma (1) при повторении циклов охлаждения-нагревания претерпевает обратимый двухступенчатый спиновый переход, соответствующий поочередному переходу ионов Fe2+ внутри фрагментов L/Fe(NC)2 из высокоспинового (HS) в низкоспиновое (LS) состояние [1]. В комплексе с L = phen и L/ = tpma (2) эти ионы переходят из одного состояния в другое одновременно [2]. При введении же в tpma метильных групп (L = phen, L/ = Me-tpma или Me2-tpma: 3 и 4) ионы Fe2+ внутри фрагментов L/Fe(NC)2 находятся в HS-состоянии во всем температурном интервале [2]. В рамках теории функционала плотности получены пространственные структуры комплексов 1-4, отвечающие всем возможным минимумам на ППЭ для электронных состояний с S = 0, 4 и 9. В точках, соответствующих глобальным минимумам, изучена относительная стабильность электронных конфигураций c S = 0 [LS-LS-LS-LS], S = 4 [HS-LS-LS-LS] и [LS-HS-LS-LS], S = 9 [HS-HS-LS-LS] и [HS-LS-HS-LS]. Полученные результаты позволяют объяснить различное магнитное поведение рассматриваемых комплексов.
Использованные сокращения: bpy = 2,2/-бипиридин; phen = 1,10-фенантролин; tpma = трис(2-пиридилметил)амин; Me-tpma = ((6-метил-2-пиридил)метил)бис(2-пиридилметил)амин; Me2-tpma = бис((6-метил-2-пиридил)метил)(2-пиридилметил)амин
[1] H. Oshio et al., Angew. Chem. Int. Ed., 2005, 44, 6484-6487.
[2] J. A. Real et al., Inorg. Chem., 2009, 48, 3710-3719.
Термодинамика электронного транспорта в белке определяется его стандартным электродным потенциалом E0 относительно стандартного водородного электрода (S.H.E.). Значение E0 может быть рассчитано из термодинамического цикла, который включает стандартную энергию Гиббса ионизации восстановленной формы простетической группы, стандартные энергии Гиббса сольватации восстановленной и окисленной форм, а также потенциал S.H.E.
Железо-серные белки (ISP) представляют собой белки с широко изменяющимися свойствами. Среди них белок Риске обладает наиболее положительными редокс-потенциалами. Для выяснения природы такой особенности были проведены расчеты редокс-потенциалов этого белка с использованием следующего комбинированного подхода. Активный центр [2Fe2S] и его лигандное окружение были включены в квантово-химическую расчетную схему метода функционала плотности (обменно-корреляционный функционал B3LYP) программного пакета GAUSSIAN 03. Эффекты спинового спаривания между электронами двух центров из атомов Fe оценивались с использованием приближения нарушенной симметрии (broken symmetry). Взаимодействие квантово-химической подсистемы с внутрибелковым электрическим полем (с использованием оптической диэлектрической константы белка), а также с диэлектрическим окружением (статическая диэлектрическая константа) учитывалось с помощью решения уравнения Пуассона-Больцмана методом конечных разностей (программный пакет DelPhi) с фиттиноговыми зарядами на железо-серном кластере, полученными в рамках процедуры Мерца-Кольмана.
Комбинация квантово-химического и электростатического расчетов редокс-потенциалов белка Риске приводит к достаточно хорошему согласию с экспериментом и позволяет объяснить их высокие значения. Для сравнения использовались три атомных базисных набора: 6-31G(d,p), 6-31++G(d,p) и TZVP. Базис 6-31G(d,p) дает наиболее реальную картину распределения парциальных зарядов, а поэтому использовался в электростатических расчетах. Наилучшее согласие рассчитанного редокс-потенциала с экспериментальным значением для полностью протонированной простетической группы достигается с базисом 6-31++G(d,p), причем базис TZVP дает близкие результаты. Для депротонированных редокс-центров несколько лучшее согласие с экспериментом наблюдается в расчетах с базисом TZVP. Детально анализируется роль структурных аспектов и выбора диэлектрических констант в расчетах редокс-потенциалов.
Авторы благодарны РФФИ за финансовую поддержку (проект №09-03-00085).
Starting with analysis of electronic density and Coulomb repulsion we study multipolar interactions and energy spectrum of C60 molecular ions. Our basic idea is that we consider C60n- as a quasi-element or quasi-atom of the icosahedral symmetry (Ih) in many ionic compounds (for example, in alkali doped fullerides AC60, A = K, Rb, Cs). Using the formalism of multipolar expansion we study many electron on-site effects (molecular terms of C60n-) and inter-site ones. First, we apply the formalism to the problem of finding energy spectrum of C60n± molecular ions [1]. We have also calculated the corresponding magnetic moments and found that they are independent of molecular orientation with respect to the external magnetic field, albeit the coupling of spin and orbital momenta differs from the atomic case. The ground state of C602- is either 3T1g or 1Ag, depending on the one electron energy separation between t1u and t1g levels. We analyze the electronic dipolar transitions and compare our results with the experimental data for C60n- in solutions and with other theoretical studies. Our method requires a many determinantal wave function of the C60 molecule. Other problems include consideration of the crystal field of C60- in AC60, phase transitions to polymer structures [2], indirect exchange (superexchange) in molecular complex C60- – A+ – C60- [3] and some others [4].
[1] A. V. Nikolaev and K. H. Michel, J. Chem. Phys. 117, 4761 (2002).
[2] K. H. Michel and A. V. Nikolaev, Phys. Rev. Lett. 85, 3197 (2000).
[3] A.V. Nikolaev and K.H. Michel, J. Chem. Phys. 122, 064310 (2005).
[4] K. H. Michel, B. Verberck, and A. V. Nikolaev, Phys. Rev. Lett. 95, 185506 (2005).
There is a variety of iodine polymer complexes having a wide spectrum of anti-microbic and anti-viral effects, including the HIV infection. One of these is Armenicum, a drug intended for curing the HIV infection. Its distinctive feature is that its active substance contains not only an iodine-containing polymer complex (a complex of iodine with mono-, oligo- and polysaccharides), but also lithium halogenides. The recently patented new anti-infective drug contains polypeptides in addition to polysaccharides. A model of the active complexes (AC) of the above drugs is proposed in this paper. The method RHF/3-21G** was used for calculating the spatial structure and stabilization energy of complexes containing a molecule of I2, LiCl and LiI salts and organic ligands which model the donor-active part of polysaccharides (ethanol) and peptides (amid, imidazole). In these complexes, molecular iodine exhibits acceptor properties with respect to the organic ligands forming a charge transfer complex and donor properties with respect to the ion pair LiX (X=I, Cl). The calculations showed that the AC stability is determined by the stability of the complex formed by molecular iodine and an organic ligand. A complex containing amid or imidazole significantly stabilizes the structure as in this case the charge is transferred to I2 both from the n-pair of the heteroatom and the π-density of the ligand. The intercalation of the active substance of the drug to the DNA structure is viewed as possible reason for the inhibition of the action of replication enzymes of virus DNAs. The method RHF/3-21G** was used for calculating the structures modeling the interaction of the proposed model of the drug’s active complex with blood protein (amid or imidazole) and nucleotides of virus DNAs (guanosine, adenosine). These structures include two ligands with conjugated π-bonds which compete for complexing with I2. The calculation results show that the stability of the charge transfer complex is determined by the energy of the π-antibonding HOMO of the ligand - the higher the HOMO energy, the more charge is transferred to I2 and the more stable is the complex. Among amid, imidazole, guanosine and adenosine, guanosine and adenosine have the highest HOMO energy, therefore the action of the AC on virus DNAs produces an AC metabolite and a I2 – nucleotide complex. Thus, the calculations showed that the stability of molecular iodine complexes with unsaturated organic compounds is determined by the transfer of the π-electron density to I2, therefore, the action of iodine-containing drugs produces changes in the structure of virus DNAs, nucleotides, which are more π-donor active than proteins or peptides, form a stable complex with molecular iodine.
The new electron propagator (EP) method oriented to approximation of principal and shake-up ionization potentials (IPs) and electron affinities (EAs) of molecules as functions of nuclear geometry parameters in wide intervals of their variation is constructed. Prerequisites for adequate modeling of these functions are created with tools of consistent accuracy regulation of IPs and EAs estimates both within subsystem of transitions between electronic states at fixed nuclear geometry and under variation of its parameters. In propagator methods exploited nowadays to estimate IPs and EAs for systems of quasidegenerate levels in molecules and its ions the construction modes of the main components in propagator expression and corresponding eigenvalue problem are not rigorously subordinated to the requirement of correspondence to some common accuracy criterion. In our approach the part of unifying accuracy regulator plays the order of perturbation theory for multidimentional model spaces (PTMMS). Idea foundations of our approach were formulated and applied earlier [1] for approximation of poles and residues of polarization propagator (PP). The corner stone in the design of our approach is the original interconnected choice of the two project forming components for construction of the exact propagator expression: (i) compositions of model subspaces of Hilbert state vector spaces for the molecule, its cation, and anion, and (ii) composition of the complete system of excitation and deexcitation operators (SEDO). An adequate choice of these components creates a base for constructing approximate propagator expression in the framework of prescribed order of PTMMS through coordination of approximation mode for the reference state wave function and reduction of complete SEDO to some its subsystem. In our method this approach was developed in the following directions. The interconnected requirements, which must meet the compositions of model subspaces of the three mentioned Hilbert spaces to allow PTMMS approximation of the EP expression, are formulated. The principal EP expression and eigenvalue problem for determination of this EP poles are constructed in the framework of both the first and the second order of PTMMS. The mode of taking into account spin and space symmetry properties of the electronic states concerned is determined. Matrix elements, which form EP expression in the constructed approximations, are rewritten as matrix elements of operators, which do not alter the quantity of particles in the system. This transformation enables on the one hand to exploit the technique of Hugenholtz and Brandow diagrams for calculation of these matrix elements and on the other hand to form a common algorithm base for approximation of EP and PP poles. 1. V.F. Khrustov, D.E. Kostychev. Multiconfigurational Green’s Function Approach with Quasidegenerate Perturbation Theory. International Journal of Quantum Chemistry, Vol.88, 507-518 (2002).
Results of quantum-chemical calculation of the charge and spin of iron and arsenic atom states and quadrupole splitting (QS) of 57Fe Mossbauer spectra are reported in this work for the newly discovered supercontuctors family LnFeAsO1-xFx with Ln = Sm (P4/nmm space group, N 129 [1]).
Calculations are carried out for three charge distribution models I, II, III within the crystal lattice of SmFeAsO0.86-xFx: the ionic model I corresponds to the crystal lattice with the formal degree of oxidation (FDO) of atom charges Sm3+, Fe2+, As3-, O2-, F1-; model II corresponds to FDO within the sublattice of Sm-O(F) atoms and the total metallic bonding of the Fe-As atom sublattice; model III is constructed to correspond to metallic bonding both within Sm-O(F) atom and Fe-As atom sublattices. The geometry of all clusters is the same as the structural data for the high-temperature tetrahedral crystal structure [1] without T->O structure transition, which takes place at 145 K [1] and depends on the fluorine atom concentration. The electronic structure of clusters I-III is calculated by means of the non-empirical Xa-discrete variation method (Xa -DVM) [2].
The calculations performed show that the effective charges of iron atoms vary within the row +1.75 (model I), +1.65 (model II), +1.06 (model III) |e|. The calculated local magnetic moments on iron and arsenic atoms are absent in models I and III and become 2.02 μB (Fe) and 0.5 μB (As) for model II.
The real charge and spin states of iron and arsenic atoms is analyzed on the basis of the calculated results on the quadrupole splitting of the Mossbauer spectrum of 57Fe.
In conclusion, the largest probability of existence of La-O(F) and Fe-As sublattices is in the form of semimetal ([FeAs4]4- , II cluster) or metal ([FeAs4]0 , III cluster). Our results agree best with data [3].
References
1. Margadonna S., Takabayashi Y., McDonald M.T., et al. // arXiv: 0806.3962 (June 2008).
2. Averill F.W., Ellis D.E. // J. Chem. Phys. 1973. Vol. 59, No. 12. P. 6412-6418.
3. Rahlenbeck M., Sun G.L., Sun D.L., Lin C.T., Keimer B., Ulrich C. // arXiv: 0907.0560vl [cond-mat.surp-con] 3 Jul 2009.
Polarization propagator (PP) method oriented to approximation of transition characteristics between electronic states of molecules as functions of nuclear geometry parameters in wide intervals of their variation is constructed. Prerequisites for adequate modeling of these functions in the method are created with tools of balanced account of quasidegeneracy and correlation effects in the electronic states concerned. The part of unifying accuracy regulator herein plays the order of perturbation theory for multidimentional model spaces (PTMMS). In our opinion, there is no alternative to this regulator when making a consistent choice of approximation modes for the components of PP expression on the base common accuracy criterion as applied to a system of quasidegenerate levels. Idea foundations of our approach were formulated and applied earlier [1] for approximation of poles and residues of PP in the framework of the first order of PTMMS. Reasoning from (i) the particular fragmentation of molecular Hilbert state vector space constructed in the selected basis of molecular orbitals into the model subspace and its orthogonal complement and (ii) the corresponding composition of complete system of excitation and deexcitation operators, the PP expression and the matrix eigenvalue problem (EP) in the framework of the second order of PTMMS are constructed. The logic of this procedure may be considered as development of the logic exploited when forming SOPPA method based on the apparatus of perturbation theory for non-degenerate energy level. As in the SOPPA method, EP matrix elements in our method depend nonlinearly on the energy parameter, and this EP is to be solved iteratively. Means of work content reduction under realization of this iterative procedure are proposed. The structure and efficiency resources of the constructed approximation are compared with the corresponding characteristics of existing propagator and traditional quantum-chemical methods. 1. V.F. Khrustov, D.E. Kostychev. Multiconfigurational Green’s Function Approach with Quasidegenerate Perturbation Theory. International Journal of Quantum Chemistry, Vol.88, 507-518 (2002).
Quantum mechanics calculations at MP2/6-311++G(d, p) level were utilized to study the process of activation of a dioxygen in strong acids, namely, FSO3H and CF3COOH. We have designed donor/acceptor model systems with well-defined electron transfer distances and proton hydrogen bond geometries. We concentrated on the situation where the electron and proton have different sources within a reaction complex, as indicated below (CF3CO2(-)…O2(T)…H2O2CCF3(+)) or (FSO3(-)…O2(T) H2O3SF(+)). In this complex protonated acid molecule can react with a dioxygen to give the HOO radical in case if an electron transfers from the anion. This reaction could occur by (i) initial proton transfer (PT) to form OOH(+) followed by electron transfer (ET), (ii) ET to form superoxide anion-radical followed by PT, or (iii) proton-coupled electron transfer (PCET) with no intermediates. Theoretical calculations have revealed that the reaction of dioxygen with protonated acid occurs via a single pathway by a mechanism that has proton-coupled electron transfer character. In this reaction, the mechanism can be partially described as a process in which the O-H hydrogen from FSO3H2(+) or CF3CO2H2(+) is transferred as a proton to dioxygen with the accompanying electron coming from the electron system of the anion FSO3(-) or CF3CO2(-), respectively. Thus, the anionic species of the complex participate only as electron-transfer partners. A major goal of our current research is to to monitor the fate of the proton in response to the electron and vice versa. The changes in the geometrical parameters, charge, and spin densities distribution along the reaction coordinate are discussed. Some relationships between the amount of transferred electron density and the changes in geometrical parameters and energies are given. The peculiarities of potential energy surfaces of complex (CF3CO2(-)…O2(T)…H2O2CCF3(+)) in the ground and excited electronic states were also investigated by means of DFT/B3LYP method with 6-311++G(d, p) basis set. Theoretical results obtained employing DFT method well agree with data obtained by MP2/6-311++G(d, p) method. The present work represents an initial study to utilize PCET as a mechanistic framework for exploring small-molecule activation chemistry. Therefore, in spite of limited sampling, that provides a mostly qualitative picture, we proposed here a scheme of peroxyl radical formation in strong acids. Acknowledgments: We thank the Russian Foundation for Basic Research (Grant No. 08-03-00388-a) and the Program of the Department of Chemistry and Material Sciences of the Russian Academy of Sciences, “Theoretical and experimental study of nature of chemical bonds and of most important chemical reactions and processes”, for financial support.
Many fundamental small-molecule transformations in nature require the coupled transport of both proton and electron equivalents to effect bond-making and bond-breaking catalysis. Quantum mechanics calculations at MP2/6-311++G(d, p) level were utilized to study the process of activation of a dioxygen in HF. We have designed donor/acceptor model systems with well-defined electron transfer distances and proton hydrogen bond geometries. We concentrated on the situation where the electron and proton have different sources within a reaction complex, as indicated below (Me2C=CMe2…O2(T)…HFH(+)…HF). In this complex protonated acid molecule can react with a dioxygen to give the HOO radical in case if an electron transfers from the Me2C=CMe2 molecule. This reaction could occur by (i) initial proton transfer (PT) to form OOH(+) followed by electron transfer (ET), (ii) ET to form superoxide anion-radical followed by PT, or (iii) proton-coupled electron transfer (PCET) with no intermediates. Theoretical calculations at MP2/6-311++G(d, p) level have revealed that the reaction of dioxygen with protonated acid occurs via a single pathway by a mechanism that has proton-coupled electron transfer character. In this reaction, the mechanism can be partially described as a process in which the hydrogen from HFH(+) is transferred as a proton to dioxygen with the accompanying electron coming from the electron system of the Me2C=CMe2 molecule which converted to cation-radical. The changes in the geometrical parameters, charge, and spin densities distribution along the reaction coordinate are discussed. Some relationships between the amount of transferred electron density and the changes in geometrical parameters and energies are given. The peculiarities of potential energy surfaces of complex (FHF(-)…Me2C=CMe2…O2(T)…HFH(+)…HF) in the ground (T) and excited (S) electronic states were also investigated by means of MP2 method with 6-311++G(d, p) basis set. We proposed here a scheme of peroxyl radical formation in HF. The present work represents an initial study to utilize PCET as a mechanistic framework for exploring small-molecule activation chemistry. Acknowledgments: We thank the Russian Foundation for Basic Research (Grant No. 08-03-00388-a) and the Program of the Department of Chemistry and Material Sciences of the Russian Academy of Sciences, “Theoretical and experimental study of nature of chemical bonds and of most important chemical reactions and processes”, for financial support.
Nitrous oxide (N2O) is a potent greenhouse gas and contributes to ozone layer depletion. This has prompted the development of several abatement technologies based mainly on the catalytic decomposition. The reaction mechanism for nitrous oxide decomposition has been studied on aluminum site in Al-ZSM-5 using the DFT/B3LYP/6-31+G(d) method. The active centers were taken to be mononuclear [Al]+, [Al=O]+, and [AlO2]+ and the surrounding portion of the zeolite was represented by a 3T cluster, namely [AlSi2O4H8]-. The first elementary step of N2O decomposition involves the formation of [AlO]+ and the release of N2. The metal-oxo species produced in this step then reacts with N2O again, to release N2 and form [AlO2]+. The calculated activation energies at DFT/B3LYP level for N2O dissociation on Al-ZSM-5 and AlO-ZSM-5 are 9.86 and 15.07 kcal/mol at 298 K, respectively. The third elementary step of N2O decomposition on AlO2-ZSM-5 involves the formation of [AlO3]+ and the release of N2. The calculated activation energy at DFT/B3LYP level for N2O dissociation on AlO2-ZSM-5 is 18.24 kcal/mol. Four-order perturbation theory (MP4// DFT/B3LYP) predicts that the activation barriers for nitrous oxide dissociation at 298 K on Al-ZSM-5, AlO-ZSM-5, and AlO2-ZSM-5 are 13.97, 17.89, and 32.71 kcal/mol, respectively. The calculated energy for desorption of singlet O2 from the 3T-[OAl(O)2]+ cluster at DFT/B3LYP level is 57.8 kcal/mol. When one takes into account the entropy gained upon desorption of singlet O2, the contribution of entropy to the free energy of desorption is TDS =10.8 kcal/mol at 298 K. The calculated activation energies at MP2/6-31+G(d) level for N2O dissociation on Al-ZSM-5 and AlO-ZSM-5 are 13.90 and 26.87 kcal/mol at 298 K, respectively. The calculated activation energy at MP2/6-31+G(d) level for N2O dissociation on AlO2-ZSM-5 is 38.25 kcal/mol. The calculated energy of the singlet oxygen desorption from 3T-[AlO3]+ cluster DH (298 K)=+46.4 kcal/mol at MP2/6-31+G(d) level is significantly higher than the barriers of oxidation reactions. When one takes into account the entropy gained upon desorption of singlet O2, the contribution of entropy to the free energy of desorption is TDS =11.0 kcal/mol at 298 K. Thus, the method B3LYP seriously underestimates the activation energy for N2O dissociation on Al/AlO/AlO2-ZSM-5. The problem here, of course, is that current functionals do not correctly describe the dispersion energy, which is well described by MP2 calculations. Therefore, further DFT investigations are needed that are validated by comparison to available experimental data or high-level quantum chemistry methods that treat electron correlation more accurately. Acknowledgments: This work was supported by the RFBR (project 05-03-33103).
The first-principles calculations of titania-based nanotubes are made
in LCAO approximation using hybrid HF-DFT (PBE0) exchange-correlation
functional. One-periodic translation symmetry is adopted for nanotube
calculations as it is implemented with POLYMER option in CRYSTAL06
code [1]. The nanotube models are obtained by rolling-up a six-plane (101) anatase
monolayer. Optimized anatase (101) monolayer has a centred
rectangular 2D lattice with 12 atoms in conventional unit cell with
translations a and (a2+c2)1/2,
where a and c are the bulk anatase lattice constants.
Depending on the rolling direction, two different types of TiO2
nanotubes, (n, 0) and (0, m) can be constructed.
The small-core pseudopotential [2] (only 1s, 2s, and
2p-electrons are included to core) and the corresponding basis
set is used for Ti atom. The all-electron basis set for oxygen atom
is taken from [3]. The diffuse exponents of valence s, p
and d-orbitals were optimized in bulk anatase, six-plane (101)
monolayer, and (0, 3), (0, 6), and (6, 0) nanotube calculations.
The calculations are made for the (n, 0) and (0, m)
nanotubes containing up to 180 atoms in 1D unit cell (The values n
= 6, 9, 12, 15 and m = 3 - 6 were considered). It is shown
that:
References:
[1] R. Dovesi, et al., CRYSTAL06 User's Manual, University of Torino, Torino, 2008. The study of water adsorption on the (001) surface of cubic
BaHfO3 is made using periodic PBE0 LCAO calculations via the CRYSTAL06 [1] computer code. The Stuttgart [2]
scalar-relativistic, small-core pseudopotentials and the corresponding basis sets have been
used for the core-valence interactions of Ba and Hf atoms.
Both types of possible BaHfO3 surface terminations (BaO and HfO2) are considered.
The surface is simulated by symmetric 2D-slabs consisting of 9 atomic planes. The minimal
and double 2D surface unit cells have been used for the study of monolayer water adsorption.
There are two nonequivalent electropositive adsorption centers per double 2D unit cell,
whereas it is the only one metallic center per minimal unit cell. Several initial water molecule
positions are considered for each of two possible terminations. The dissociation possibility
was also taken into account.
BaO-terminated surfaces are found to be more hydrophilic than HfO2-terminated ones.
The dissociative adsorption is the most preferable for all the BaO-terminated
surfaces under consideration. This agrees with the results of our previous study
of water adsorption on the (001) surfaces of cubic SrHfO3 [3]. The molecular adsorption energy (67
kJ/mol) almost twice is less than dissociative adsorption energy (121 kJ/mol) using of the
primitive unit cell. However, the corresponding values are 109 kJ/mol and 126 kJ/mol when
the double 2D unit cell is used. Thus, the additional opportunities for H-bonding between
neighbor water molecules arising in the double-sized 2D unit cell, lead to relative increasing
of molecular adsorption energy.
As it was found earlier [3], the molecular adsorption is preferable on the
HfO2-terminated surface when the primitive unit cell is used for calculation. Contrastly,
the dissociative adsorption types dominate on the same surface when the double unit cell is applied:
the corresponding adsorption energies are 98 kJ/mol (molecular case) and 137 kJ/mol (dissociative case).
An orthorhombic distortion proved to be the reason for this difference. Such a
distortion leads to a considerable lifting of surface bridging oxygen atoms. The latter appeared
to be more effective proton acceptors than oxygens on the unchanged HfO2-termianted surface of the cubic hafnates.
Acknowledgment. The authors are grateful for the support by the Russian Basic Research
Foundation (grant 08-03-00438-a).
References:
[1] R. Dovesi, et al., CRYSTAL06 User's Manual, University of Torino, Torino, 2008.
[2] W. Kuechle, M. Dolg, H. Stoll, H. Preuss, J. Chem. Phys., 1994, 100, 7535.
[3] R.A. Evarestov, A.V. Bandura E.N. Blokhin, J. Phys.: Conf. Ser., 2007, 93, 012001.
The spin transition in the Fe(phen)2(NCS)2 crystal was studied by the method of atom-atom potentials. The geometries of the high spin (HS) and low spin (LS) forms were taken from the X-ray experimental data [1] and assumed to be frozen. The Buckingham potential with the parameters from [2] and the Lennard-Jones potential with the parameters from [3] were used. Adequacy of the method was corroborated by comparison of calculated and experimental unit cell parameters of the pure LS and HS crystals. The contribution of intermolecular interactions to the total &Delta H of the transition was found to be prevailing (&sim 60-90%), and thus explicit consideration of intermolecular interactions is vital for modeling the spin transitions. The effective Ising model representing the enthalpy of the mixed crystal as a function of occupation numbers was elaborated. The relations between the coefficients Jij arising from the crystal symmetry were derived. The numerical values of Jij, as well as the &Gamma parameter of the Slichter-Drickamer model, were estimated by the least-squared treatment of the enthalpies of various mixed crystals, which in their turn were calculated by minimization of the enthalpy as a function of the unit cell parameters, c.m. positions and rotation angles of molecules. The values of Jij and &Gamma calculated with the two potentials are pretty close to each other. At the same time, the predicted character of the spin transition (a sharp transition from x&sim 0.3% to 99.7%) contradict to the experimental data (the transition within the range of 10-20 K, with x&sim 25% at Tc-5 K and x&sim 75% at Tc+5 K), which opens a new field for further research.
This work has been supported by the RFBR through the grant No 07-03-01128. The financial support of this work through the JARA-SIM research project "Local Electron States in Molecules and Solids" is gratefully acknowledged.
<&nsub>The model analysis of electronic states of an atomic particle situated inside an impenetrable cavity has a wide range of scientific and technical applications. Formally, it may be considered as the Dirichlet boundary problem for the Schr?dinger Equation, i.e. vanishing of the wave functions at the boundary of the region. For the history and review of exact statements in confined atom problem see, e.g., [1] and other chapters of the same book.
<&nsub> Recently a new numerical method was proposed for the energy levels calculations of the one-electron Dirichlet problems in an arbitrary region. The method is based on minimization of the L2 norm of a solution of the differential Schroedinger Equation on the surface of the region with respect to arbitrary energy value. Details, simple applications and testing of this method for cylindrical and cubic cavities are described in [2,3].
<&nsub> The numerical estimates of the energy levels for a hydrogen atom in impenetrable cavities of simple forms, such as a tetrahedron or truncated tetrahedron (up to octahedron), and regularities in the states of confined atom ordering for such polyhedrons are presented.
The analysis of the ordering of the lowest electronic states for confined atom, associated with 1s - 3d-states of a free system, in particular, the ordering of the eg(3d) and f2g(3d) states, is reported. Some regularity in discrepancy of the states ordering for tetrahedron and more symmetrical problems (e.g. cube, octahedron or sphere) are analyzed.
<&nsub> The work is supported by Russian Foundation for Basic Research (project 07-03-01021).
[1] Sen K.D., Pupyshev V.I., Montgomery Jr H.E. Exact Relations for Confined One-Electron Systems. In: J.R. Sabin, E.Brandas, editors; Theory of Confined Quantum Systems: Part One, v. 57, Advances in Quantum Chemistry, Academic Press, 2009, p. 25-77.
[2] Yurenev P.V., Scherbinin A.V., Pupyshev V.I. Int.J.Quant.Chem. 2008, v. 108, №14, p. 2666-2677.
[3] Kretov M.K., Scherbinin A.V. and Pupyshev V.I. Phys.Script. 2009, v. 80 (in press).
A direct nucleophilic addition of the lower alcohols and thiols to the acetylenic triple bond (vinylation) in the KOH/DMSO superbase medium yields diverse vinyl ethers and vinyl sulfides – promising monomers, cross-linking agents and precursors of bioactive substances. Thiols are known to be substantially more active in the base-catalyzed vinylation reaction then their oxygen analogs.
The MP2/6-311++G**// B3LYP/6-31+G* comparative study of methanol and methanethiol interactions with the KOH/DMSO/acetylene system was studied in a gas phase as well as with solvent (DMSO) effects included within the RHF/6-31+G* IEFPCM solvation model.
Both methoxide and methanethiolate anion are readily formed under interaction of reagents with either hydroxide ion or non-dissociated KOH molecule. The latter results in the dynamical equilibrium between approximately equal in energy СН3ОН•KОН and СН3ОK•Н2О structures with a negligible proton transfer barrier in case of methanol, while the in methanethiol interaction with KOH yields mainly СН3SK•Н2О. These indicate an increased concentration of active nucleophilic particles in the KOH/DMSO/CH3SH system when compared to that in the methanol containing one.
Addition of the anions formed to the acetylene molecule is a limiting stage of vinylation process. It starts from a pre-reaction complex, which is thermodynamically stable in both gas phase and DMSO solution and rearranges towards the corresponding methoxyethenide or methylthioethenide carbanion through a transition state of similar structure for methoxy- and methylthioanion addition. The activation barriers of this stage are close in a gas phase (15.9 kcal/mol and 15.1 kcal/mol for methoxy- and methylthioanion, consequently) and DMSO solution (15.5 kcal/mol and 15.7 kcal/mol). Hence, a difference in alcohol and thiol activity in vinylation reaction is only slightly associated with their activation energies.
The ethynide ion formation followed by the acetylene oligo- and polymerization is a concurrent process in alcohol vinylation. Indeed, the calculation results indicate a proton transfer from the acetylene molecule to the methoxide moiety to occur with a small or no activation barrier, yielding a stable complex with a stabilization energy –12.5 kcal/mol. By contrast, the acidity of methylthiol is much higher than that of acetylene, and the etynide ion formation in thiol-containing system is thermodynamically unfavorable.
Thus, an increased activity of thiols in vinylation reaction could be rationalized by the increased concentration of active nucleophile and the lesser participation of side reactions, but not a difference in the anion nucleophilic addition to acetylene reaction stage.
This work was supported by the RFBR grant No. 09-03-00618-а.
Eigenvalue-type spin-polarized equations for Löwdin-Amos-Hall spin-paired (corresponding) orbitals are reported. These equations called “paired orbitals for different spins” (PODS) equations are alternative to the standard Hartree-Fock or Kohn-Sham equations. PODS equations are constructed as non-canonical unrestricted Hartree-Fock-type equations in which non-canonical orbitals are fixed to be biorthogonal spin-paired orbitals by means of the Adams-Gilbert “localizing” operator approach. The PODS equations contain different operators for different spins the eigenvectors of which are paired orbitals. Although the spectrum of possible applications of the PODS equations seems to be quite wide they appear to be especially useful for finding the broken-symmetry solutions (of the spin-density-wave type) unreachable by means of the standard equations. The effectiveness of the PODS equations is demonstrated using the hypothetical molecule H6. The close-shell symmetry adapted (SA) solution for this molecule becomes unstable at the hexagon geometry with elongated H-H bonds. Such solution for the HH distance of 2.0 Angstrom represents a saddle point with zero spin density versus two local minima of the spin-density-wave type on the total energy hypersurface (see a schematic view below). The lowest BS solution has <S**2>=2.51 and magnitude of Mulliken atomic spin density of 0.9 au (designated as BS-1). Another solution has <S**2>=2.80 and magnitude of Mulliken atomic spin density of 1.0 (BS-2). The PODS equations allow one to find all these broken-symmetry local minima unlike unrestricted Hartree-Fock equations which predict lowest BS solution alone. Unlike standard unrestricted solutions, PODS orbitals for either spin are all biorthogonal (paired) providing a conceptually very attractive tool to consider the electron structure in terms of paired or unpaired orbitals. Another feature of the PODS equations is that the eigenvalues of paired spin-up and spin-down orbitals are exactly the same being determined by the orbital-pair overlaps. The major advantage of the PODS equations in comparison with the standard UHF (UKS) equations is the possibility to locate some additional low-lying states. The latter problem of determining all local minima to select a global minimum represents a well known challenge for quantum chemistry which arises from nonlinearity of the self-consistent-field equations. This presentation has been supported by interdisciplinary integration project #26 of SB RAS. I. Zilberberg, S.Ph.Ruzankin, Paired Orbitals for Different Spins Equations, J.Comput.Chem. 2009, accepted I. Zilberberg, S.Ph.Ruzankin, Paired Orbitals for Different Spins Equations, arXiv:0804.0967
We present a detailed analysis of the results of our numerical study of the crystal and electronic structure of the room temperature organometallic ferrimagnet of general composition V(TCNE)x with x = 2. The results of the LSDA+U study show that the experimentally determined structure complies with the magnetic measurements and thus can serve as a prototype structure for the entire family of the M(TCNE)2 organometallic magnets. The results of the numerical study and of the magnetic experiments are interpreted using model Hamiltonians proposed here. This allowed us to obtain estimates of the critical temperature in three- and two-dimensional regimes and to give an explanation of the differences in behavior of probably isostructural V(TCNE)2 and Fe(TCNE)2 species.
A direct vinylation of lower alcohols with acetylene yielding vinyl ethers occurs in the KOH/DMSO superbase medium at atmospheric pressure and up to 120°C temperature, while the original Reppe process involved heating the alcohol–acetylene charge at 150–180°C using 1–2% KOH or sodium as catalyst under pressure, with a partial nitrogen atmosphere.
The reaction mechanism of methanol vinylation with acetylene involving a non-dissociated KOH molecule was studied using the MP2/6-311++G**//HF/6-31+G* approach with one DMSO molecule explicitly included into reaction system.
The non-dissociated KOH molecule interaction with a single dimethyl sulfoxide particle in a gas phase results in a DMSO-KOH complex (1) with a stabilization energy -25.0 kcal/mol, which could undergo further transformation in the interaction with either acetylene or methanol molecule.
The former reaction route yields a DMSO-KOH-acetylene complex (2) with the energy -31.3 kcal/mol below the separate contaminants level. The acetylene molecule proton in 2 is coordinated to oxygen atom of the KOH hydroxyl. Structures of this sort are pre-reaction complexes of ethynide ion formation. Further addition of methanol to 2 results in a four-component complex 3 with a stabilization energy -48.6 kcal/mol. The KOH hydroxyl group in 3 coordinates both acetylene and methanol molecule, hence 3 could produce both etynide and methoxide ions. Proton transfer from methanol to KOH hydroxyl decreases a system relative energy to -49.2 kcal/mol and takes negligible small activation energy. A methoxide moiety in complex 4 formed it this reaction is bonded to both acetylene and water molecules, that prevents a methoxide ion addition to the acetylene triple bond and increases the activation barrier with respect to one obtained in a pure anionic mechanism [1].
When 1 reacts first with a methanol molecule, the latter forms complex 5 with stabilization energy -44.3 kcal/mol and the methanol proton oriented to KOH oxygen atom. Acetylene addition to 5 again yields 4. However, when a proton transfer in 5 precedes the acetylene molecule coordination, a structure of the resulting four-component acetylene-KOCH3-DMSO-water complex with a water molecule removed from the reaction region turns more favorable for the methoxide ion addition to acetylene, and the reaction activation energy drops down to 21.0 kcal/mol comparable to that in anionic mechanism [1].
This work was supported by the RFBR grant No. 09-03-00618-а.
Reference:
1. E.Yu. Larionova, N.M. Vitkovskaya, V.B. Kobychev, et al., J. Struct. Chem., 48, S94–S99 (2007).
The Favorsky base-catalyzed isomerization of alkynes in superbase media now became a powerful tool of organic synthesis. Particularly important are regioselective prototropic shifts of the triple bond in functional acetylenes and those versions of the isomerization which allow heteroallenes to be selectively synthesized. In particular, allylpropargyl ether in the KOH/DMSO medium selectively rearranges to its allylallenyl isomer at a room temperature, while the further heating gives rise to the double bond isomerization.
The mechanism of multiple bonds migration involving hydroxide ion was studied using the MP2/6-311++G**//RHF/6-31G* and MP4(SDQ)/6-311++G**//RHF/6-31G* approaches both in the gas phase and with solvent (DMSO) effects included within Onsager SCRF and IEFPCM continuum model at the HF/6-31+G* level.
The double bond migration towards the oxygen atom is thermodynamically more preferable then the propargyl group isomerizatiion to allenyl form. The corresponding reaction heats are -6.3 kcal/mol and -1.7 kcal/mol in a gas phase and -4.1 kcal/mol vs. -1.3 kcal/mol in the DMSO solution.
The suggested mechanism of proton transfer in a gas phase starts from a stable pre-reaction complex of allylpropargyl ether molecule and hydroxide ion with the stabilization enthalpy -19.9 kcal/mol and involves the intermediate formation of the corresponding anion complexes with the water molecule formed. The activation barrier of proton abstraction from the methylene group adjoined to triple bond, 2.6 kcal/mol, is lesser than that of allylic methylene deprotonation, 6.5 kcal/mol. The intermediate complex on the propargyl group isomerization pathway is by 11.2 kcal/mol more stable than one formed in the allyl moiety rearrangement process.
Since the hydroxide ion in the DMSO solution is possessed of the most solvation energy, the overall reaction profile changes significantly when solvent effects included. Particularly, the pre-reaction complex becomes a low-stable structure in the solvent surrounding. However, accounting of the solvation effects keeps structures of the transition states as well as ones of the intermediate complexes. The activation barrier of the propargyl moiety rearrangement towards allenyl structure in the DMSO solution (10.8 kcal/mol) is lesser than that of allyl group isomerization (21.3 kcal/mol).
This work was supported by the RFBR grant No. 09-03-00618-а.
Many chemical compounds, such as halogenide ions and some transition metal complexes in water solutions, demonstrate the so-called "charge-transfer-to-solvent" (CTTS) bands in the UV absorption spectra. These effects are of wide interest in photochemistry and spectroscopy, however, their physical nature is still not well-investigated, especially by means of modern quantum-chemistry methods.
In earlier studies [1-2], the absorption spectrum of the simplest coordination compound, hexaammineruthenium (II) ion in water solution, exhibiting a broad CTTS absorption band at 36400 cm-1 [3] and also less prominent ligand field (LF) bands, was studied using both traditional ab initio methods (CASSCF, MCQDPT) and TDDFT with a variety of exchange-correlation potentials. The effective fragment potential (EFP) approach was used to account for water solvation effects, and in order to verify the correctness of the solvation model, test calculations were also performed with the 16 nearest water treated quantum-mechanically. CASSCF/MCQDPT approach gives qualitatively correct order of the excited states of the complex only with rather extended active spaces (up to 14 MOs) and large number of states included in the state-average (up to 40), whereas conventional TDDFT methods (based on pure and hybrid functionals) lead to substantial underestimation of the CTTS transition energy unless the contribution of the HF exchange is about 50%.
In the present study, the so-called Long-range Correction (LC) scheme of TDDFT method [4] is examined in order to predict transition energies for the above transitions of the aqueous hexaammineruthenium (II) ion, and very good quantitative agreement with the experimental absorption band positions is achieved. Unlike the earlier studies, the relative intensities of the LF vs CTTS bands are in a good agreement with the calculated oscillator strenghts. Basing on the simple Pekar model of homogeneous broadening [5], we also estimated the widths of the calculated absorption bands from the present ab initio data, and found reasonable agreement with the data extracted from the experimental absorption spectrum.
The quantum chemical studies are performed using PC GAMESS 'Firefly' and GAMESS US codes.
The work was supported by the Russian Foundation for Basic Research (project 07-03-01021-a)
References
[1] Yurenev, P.V., Scherbinin, A.V., Stepanov N.F. Int J Quant Chem 2008, 108, 2711.
[2] Yurenev, P.V., Scherbinin, A.V., Stepanov N.F. Book of Abstracts of the NATO ARW, Kyiv, 2008, p.200.
[3] Matsubara, T., Efrima, S., Metiu, H.I., Ford, P.C. J Chem Soc
Faraday Trans 1979, 75, 390.
[4] Iikura H., Tsuneda T., Yanai T., Hirao K. J Chem Phys 2001, 115, 3540.
[5] Pekar, S.I. Uspekhi Fiz Nauk 1953, 50, 197.
Europium atom in its ground 8S electronic state has very stable half-filled 4f shell with aligned unpaired spins
submerged under the filled 5p and 6s shells. Interaction of two Eu atoms gives rise to eight states with the total spin S ranging
from 0 to 7. This manifold is investigated ab initio to establish the bonding and, for the first time, magnetic properties of the
europium dimer. The plain multireference configuration interaction (MRCI) calculations on the states of highest spin reveal that their
ordering follows the Heisenberg spin-exchange model with the small negative spin-coupling constant J. This firmly establishes
the antiferromagnetic nature of the dimer. The Heisenberg model is used to obtain improved interaction potentials for the whole
manifold of spin states by combining the reference interaction energy for the spin-polarized S = 7 state computed at the
single-reference coupled cluster CCSD(T) level of theory and exchange energy derived from the multireference averaged quadratic
coupled cluster (AQCC) calculations. This model estimates the dissociation energy of the dimer as 710 cm-1 and predicts
the spin-coupling constant -J as small as 0.3 J. The bonding has predominantly dispersion origin and therefore keeps
the identity of atomic 6s orbitals, which screen and suppress the exchange interaction between the inner spin-bearing 4f shells. Similar
picture is observed for the lowest electronic states of the manganese dimer [1-3]. The Mn2, however, has weaker bond (550
cm-1) and spin-coupling constant J = -4 cm-1. It can be said that suppression of the coupling
between 4f shells is by order of magnitude stronger than that of 3d shells.
This work was supported by the Russian Basic Research Fund (project 08-03-00414).
1. A. A. Buchachenko, Chem. Phys. Lett. 459, 73 (2008).
2. D. Tzeli, U. Miranda, I. G. Kaplan, and A. Mavridis, J. Chem. Phys. 129, 154310 (2008).
3. G. Chalasinski, M. M. Szczesniak, and A. A. Buchachenko, to be published.
a Physics Department, St.Petersburg state university, RUSSIA
b Physics and Astronomy Department, University College London, UK
This contribution is dedicated to Prof. N.F. Stepanov on occasion of his 75-th birthday.
In calculation the electronic structure of crystals, especially with point defects, the embedding approach is proved to be usefull and convenient. In this approach instead of infinite crystal a finite part of the crystal, referred to as cluster, is considered, the influence of the rest of the crystal being simulated by the embedding potential. The key problems of this approach are the cluster selection and the embedding potential generation. The present paper is devoted to the first problem.
The common practice is to employ a large cluster with a comparatively simple embedding potential and to increase the size of the cluster until the errors due to the boundary effects will be small enough. However, it is more expedient to divide the perfect crystal into a collection of clusters preserving both point and translational symmetry. A method to generate clusters preserving both symmetries is proposed in the present paper.
The valence electrons only approximation is used for simplicity. The Wigner-Zeitz unit cell is considered and every atom at the unit cell surface is symmetrically "divided" among connecting unit cells, the number of "parts" being equal to the number of nearest neighbours. For this orbitals localized on the atom are considered, but instead of pure s-, p-, d-, etc atomic orbitals the hybrid orbitals are employed. In the conventional hybridization scheme two conditions are imposed: the hybrid orbitals must be equivalent and they must be orthogonal. In this case it is evident that the number of possible hybrid orbitals, which is defined by the atomic electron shells, may differ from the number of nearest neighbours, which is defined by the crystal geometry. In the present paper it is shown that employing the non-orthogonal and even linearly dependent orbitals it is possible to generate equivalent hybrid orbitals so that i) the number of hybrid orbitals is equal to the number of nearest neighbours, and ii) the first-order reduced density matrix of the atom is the sum of the first-order reduced density matrices for each hybrid orbital (the equation for the first-order reduced density matrix of atom has the same form as in the case of orthogonal orbitals).
Several variants of the embedding potential to reproduce the electronic structure are considered and, in particular, the equation for the potential is developed such that the wave function of the electron in this potential is exactly one of the generated hybrid orbitals.
The MgO, ZrO2, and TiO2 crystals are considered as examples.
The work was supported by the FRBR grant N 09-03-00733-a
The crystal electronic structure calculation in the embedded cluster approach is considered in the present paper with application to the high-temperature cubic phase of ZrO2 crystal with FCC lattice. A method is proposed to generate the embedding potential which enable one to employ the smallest possible clusters containing only few atoms.
The smallest clusters, preserving crystal point symmetry have an ion at the cluster center and its nearest neighbours as terminating ions at the cluster border. The terminating ion is divided into equivalent parts, the number of parts being equal to the number of nearest neighbours. The division is made with the help of modified hybridization procedure. In result 8 non-orthogonal and linearly dependent spd-hybrid orbitals of Zr and 4 sp-orbitals of O are produced. From hybrid orbitals only directed at the central ion are attributed to the cluster.
For the long-range part of the embedding potential, simulating the influence of the crystal environment, the point-ion lattice potential is taken. Besides, a short-range part of embedding potential is added as a sum of atomic "hybrid" potentials centered at the positions of terminating atoms. The hybrid potential is generated to produce exactly the terminating atom hybrid orbital attributed to a cluster. The hybrid potentials are generated self-consistently, namely the hybrid potential of Zr ion is generated from results of ZrO8 cluster calculations, where Zr is the central ion. The generated potential is employed in the OZr4 cluster calculations, where Zr is the terminating ion. Similar procedure is applied to O ion.
In addition, the very small ZrO cluster consisting of two centers and four electrons and corresponding to the Zr-O bond is considered. In this cluster both hybrid potentials of Zr and O ions are employed. The results of calculations of all three clusters are in good agreement with each other.
The relation of the described clusters with the crystal unit cell is considered. The ZrO8 cluster is in fact the Wigner-Setz unit cell for FCC lattice, although the OZr4 cluster is not. However, the Wigner-Setz unit cell generated around O ion in ZrO2 lattice considered as simple cubic is the union of four ZrO8 clusters. Similarly, the Wigner-Setz unit cell generated around Zr ion in ZrO2 simple cubic lattice is the union of eight OZr4 clusters. With the help of the said cluster - crystal unit cell relation some properties of ZrO2 crystal are calculated
The work was supported by the FRBR grant N 09-03-00733-a
The thermochromatographic registration of superheavy element 112 (E112, Cp, eka-Hg) on gold surface [1] remains the only reliable way of its chemical identification. Experimental data indicate that the E112/Au adsorption energy is rather large (0.5-0.8 eV) and notably exceeds the corresponding value for element 114 (E114), whereas recent relativistic DFT (RDFT) calculations predict that the binding energies between E112 and gold clusters are smaller than the corresponding energies for E114. Moreover, two-component RDFT estimates for E112-Aun binding energies for large n seem to converge to the values well below the range compatible with the experimental data. To check the validity of RDFT methods in application to E112-Au interactions, we estimated the parameters of few E112-Aun systems by combining the results of scalar relativistic many-body perturbation theory calculations with geometry-dependent spin-orbit contributions to interaction energies [2] evaluated at the DFT level (MBPT+SO). The latter contributions are nearly independent on the choice of exchange-correlation functionals (XCFs). All calculations were performed within accurate two-component small-core relativistic pseudopotential model. While a reasonable agreement of relativistic DFT and MBPT+SO results for the bond parameters in the E112Au diatomic is readily achieved with simple gradient or hybrid XCFs, MBPT+SO estimates of E112 - Aun binding energies for Au clusters simulating adsorption sites are found to be systematically much larger than their DFT counterparts. This result can be explained by the peculiarity of the atomic structure of E112 consisting in highly polarizable though still compact filled 6d-shell. This suggests a rather strong dispersion-like interactions of quasi non-overlapping d-shells of E112 and Au, in a sense resembling the aurophilic attraction. DFT approaches with conventional XCFs are not suitable for describing this kind of interactions and seem to fail in this case.
The authors express their gratitude to A.A. Granovsky and C. van Wuellen. The work was partially supported by the Russian Foundation for Basic Research (grants no. 09 03 00655 and 09 03 12255 ofi-m).
1. R. Eichler et al., Nature 447, 72 (2007)
2. A. Zaitsevskii et al., Cent. Eur. J. Phys. 4, 448 (2006)
Квантовохимическими методами проведен конформационный анализ диметилфосфористой и диэтилфосфористой кислот, применяемых при синтезе ингибиторов полифункционального действия эластомерных композиций.
Конформационный анализ органических соединений вносит существенный вклад в выявление реакционной способности молекул. Наиболее подробно такой анализ может быть осуществлен с помощью квантовохимических методов. Современный уровень развития технических средств позволяет за приемлемые сроки осуществить квантовохимическое моделирование не очень сложных молекулярных систем методами функционала плотности, точность которых вплотную приближается к неэмпирическим методам, а зачастую дает даже более точный результат.
Из всего количества степеней свободы молекулы, определяющих конформационную энергию (длин связей, двугранных и диэдральных углов), для конформационного анализа необходимо выбрать одну или несколько степеней, приводящих к наибольшим геометрическим изменениям структуры при наименьших энергетических затратах. Если такая степень свободы одна, то изменение конформационной энергии иллюстрирует кривая конформационной энергии, если степеней свободы две или более, – строятся многомерные поверхности конформационной энергии. Наиболее приемлемой в нашем случае является трехмерная поверхность, соответствующая двум степеням свободы, при этом в качестве них выступают диэдральные углы, характеризующие расположение радикала относительно двойной связи P=O.
Для подтверждения этих предположений нами проведены квантовохимические расчеты методами PM3 и функционала плотности B3LYP в базисе 6 311G(d,p).
Оптимизация структур проводилась методами PM3 и B3LYP таким образом, что указанные углы фиксировались в интервале от 0 до 360º с шагом 30º, после чего осуществлялась геометрическая оптимизация молекулы. Далее при построении поверхности конформация с минимальной энергией принималась за базовую, все остальные энергетические показатели пересчитывались относительно нее.
Так, по методу РМ3 наименьшая конформационная энергия диметилфосфористой кислоты наблюдается при координатах 330×60º, тогда как по методу B3LYP таких минимума два – при координатах 60×30º и 330×300º. При этом максимальное значение конформационной энергии достигает 51,33 кДж/моль при координатах 120×240º.
Расчеты методом B3LYP в базисе 6-311(d,p) привели к несколько иным результатам по сравнению с расчетами методом РМ3. Изменились координаты минимумов и максимумов энергии на потенциальной поверхности, выросли абсолютные значения максимальных энергий.
Проведенный конформационный анализ молекул диметилфосфористой и диэтилфосфористой кислот квантовохимическими методами показал, что метод функционала плотности B3LYP 6-311(d,p) является более точным по сравнению с методом РМ3, что немаловажно при выявлении реакционноспособных конформаций молекул этих кислот для дальнейшего синтеза ингибиторов полифункционального действия.
В шинной промышленности широко применяются аминсодержащие ингибиторы процессов теплового и озонного старения резин. Однако в ходе эксплуатации автомобильных шин эти вещества в результате диффузионных процессов попадают в окружающую среду. Данные ингибиторы являются веществами дифениламинового ряда и при взаимодействии с различными окислителями, присутствующими в атмосфере, приводят к образованию канцерогенных нитрозоаминов.
Существенного повышения экологической безопасности при эксплуатации резиновых изделий можно достичь заменой классических аминсодержащих ингибиторов так называемыми ингибиторами полифункционального действия (ИПД), одним из представителей которых являются дифенилгуанидиниевые соли диалкилфосфористых кислот. Такие ингибиторы проявляют одновременно свойства нескольких ингредиентов резиновых смесей.
Несмотря на имеющиеся способы синтеза ИПД и большое количество экспериментально полученной информации об их свойствах, механизм взаимодействия N,N'-дифенилгуанидина (ДФГ) и диалкилфосфористой кислоты (ДАФК), приводящий к образованию соли, до настоящего времени не исследован. Это, в свою очередь, препятствует разработке теоретических основ технологии получения ИПД, подбору исходных реагентов для проведения оптимального процесса синтеза с получением ингибиторов с заданными свойствами. Данный недостаток может быть устранен исследованием конформационных и электронных свойств молекул ДАФК и ДФГ и механизмов реакций между ними с привлечением современных вычислительных методов.
Методом функционала плотности B3LYP в базисе 6-311G(d,p) проведен конформационный анализ диалкилфосфористых кислот и ДФГ, каждый по двум степеням свободы, соответствующим наименее прочным структурным элементам молекул. Такой подход позволяет установить конформеры с минимальной и максимальной конформационной энергией и прогнозировать наиболее реакционноспособные конформации этих кислот, оказывающие существенное влияние на энергетику при их взаимодействии с ДФГ с получением ИПД.
Ведущей идеей физико-химической модификации ингибиторов шинных резин в бинарных расплавах, приводящей к уменьшению летучести и миграции, является значительное повышение их экологической безопасности за счет образования легкоплавких и гранулируемых эвтектических смесей, твердых растворов замещения и молекулярных комплексов с большим мольным объемом. Такие смеси обладают не только минимальными летучестью и миграцией из шинных резин, но и наилучшим распределением в резиновых смесях и наибольшей активностью по функциональному назначению. Последнее обусловлено тем, что с термодинамической точки зрения в одной и той же среде расплавленное вещество распределяется лучше, чем в кристаллическом состоянии [1].
Нами проведены исследования, которые позволяют судить о возможности образования между молекулами агидола-2 и диафена ФП различных типов водородной связи. Для определения характера межмолекулярного взаимодействия между молекулами агидола-2 и диафена ФП проводились квантовохимические расчеты их молекулярных комплексов методом функционала плотности B3LYP в базисе 6 311G(d,p).
Длина NН...О водородной связи составляет 0,32 нм, энергия образования такой связи равна -17,69 кДж/моль, что вполне соответствует литературным данным [2]. Образование NН...О связи между NH-группой, расположенной между фенильными фрагментами диафена ФП и ОН-группой агидола-2 характеризуется длиной 0,30 нм и энергией образования -18,02 кДж/моль. При этом наблюдается уменьшение энтропии в обоих случаях на -111,7 и -193,8 Дж/(моль.К) соответственно. Следовательно, вероятность образования Н-связей с атомом азота NH-группы, расположенной между фенильными фрагментами будет гораздо больше, чем с атомом азота, расположенным между изопропильным и фенильным фрагментами молекулы диафена ФП.
Проведенные нами исследования показывают возможность образования водородных связей между молекулами агидола-2 и диафена ФП как классического типа NН...О связи, так и с участием pi-электронов фенильных групп. C учетом образования ОН...pi связи можно ожидать формирование довольно прочных молекулярных комплексов между молекулами агидола-2 и диафена ФП, имеющих полимерные формы Н-связей.
При образовании типичных водородных связей НN...О между молекулами следует учесть сродство к электрону молекул, которое для агидола-2 равно 0,69 эВ, а для диафена ФП – 1,05 эВ. Следовательно, в бинарных смесях данных ингибиторов донором протона при образовании Н-связи будет выступать тот ингибитор, который имеет меньшее значение сродства к е-. Ингибитор с большим значением сродства к электрону будет донором е-.
Литература:
1. Экологические аспекты модификации ингредиентов и технологии производства шин. Под науч. ред. проф. А.А. Мухутдинова. Казань: Изд-во «Фэн», 1999. – 400 с.
2. Nishio M. CH/pi hydrogen bonds in crystals // CrystEngComm, 2004. – V. 27. – #6. – P. 130 158.
Вторичные ароматические диамины, производные п-фенилендиамина, обладают высоким защитным действием шинных резин от теплового и озонного старения, утомления, пассивируют металлы переменной валентности. Высокое защитное действие диаминов объясняется наличием в их молекуле двух активных центров. Широко применяемыми ингибиторами этого класса являются N-фенил,N’-изопропил-n-фенилендиамин (диафен ФП) и N,N’-дифенил-n-фенилендиамин (ДФФД) [1].
Квантовохимические расчеты проводились методом функционала плотности B3LYP в базисе 6-311G(d,p) посредством программного пакета Gaussian [2].
Энергии образования свободных радикалов для диафена ФП составляют: при образовании радикала между арильными группами 347,7 кДж/моль, между арильным и изопропиловым (со стерическим эффектом) группами 364,47 кДж/моль. Для ДФФД такая энергия составляет 353,93 кДж/моль.
При образовании синглетного бирадикала диафена ФП затраты энергии на 59,5 кДж/моль ниже энергии образования двух радикалов. Для ДФФД эта разница составляет 57,05 кДж/моль. Для триплетного бирадикала диафена ФП затраты энергии больше на 42,3 кДж/моль, ДФФД – 36,34 кДж/моль. Это может быть обусловлено триплетным отталкиванием [3]. Разница энергий образования синглетного и триплетного бирадикалов диафена ФП и ДФФД составляют 101,33 и 93,39 кДж/моль соответственно.
Полученные результаты квантовохимических расчетов позволяют прогнозировать механизм ингибирующего действия термоокислительного и озонного старения шинных резин молекулами диафена ФП и ДФФД в следующей последовательности:
– под действием тепла или солнечной радиации молекулы диафена ФП и ДФФД переходят в возбужденное состояние с уменьшением ΔЕНСМО-ВЗМО, что способствует уменьшению энергии связи между водородом и азотом в NH-группе, в результате чего атом водорода становится лабильным;
– гомолитический отрыв лабильного атома водорода аминной группы, последующее взаимодействие образующихся свободных радикалов со свободными радикалами макромолекул каучука и в итоге – обрыв цепных реакций разрушения макромолекул озоном с образованием неактивных соединений.
Список литературы
1. Пиотровский К. Б., Тарасова З. Н. Старение и стабилизация синтетических каучуков и вулканизатов / К. Б. Пиотровский, З. Н. Тарасова // М.: Химия, 1980. – 264 с.
2. Frisch M. J., Trucks G. W., Schlegel H. B. et al. Gaussian 98. Gaussian, Inc., Pittsburgh, PA. 1998.
3. Денисов Е. Т. // Кинетика и катализ, 1995. – Т. 36. – №3. – С. 381-186.
Нами методом функционала плотности по алгоритму B3LYP в базисе 6-31G(d,p) проведено квантовохимическое моделирование параметров строения молекул стеарата цинка и диафена ФП, а также их молекулярных комплексов.
При расчете молекулярного комплекса диафен ФП–стеарат цинка на основе одной молекулы стеарата цинка получена структура, в которой из-за сильных стерических эффектов со стороны диафена ФП молекула стеарата цинка значительно изгибается в центральной части. Энергия образования такого комплекса составляет -112 кДж/моль, что согласуется с литературными данными по образованию молекулярных комплексов.
Однако следует отметить, что, согласно литературным данным [1], две молекулы стеарата цинка способны вступать во взаимодействие с образованием мостиковых связей. Выгодность мономерной или димеризованной структуры стеарата цинка можно оценить по величине энергии образования димера, которая, согласно нашим расчетам, составила -199 кДж/моль. Это свидетельствует о преимущественном существовании стеарата цинка в виде такого димера.
В случае димера стеарата цинка молекулы по атому цинка не изгибаются. При образовании молекулярного комплекса молекулы диафена ФП могут подойти с обеих сторон димера. Такой комплекс характеризуется энергией, равной -132 кДж/моль.
Таким образом, можно сделать вывод, что молекулярный комплекс диафен ФП–стеарат цинка может существовать на основе как мономерной, так и димеризованной формы стеарата цинка, при этом последний вариант является энергетически более предпочтительным.
Квантовохимические расчеты проводились при помощи программного пакета Gaussian 98 [2].
Литература
Методом функционала плотности B3LYP в базисе 6 311G(d,p) было проведено квантовохимическое моделирование молекул ингибиторов теплового и озонного старения шинных резин N фенил,N изопропил п фенилендиамина (диафена ФП) и N,N’ дифенил п фенилендиамина (ДФФД).
Согласно полученным результатам, между молекулами диафена ФП наблюдается образование NH...N-связи длиной 0,24 нм, а также проявляется CH...pi-взаимодействие длиной 0,31 нм. При моделировании димера ДФФД проявляются NH...pi- и CH...pi-взаимодействия, имеющие следующие характеристики: длина NH...pi-связи 0,31 нм; длина CH...pi-контакта 0,29 нм. При этом классическая NH...N-связь не образуется. Энергетически выгоднее образование димера диафена ФП (энергия образования из исходных соединений составляет 18,52 кДж/моль), менее выгодно образование димера ДФФД (10,46 кДж/моль).
Исследования данных соединений были проведены методом рентгеноструктурного анализа на автоматическом дифрактометре «Bruker Smart Apex II». Для этого получен монокристалл диафена ФП. Для ДФФД были найдены структурные параметры кристаллов в Кембриджской базе кристаллоструктурных данных [1, 2, 3].
Согласно результатам рентгеноструктурного анализа для диафена ФП, он кристаллизуется в триклинной сингонии, размеры элементарной ячейки равны 0,86x0,95x0,99 нм. В кристалле диафена ФП имеется NH...pi-контакт длиной 0,28 нм. Расхождение с результатами квантовохимического моделирования объясняется различными стерическими эффектами, связанными с изопропильным фрагментом, в газовой и кристаллической фазах.
ДФФД в кристаллическом состоянии может характеризоваться двумя типами сингонии – моноклинной и триклинной. В случае моноклинной сингонии [1] размеры элементарной ячейки равны 2,57x0,75x0,70 нм, при этом наблюдаются NH...pi-контакты длиной 0,29 нм.
Авторы [2] получили кристалл ДФФД триклинной сингонии, размеры элементарной ячейки равны 0,79x0,90x1,11 нм. При этом образуются NH...pi-связи длиной 0,29 нм, а также CH...pi-контакты длиной 0,29 нм. Приблизительно к таким же результатам приводит квантовохимическое моделирование взаимодействия молекул ДФФД.
Полученные данные полностью согласуются с современными представлениями о характеристиках NH...pi- и CH...pi-контактов [4, 5, 6] и хорошо коррелирует с результатами квантовохимического моделирования.
СПИСОК ЛИТЕРАТУРЫ
Since the classic work of Roothaan (1960), the one-electron energies in a ROHF method are known as ambiguous quantities having no physical meaning. On the basis of this result, it was “proved” by different authors that Koopmans’ theorem (KT) is not valid in the ROHF method, i.e., the eigenvalues of a ROHF Hamiltonian cannot be equated to ionization potentials. In the lecture we present a complete solution of this problem.
I. Canonical form for the Hartree-Fock Hamiltonian.
We derive the new (canonical) form for the ROHF Hamiltonian [1], the eigenvalues of which obey KT for the whole energy spectrum, i.e., for a removal of an electron from the occupied orbitals (both closed-shell and open-shell) and for an attachment of an electron to the virtual shell. A discussion of new orbital energies is presented on the examples of free atoms N and Mn and of endohedral N@C60 (I_h). The vertical ionization potentials and electron affinities estimated via KT are compared with the respective observed data and, for completeness, with the respective estimates derived with a delta-SCF method.
II. CI-based formulation of Koopmans' theorem.
In the paper [2] we give a general formulation of KT in the ROHF method based on a variational treatment of both the initial (non-ionized) open-shell system under study and the corresponding high-spin ions. The ions are treated within a FCI-RAS (Full CI in the Restricted Active Space) method with a use of arbitrary ROHF orbitals optimal for the initial system. We show that the desired canonical ROHF orbitals and orbital energies satisfying KT, first defined in [1], generally appear as the natural CI orbitals and the eigenvalues of CI matrices for the respective ions.
III. Two different sets of orbitals and orbital energies in the canonical ROHF method.
We analyze the problem of the “duality” of the canonical ROHF method [3]. This problem arises if we consider two alternative ionization processes within the same electronic shell, for example: (A1) a removal of a beta electron from the closed-shell orbital and (A2) a removal of an alpha electron from the same closed-shell orbital; or (B1) a removal of an alpha electron from the open-shell orbital and (B2) an attachment of a beta electron to the open-shell orbital. A treatment of these alternative cases shows the necessity of introducing in the canonical ROHF method TWO DIFFERENT SETS of canonical orbitals and orbital energies. We give [3] a detailed analysis of this duality of the canonical ROHF method within both the approximation of “frozen” orbitals and the CI level.
This work was supported by RFBR (09-03-00113) and OXHM RAS (2009/5.1.9)
[1] B. N. Plakhutin, E. V. Gorelik, and N. N. Breslavskaya, J. Chem. Phys., Vol. 125, 204110 (2006).
[2] B. N. Plakhutin and E. R. Davidson, J. Phys. Chem. A. in press (published on-line 12 May, 2009).
[3] E. R. Davidson and B. N. Plakhutin, to be submitted.
Ван-дер-ваальсовы (ВдВ)комплексы, формируемые посредством слабых дальнодействующих межмолекулярных сил и находящиеся на грани стабильных образований, в последнее время привлекают повышенное внимание экспериментаторов и теоретиков. Выявление принципов организации таких систем, занимающих промежуточное положение между молекулярным и конденсированным состояниями вещества, открывает перспективы для глубокого понимания строения вещества в конденсированной фазе и создания общей теории невалентных взаимодействий. При помощи метода ab initio MP2(full)/6-311++G(d,p) в даной работе исследованы структурные и электронные характеристики ванн-дер-ваальсовых кластеров водорода, азота и монооксида углерода (CO), включающих от шести до двенадцати молекул.
Как показывают результаты расчетов, каждый тип кластеров одинакового количественного и качественного состава включает в себя несколько практически изоэнергетичных структурных изомеров с весьма низкими энергиями перехода (менее 0.5 ккал/моль). При этом, если все обнаруженные структуры отвечающие минимуму на поверхности потенциальной энергии (ППЭ) для кластеров водорода в полной мере воспроизводятся и в чистых и смешанных кластерах азота и монооксида углерода CO, то обратное неверно. Так, для кластеров, состоящих исключительно из молекул водорода, не удалось обнаружить точки минимума на ППЭ, соответствующих структурам с осью симметрии выше третьего порядка.Для всех исследованных случаев формирование плоских структур оказывается невозможным, и стабильными оказываются исключительно «глобулярные» системы. При этом реализуется большое количество симметричных многопалубных кластеров. Геометрически центры тяжести молекул азота, входящих в состав полимолекулярных кластеров, формируют полиэдрические формы, что соответствует принципу наиболее плотной упаковки.
Замещение молекул в чистых кластерах сопровождается увеличением числа возможных конформаций системы и обеспечивает исключительную стереохимическую нежесткость этих систем за счет незначительных энергий перехода. Результаты расчетов свидетельствуют о возможности реализации необычных кооперативных эффектов, проявляющихся на структурном и энергетическом уровнях, в сложных полимолекулярных кластерах, стабилизированных слабыми невалентными взаимодействиями.
Увеличение количества взаимодействующих молекул в кластерах приводит к упрочнению межмолекулярных контактов, повышению компактности систем и к усилению в них кооперативных эффектов.
Благодарность. Работа выполнена при финансовой поддержке Совета по грантам Президента Российской Федерации для государственной поддержки молодых российских ученых (грант МК–3536.2008.3).
The mechanism of complex formation of biopolymers with different ligands including the solvent molecules and the correct calculation of binding energy are an actual problem of modern biophysical and biological science.
There are increasing amount of research works studying the interaction of individual amino acids and a solvent molecule. Account the secondary structure appears to improve the reality of used model. Helical structure of polypeptides mimics an alpha helical motif of the protein architecture. Therefore, the study of interaction between helical polypeptide and solvent molecule leads to deeper understanding of the basic interaction of biopolymers with environment at atomic level.
We investigated the complexes of alpha helical polypeptides and individual molecules of water, acetonitrile and 1,4-dioxane. We used 16-mer of polyalanine (PA), protonated polyglutamic acid (PGA) and poly-gamma-benzyl-l-glutamate (PBG). The polypeptides differ in the side chain long, hydrogen bonding ability, polarizability and hydrophobic properties. Water was chosen as a molecule of essential environment of proteins. Acetonitrile and dioxane are usual solvents for nonaqueous biocatalysis.
Full geometry optimization was performed for polypeptides and their complexes with ligands based on DFT theory level using PRIRODA program [1-3]. Each structure has been characterized by the vibrational analysis and interaction energy included the zero-point vibrational correction. Influence of polypeptide secondary structure on the complex formation was analized. PA creates one complex with water molecule and with acetonitrile and dioxane, PGA forms five different complexes with water molecule, and only two complexes with acetonitrile and dioxane. It was found tree complexes of PBG with water, one complex with acetonitrile and two complexes with dioxane. Strong red shift for water stretch vibrations is detected. Also notable red shift is observed for nitrile stretch. Significant changes were observed in dioxane spectrum. Obtained frequencies are in a good agreement with known experimental data.
1. D.N. Laikov, Chem. Phys. Lett. 281, (1997), 151.
2. D.N. Laikov, Chem. Phys. Lett. 416, (2005), 116.
3. D.N. Laikov, Yu.A. Ustynyuk, Russ. Chem. Bull., Int. Ed., 54 (2005), 820.
The support of Russian Academy of Sciences for Basic Research under the program “Molecular and Cellular Biology” and Russian Foundation for Basic Research Grant N 09-03-00778-is acknowledged.
Recent experimental study of the chloride ion formation under low-energy electron capture by the mono-chlorophenol molecules [1] has shown that intensity of the Cl(-) peaks in mass-spectra of para-chlorophenol was sufficiently lower in comparison with ortho- and meta-isomers, and its temperature dependence was stronger. To explain this data we performed DFT (BHHLYP/6-31+G* and PBE0/6-31+G*) investigation of Cl(-) elimination from isomeric Cl-Ph-OH(-) radical anions. According to our results in the lowest anion states of the chlorophenols an add electron occupies pi-MO which nodal plane passes through C-O bond and para-position of the ring (a2 type MO in terms of C2v group). Geometry optimization of these states leads to planar stationary structures of the radical anions. For para- and meta-Cl-Ph-OH(-) these structures correspond to local PES minima, while in case of ortho-Cl-Ph-OH(-) it corresponds to transition state for inversion of the C-Cl bond out-of-plane deviation. Moving along the active coordinate leads to barrier-less elimination of Cl(-). The meta-Cl-Ph-OH(-) reveals analogous mechanism of C-Cl bond dissociation. Only insignificant stretching of C-Cl bond is sufficient to out-of-plane deviation of Cl atom and the bond cleavage. The respective barrier height is ~0.1-0.2 kcal/mol. The C-Cl bond dissociation in ortho- and meta-Cl-Ph-OH(-) is accompanied by its deviation from the benzene ring plane that allows the system to avoid the pi and sigma terms crossing. Such mechanism is realized for symmetry-forbidden fragmentation of pi- radical anions when Hal(-) ion eliminates from the ring position bearing significant density of unpaired electron. As shown earlier [2,3], when the unpaired electron density is low, the reaction coordinate becomes more complicated and, beside the C-Hal bond stretching and out-of-plane deviation, includes pseudorotation (in-plane ring distortion) to transfer electron density to the breaking bond. However, for para-Cl-Ph-OH(-), where unpaired electron density in para-position is about zero, we have found another reaction mechanism. The change of the mechanism is due to high excitation energy to pi-state of 2B1-type. In this case the pi-sigma crossing avoidance comes true by the ring twisting that allows the 2A2-type pi-state to mix directly with the sigma state. The energy barrier for C-Cl bond dissociation is relatively high, ~3-4 kcal/mol, that explains the experimentally observed trends. The work was supported by the RFBR (Grant No 08-03-00495). 1. Khatymov R.V., Muftakhov M.V., Mazunov V.A. Structure and dynamics of molecular systems, 2004, XI (2), 317-320. 2. Beregovaya I.V., Shchegoleva L.N., Chem. Phys. Lett., 2001, 348, 501-506. 3. Beregovaya I.V., Vysotsky V.P., Shchegoleva L.N., J. Struct. Chem., 2006, 47, 220-227.
Low-lying electronic terms of hydrocarbons [С7]q (q=1,3…9) are calculated within CASSCF. The [С7]q is a fragment of zigzag carbon nanotube (7,0) containing q cyclacene chains; hydrogen atoms are added for filling free valences of carbon atoms. The [С7]q with odd q has D7h point symmetry. According to analytical estimations within Huckel model [1] it is established that these systems have specific set of one-electron states characterized by exponentional damping along cylinder axis. These MOs are localized near bases of cylinder and they are boundary in all systems [С7]q. By hypothesis spectrum of low-lying electronic terms is defined by four quasi-degenerate MOs e′3, e″3, which are included in active space CASSCF.
Basis set 6-31G* is used for estimations of terms positions. Low-lying electronic terms have stage structure and systems with various q have the same order of states. The distance between stages tends to asymptotic limit with increasing q. In this case states in stage become quasi-degenerate. Lowest stage consists of close set of states 1A′1, 3A″2, 5A′1 each of which is characterized by single occupation of localized MOs. Ground state of [С7]q is singlet; values of splitting are well described by Heisenberg hamiltonaian.
The calculation results can be interpreted as reducing interaction of states localized on opposite cylinder bases with increasing q. According to approximation CASSCF this interaction reduces exponentially in exact accordance with the similar characteristics of localized MOs. There is reason to believe that the value of splitting decreases less rapidly with increasing q if level of calculation is improved.
This work is supported by RFBR (grant № 07-03-01021-а).
It is well known that interactions of atoms in molecules lead to their polarization and, in a general case, to changing their partial atomic charges, which depends on coordination of atoms. In the present ab initio theoretical study it is found that similar effects are also observed for the amino acids in biomolecules. This was discovered by analyzing partial atomic and partial amino acid charges (introduced in the present study) obtained with ab initio wave functions. The partial amino acid charge has been defined in the present study as sum of the partial atomic charges of all amino acid atoms. The ab initio Hamiltonians and corresponding energy functionals correctly describe effects of amino acid polarization and their mutual coordination because the partial atomic charges are not fixed in them. On other hand, the classical force field Hamiltonians and corresponding energy functionals do not taken into account these effects because the force field Hamiltonians do not include corresponding terms and because they use the constant atomic charges. An importance of these effects for correct calculations of the total energies of biomolecules by force field methods has been investigated by comparing the relative total energies of different conformers of biomolecules calculated with the AMBER 99 and CHARMM 27 force fields as realized in TINKER program with those calculated by the Hartree-Fock and density functional theory method with B3LYP functional. The calculations have been performed for the 1VM2 and 1CKW biomolecules which are formed by 13 and 25 amino acids and include 215 and 413 atoms correspondingly. The different conformers of these molecules have been found by optimizing initial experimental x-ray geometries of these molecules by different minimization methods available in the TINKER program. The ab initio calculations have been performed with 6-31G and 6-31G** bases. A comparison of the obtained relative total energies shows huge deviations of the relative total energies calculated by the force field methods from the corresponding Hartree-Fock and density functional theory energies. A comparison of the errors for the 1VM2 and 1CKW molecules indicates that the error increases proportionally to the size of molecules. To reduce it a parameterization of atomic and amino acid charges in dependence on their coordination is proposed.
The geometric structures and forms of Potential Energy Surface (PES) of α,β-unsaturated and dicarbonyl molecules in the ground and a series of the lowest excited singlet and triplet electronic states of types n,π* were investigated with high-level quantum-chemical methods (CASSCF, CASPT2, and others with bases of cc-pVTZ quality). The acrolein CH2=CHCHO, its derivatives (CH2=CHCFO and all possible monomethylacroleins) and dicarbonyls: glyoxal (CHO)2 and its symmetrically (CXO)2 and asymmetrically CXO-CYO substituted halogen derivatives (X,Y = H, F, Cl) as well as methylglyoxal were investigated.
The vertical and adiabatic electronic transition energies, frequencies of molecular vibrations (including anharmonic approaches), geometries of conformers, and potential functions of internal rotation were obtained. The α,β-unsaturated carbonyl molecules were shown to exist in the ground electronic state as planar s-cis and s-trans conformers. The dicarbonyls exist as s-trans and s-cis (X,Y = H,H, X,Y=H,CH3, and X,Y = F,F) or s-gauche (X,Y = Cl,Cl, X,Y = F,Cl and X,Y = Br,Br). In the excited electronic states of n,π* type, the calculations predict these molecules to exist s-cis and s-trans conformers. However, the PESs in these states have very complex form which differs from that for aliphatic aldehydes. This complex form causes the anomalously strong coupling of internal rotation around the ordinary CC bond with non-planar vibrations of carbonyl fragments. In present work, these vibrations were regarded in anharmonic approach accounting for the vibrational coupling found.
In the presentation, the structural peculiarities of electronic and geometric structure of molecules under study in various excited states are analyzed. The "symmetry dilemma" arising in calculations of dicarbonyls is discussed. The obtained results are compared with experimental data obtained in our group and published in literature.
This work was financially supported by Russian Foundation for Basic Research (Grant No. 07-03-00090).
The structure of Potential Energy Surface (PES) and conformational dynamics of acetone molecule (CH3)2CO in the lowest excited singlet (S1) and triplet (T1) electronic states were investigated with ab initio quantum-chemical methods.
The calculations with different methods including CASSCF, CASPT2 (CCSD and CCSD(T) for T1 state) show that the electronic excitations to S1 and T1 states are accompanied by elongation of CO-bond, pyramidal distortion of carbonyl fragment and symmetric rotation of methyl tops relative to CCC frame. The harmonic vibrational frequencies and barriers to internal rotation and inversion were calculated. The CO-bond out-of-plane angle was calculated with CASPT2/cc-pVTZ to be 38°. and 820 cm-1 in the S1 state or 41° and 1150 cm-1 in the T1 state.
The one-, two-, and three-dimensional torsion-inversion PES sections were constructed to study the conformational dynamics in the S1 and T1 electronic states. The vibrational problems of respective dimensionality allowing to describe molecular motions with large-amplitude (internal rotation and inversion) were solved. Analysis of form of three-dimensional PES section indicated very strong coupling of internal rotation and inversion for acetone in the excited electronic states.
This work was financially supported by Russian Foundation for Basic Research (Grant No. 07-03-00090).
The ground state potential curves of He2 and Be2 molecules have been calculated by extrapolating the total energies calculated by the multi-reference configuration interaction method to an infinite basis set. The calculations were performed with the large cc-pV6Z and cc-pV7Z for Gaussian basis sets He2 and the cc-pVQZ and cc-pV5Z bases for Be2. The spaces of reference configurations include about 1.5*103 and 1.6*104 configurations for He2 and Be2 correspondingly. They describe the excitations of He electrons to 2s, 2p, 3s, and 3p orbitals and Be valence electrons to 2p, 3s, and 3p orbitals. The total molecular energies have been calculated with pseudo-natural orbital which were obtained in preliminary multi-reference CI calculations. The calculated total energies have been corrected for the basis set superposition errors by using Boys-Bernardi counterpoise method. The calculated equilibrium dissociation energy of 11.0031 K and the equilibrium internuclear distance of 5.607 a. u. of He2 molecule are in an excellent agreement with dissociation energy of 11.006±0.004 K and equilibrium distance of 5.608±0.012 a. u. obtained recently by symmetry adopted perturbation theory with a super molecular energy correction. The calculated non-relativistic dissociation energy of 822 cm-1 and the relativistically corrected energy of 818 cm-1 for Be2 molecule are in a good agreement with the experimental dissociation energy of 790±30 cm-1 and the energy of 829±64cm-1 obtained recently by a quantum Monte Carlo method.
The calculations of the vibration energy levels of Be2 molecule face a significant problem. In this connection the configuration structures of multi-reference type wave functions of this and other molecules have been investigated in details. This study has shown that the configuration structure of the molecular wave functions depends on molecular geometries and significantly changes in the regions where potential energy curves or potential energy surfaces are negative. This effect explains the fact that the vibration energy levels of Be2 molecule cannot be correctly calculated by multi-reference type methods with reference lists of the fixed lengths. On other hand the vibration energy levels of Be2 molecule calculated with a full CI wave function are in excellent agreement with the corresponding experimental values.
Как известно, взаимодействие серы с диоксидом кремния в композиционных материалах затруднено ввиду высокой энергии активации. Известен способ получения производных кремнезема, основанный на способности поверхностных гидроксильных групп реагировать с соответствующими хлорсодержащими веществами. При этом на поверхности кремнезема формируются активные центры с вакантными d- орбиталями. Введение кислоты Льюиса хлорида титана, на наш взгляд, могло бы понизить энергетический барьер и облегчить химическое взаимодействие компонентов. Известно, что соли титана способны образовывать аквакомплексы при взаимодействии с молекулами воды. Присоединение одной молекулы воды к тетрахлориду титана идет экзотермически и безактивационно. Мы предположили, что внедрение серы в реакционный узел модифицированного хлоридом титана диоксида кремния может происходить аналогичным образом. Для оценки наиболее выгодного механизма взаимодействия серы с поверхностью модифицированного диоксида кремния была проведена оценка структуры переходных состояний и барьеров с использованием метода DFT PBE в базисе L11 (программа Priroda). Как показали расчеты, присоединение серы к модифицированному диоксиду кремния приводит к безактивационному образованию компактного комплекса титана с координационным числом 5 или 6, что является следствием напряженности малых циклов и наличием лишней связи Ti-Si. Было найдено состояние с низкой энергией активации (11,03 кДж/моль), рассчитаны наиболее вероятные пути этого процесса. Исследованы процессы присоединения молекулы серы различной мультиплетности (синглетной и триплетной), а также реакции присоединения молекул, содержащих различное количество атомов серы, к фрагментам модифицированного диоксида кремния. Рассчитанный процесс объясняет активирующие действие группы Ti-Cl в кремнеземсодержащем материале безактивационным образованием комплексов 5 и 6 координированного титана с последующей перестройкой образовавшихся интермедиатов. Ввиду образования новых химических связей такие композиционные материалы должны обладать высокими механическими и эксплуатационными свойствами.
The new block Lagrange iterative methods for calculations of eigenvalues and corresponding eigenvectors of the generalized eigenvalue problem AX=λBX are presented. The correction vector, used for an extension of the Krylov subspace in the new block Lagrange iterative method, is obtained from the exact Newton-Raphson correction vector by using the diagonal approximation for (A-λB)-1 matrix. The exact correction vector is derived from a solution of the Newton-Raphson equation for the Lagrange functional L(X,λ)=XtAX-λ(XtBX-1) of the generalized eigenvalue problem AX=λBX. It is equivalent to that one used in the Jacobi-Davidson [1] and the Olsen [2] methods. Thus, it has been shown that the Jacobi-Davidson vector is a Newton-Raphson correction vector for the Lagrange functional and hence the Jacobi-Davidson method is a Newton-Raphson type method for the Lagrange functional of the generalized eigenvalue problem. The numerical algorithms of the new block Lagrange type iterative methods and the block generalizations of the Newton-Rayleigh type methods [3] have been constructed as block generalizations of the iterative methods for calculations of eigenvalues and corresponding eigenvectors of the generalized eigenvalue problem presented in [3]. The calculation a new correction vector for an extension of the Krylov subspace from a solution of the Newton-Raphson equation is the most time consuming step in these algorithms. For a simplification of its solution a skeleton approximation of the Hessian matrix has been introduced. In this approximation the Hessian matrix elements are treated as zeros when their absolute values are smaller compared to a predefined threshold. Hence, the numerical complexity of a solution of the Newton-Raphson equation with skeleton approximation can be varied from the complexity of the diagonal method up to the complexity of the exact one in dependence on the threshold of this approximation. The numerical algorithms for the new methods are presented and their performances are compared in several numerical tests including the calculations of the excitation spectrum of H2O molecule by the ADC method [4].
The structure of a series of benzoaza-18-crown-6-containing styryl dyes and their aquacomplexes with alkali and alkaline-earth cations (Li+, Mg2+, Na+, and Ca2+) is studied by DFT. The electronic absorption spectra are calculated using TD DFT. The electronic and geometrical structure of the excited states responsible for the long-wave (π—π) absorption bands both in the free dyes and in the complexes is studied by TD DFT.
It is found that aquacomplexes with small cations, such as Li+ and Mg2+, are capable of ground-state recoordination previously observed in phenylazacrown-containing dyes. The two conformers, with and without cation–nitrogen bond, exhibit different absorption spectra. Namely, the presence of the cation–nitrogen bond results in the noticeable blue shift of the absorption maximum, while the absorption spectra of the complexes without cation–nitrogen bond are almost the same as the spectra of the free dye.
The effect of the cation-induced fluorescence enhancement observed in these dyes is explained on the basis of the excited-state structure of the free dyes and their complexes. The structure of the free dyes tends to change from the "quinoid" form in the ground state to the "benzenoid" form in the excited state thus facilitating rotation of amino or aminophenyl group and causing near-degeneracy of the potential energy surfaces of the ground and excited states. This results in the nonradiative relaxation and fluorescence quenching. Complexation with cations reverses the dye structure to the "benzenoid" form in the ground state and to the "quinoid" form in the excited state thus preventing amino and aminophenyl groups from rotation, which results in the fluorescence enhancement. The internal rotations in the chromophore moiety of the dyes are studied in the ground and excited states. It is found that, in the excited state of the free dye, rotations of the amino group, aminophenyl moiety, and heterocycle are barrierless and, therefore, are the most probable relaxation channels, unlike trans-cis-isomerization, which has barriers both in the ground and excited states. On the contrary, the complexes have local minima in the excited state, and their structures only slightly differ from those in the ground state. An efficient fluorescence is possible from these local minima.
As known, usually the rate of paramagnetic relaxation for radical ions of highly symmetric molecules is significantly higher that for the radicals of lower symmetry. However, recently obtained experimental data [1,2] revealed the anomalously fast relaxation for radical cations of some low-symmetric cycloalkanes. In this work we have performed comparative ab initio study of adiabatic potential energy surfaces (PES) for radical cations of some alkylcyclohexanes and isomeric decalins whose relaxation times in solutions [1,2] differed by two orders of magnitude. To obtain a qualitative view of PES structure, we considered a possibility of intersection of the radical electronic states of different symmetry at ROHF and CIS/ROHF calculation levels. The proper PES studies were performed with the UB3LYP method. Calculated for stationary PES structures hfc constants were compared with the ESR data available. According to calculation results single occupied MO (SOMO) of stationary structures of R-C6H11(+) cations are perturbed components of degenerate eg MO of c-C6H12(+). The terms of the two respective ectronic states were found to intersect. So, the PES of these cations retain the shape of pseudorotation surfaces peculiar to JT active c-C6H12(+). The pseudorotation barrier height defined as energy difference between the highest and lowest energy structures depends noticeably on the substituent: 0.5, 2.9, 2.2, 5.0, and 9.9 kcal/mol for R=H, Me, Eth, iso-Pr, and tert-Bu, respectively. These values were found to correlate with the experimentally measured times of spin-lattice relaxation [3]. Unlike the case of R-C6H11(+), SOMO of radical cation of isomeric decalins are delocalized through the two cyclohexane rings. Nevertheless, in this case the crossing of the states of different symmetry was found as well. The crossing avoidance results in pseudorotation. The height of the barrier for pseudorotation is less than 2 kcal/mole for trans- and about 9 kcal/mol for cis-isomer [4]. Note again that the spin relaxation time for trans-isomer is more than one order of magnitude higher than for cis-isomer [1]. The calculated hfc constants are in fair agreement with the experimental ESR data. The difference in spectral behavior of the isomeric decalin radical cations is completely determined by the distinctions revealed in their PES structures. The work was supported by the RFBR (Grants No 08-03-00495 and 07-03-00576).
The electron structure of several classes of selenoorganic compounds was investigated in the gas phase and in vast variety of solvents by means of quantum-chemical methods (B3LYP, HF, MP2) using different basis sets.
The tendencies in the changes of the electron population of selenium atoms (including lone pairs and bonds with neighboring atoms), dipole moments, NMR chemical shifts, characteristic frequencies in the vibrational spectra, polarizabilities, HOMO-LUMO energies etc. in dependence on the intrinsic structural factors and solvents have been analyzed. The solvent effects were considered within the framework of continuum, discrete and semi-continuum approaches.
Particular attention was devoted to the topological analysis of the electron structure within R. Bader’s theory "Atoms in Molecules". The analysis of the correlations between the different topological indexes, the integral characteristics of atoms, the energetic and geometric parameters of the structures containing the selenium atom as an active complexation center revealed the generality and the specificity of this type of compounds in comparison with the classical N, O, S – containing molecules. It is possible to make some conclusions about the nature of the donor-acceptor interactions and hydrogen bonding with the participation of the selenium atom.
We have also discussed questions concerning the cooperativity of the specific solvation effects of the complexes of different composition and type, the effectiveness of the used levels of theory, basis sets and different solvation models etc. for the correct characteristics of the intermolecular interactions involving the selenoorganic compounds.
Over the last decades researchers have turned towards octupolar chromophores, which provide better efficiency/transparency trade-off relationship for various nonlinear optical (NLO) applications and allow one to avoid the problem of unwanted dipole-dipole interactions, which prevent the stabilization of macroscopic noncentrosymmetric order [1]. Octupole molecules are assumed to exhibit high hyperpolarizability and may participate in self-association with the formation of isotropic and noncentrosymmetric 2D and 3D structures. This property is essential for the design of materials on the basis of dendrimers and hyperbranched polymer systems containing dendritic chromophore groups [2].
Here we have studied the NLO response of 1,3,5-tricyano-2,4,6-trinitrobenzene (TATB) as a prototype octupole molecule. Particular attention is paid to the dielectric medium effect on the values of (hyper)polarizabilties, their comparison with those for p-nitroaniline (PNA) molecule – the prototype dipole chromophore – and azobenzene chromophore DR1 is carried out. The medium effect is modeled by organic solvents with different permittivity: chloroform (ε=4.8) and acetone (ε=20.7).
The geometrical parameters of the systems under study were optimized in gas phase and in solvents (both chloroform and acetone) in 6-31G* basis set. The electric properties were calculated using PC GAMESS version of the GAMESS (US) QC program package [3] by Time Dependent Hartree-Fock technique in aug-cc-pVDZ Dunning basis set, the polarization functions on Hydrogen being omitted. The solvent effect was accounted by the Polarizable Continuum Model.
The large value of the modulus of the first hyperpolarizability tensor of TATB results from the availability of large off-diagonal components and it is shown to be 1.8 times greater than that of PNA, thus confirming quantitatively that octupolar chromophores are the promising ones for the design of new NLO materials. The solvent effect on the (hyper)polarizability tensor components of TATB results in their pronounced increase, in particular the modulus of the first hyperpolarizability tensor in chloroform is nearly two times as large and in acetone three times as large as that in gas, the corresponding values being equal to 15.4*10-30 esu, 32.9*10-30 esu, 41.4*10-30 esu.
The work is performed under financial support of Russian Foundation for Basic Research (project № 09-03-00696-а).
Ionic liquids (ILs), typically formed by organic cations and inorganic anions, are currently attracting considerable attention as alternatives to organic solvents. Their solvent properties are tuneable through different combinations of cations and anions, however, to a large extent the process of design remains a random event as the features that control the physical properties of ILs remain poorly understood. As shown earlier [1], ILs with weakly-coordinating anions, like BF4- or PF6-, can be regarded, to a first approximation, as consisting of ion pairs. If the ion pair performs small vibrations in neighbourhood of potential energy surface (PES) minimum, its potential energy may be approximated by the equation E(x) = a*x*x/2 - b*x*x*x/3, where a is the force constant of the oscillator and b is the coefficient of anharmonicity. It can be shown that melting point (Tm.p.) of an assemblage of the anharmonic oscillators is proportional to (a*a*a)/(b*b), while the heat capacity (Cp) should be roughly proportional to (b*b)/(a*a*a). To evaluate a and b the PES of the ion pair was scanned in the vicinity of its minimum. The resulting points were interpolated by a polynomial: E = A + B*R + C*R*R + D*R*R*R. C was taken as a/2, and D was taken as b/3. We demonstrate that computed in this way (a*a*a)/(b*b) values follow the experimentally determined trend for Tm.p. of series of 1-alkyl-3-methylimidazolium- and tetraalkylphosphonium-based ILs, and the same is true for (b*b)/(a*a*a)parameters and experimental Cp values. So, our simple approach allows to rationalize and even predict melting points and heat capacities of yet unsynthesized ILs by means of quantum-chemical computations. The latter were based in our case on DFT B3LYP/6-31G* level of theory. The financial support of the Russian Foundation for Basic Research (Grant No 07-03-00892-a) and President of the Russian Federation for young scientists (Grant No 5124.2008.03 for E.E.Z.) is gratefully acknowledged. 1. S.A.Katsyuba, E.E.Zvereva, A.Vidis, P.J.Dyson, J.Phys.Chem. A, 2007, 111 (2), 352 -370.
The dehydrogenation reaction of ethane in platinum containing zeolites was studied using density functional theory (DFT). The catalytic cracking of hydrocarbons is found to be of the great scientific and practical interest. The experimental results [1] suggest that the spectra of adsorbed ethane and propane depend on both the type of the exchanged cation and the nature of the zeolite in which this cation occurs. It is known that the Pt-zeolite catalyst is active for hydrocracking of petroleum [2]. The cation-exchanged sites of simpler acid H-ZSM-5 systems are represented by a variety of model clusters 3T and 5T. For H-ZCM-5 the hydrocarbons are not allowed to pass through the pores in a parallel manner as the chain length increases [3]. The quantum chemical calculations [4] indicate that under-coordination of the Pt atoms in the clusters is responsible for the surprisingly high reactivity compared with extended surfaces. The energetic and the structural properties of ZSM-5 containing Pt2 and three or five tetrahedral moieties (3T and 5T cluster) were also modeled for comparison. The possible reaction paths of ethane dehydrogenation were studied using B3LYP level of theory with 6-311G (d,p) and LanL2DZ basis sets. All the calculations were performed by the Gaussian 03 software package. The nature of the stationary points was then checked by counting no imaginary frequency for stable species and a single for transition states. The activation energy it was calculated and compared with available experimental and computational data. It was show that Pt2/H-ZSM5 zeolite clusters as active catalysts for the dehydrogenation of ethane. All calculations were carried out in Joint Supercomputer Center (JSCC) and Supercomputer Center of the Kazan Scientific center of Russian Academy of Science. This work was supported by Russian Foundation for Basic Research (grant No 09-03-97013-р_поволжье_а) 1. I.R. Subbotina, V.B. Kazanskii Kinetics and Catalysis, 2008, Vol. 49, No. 1, 138–148. 2. K. Murata, I. Takahara, M. Inaba React. Kinet. Catal. Lett., 2008, Vol. 93, No. 1, 59-66. 3. B.-J. Ding, S.-P. Huang, W.-C. Wang Chin. J.Chem., 2008, V.26, No 7, 1173-1180. 4. S. Vajda, M. J. Pellin, J. P. Greeley et al. Nature Materials, 2009, V. 8, 213-216.
Reactions of hydrogenation and dehydrogenation on the small iridium clusters were studied employing modern DFT methods. The hydrogenation of organic compounds is a reaction of great industrial importance. Metal nanoclusters are known to be one of the most important advanced materials. The most remarkable features of metal nanoclusters are their specific chemical and physical properties. Among the chemical properties of metal nanoclusters, catalysis is of great interest. Hydrogenation reactions of small alkenes are good probes of the catalytic properties of metals. This is especially the case when the structures containing the metals are so small as to limit the structure and bonding of the probe molecule. In accordance with experimental studies, ethene hydrogenation and propene hydrogenation display similar kinetics when catalyzed by supported metal clusters: apparent activation energies range from 24 to 40 kJ/mol. All calculations were carried out using Gaussian 03 suit of programs. PBE, OLYP and B3LYP levels of theory with various basis sets were employed to investigate the properties of the of iridium clusters. Analytical vibration frequencies were computed for all minima and transition states. Barrier heights are calculated including the zero-point energy correction, and activation energies were calculated at 298 K including the corresponding thermal correction. Exploration of hydrogen adsorption on the iridium clusters results that activation barrier for this reaction is equal zero. It was found that reaction of ethane dehydrogenation on the Ir clusters starts with formation of ethane-cluster complex. The Ir-C bond distance in ethane-cluster complex is 2.6 Å. The activation energy of ethyl-hydrido-tetra-iridium cluster formation is 4.6 kcal/mole. At B3LYP/LanL2DZ ethyl-hydrido-tetra-iridium cluster is calculated to lie 7.0 kcal/mole lower than ethane-cluster complex. Calculated data was compared with available experimental data. Ethyl-hydrido-tetra-iridium cluster has Ir-H and Ir-C bond distances of 1.552 and 2.069 Å respectively. All calculations were carried out in Joint Supercomputer Center (JSCC) and Supercomputer Center of the Kazan Scientific center of Russian Academy of Science. This work was supported by Russian Foundation for Basic Research (grant No 09-03-97013-р_поволжье_а)
Decomposition of C-nitrocompounds has been the subject of numerous experimental and theoretical explorations since long ago. Modern quantum chemical methods are widely-used for exploration of molecular structure and reactivity of nitrocompounds. Employing of ab initio and DFT (density functional theory) methods for theoretical study of elementary stages of chemical reactions, especially monomolecular decomposition reactions, are very perspective. Quantum chemistry composite methods are ab initio post-Hartree-Fock methods in computational chemistry that aim for high accuracy by combining the results of several calculations. They combine methods with a high level of theory and a small basis set with methods that employ lower levels of theory with larger basis sets. They aim for chemical accuracy which is usually defined as within 1 kcal/mol of the experimental value. Three main channels of decomposition of C-nitrocompounds: hemolytic C-N bond rapture, elimination of HONO and nitro-nitrite rearrangement, were studied employing ab initio MP4/6-31G(d), QCISD/6-31G(d), QCISD(t)/6-31G(d) methods and G3, G3B3, CBS-QB3 composite quantum chemistry methods. All calculations were carried out using Gaussian 98 and Gaussian 03 suits of programs. The cyclization reaction, proceeding through four-member cycle formation was studied for nitroamines and nitroarenes. New competitive channels of decomposition of C-nitrocompounds: 1) two-step nitro-nitrite rearrangement proceeding through formation and further decomposition of the singlet biradical complex; 2) reaction of formation of bicyclic nitrobenzenes from nitrobenzene and o-dinitrobenzene and further decomposition through singlet biradical mechanism with breaking of the four-member cycle. Formation of bicyclic intermediates seems to be the most favorable channel of gas-phase decomposition of o-dinitrobenzene. The calculated Arrhenius parameters for this reaction were compared with available experimental data. Results obtained in present theoretical study concerning main channels of decomposition of C-nitrocompounds are in good agreement with the results of the previous theoretical studies that were held employing ab initio and DFT levels of theory.
Platinum is one the most common catalyst for alkane dehydrogenations. Gas-phase reactions of free platinum clusters show interesting dependencies of their reactivity on size and charge of the cluster [1]. From experiment it is known that predominant process is the methane dehydrogenation leading to methylene-platinum cluster and H2. Mechanism of methane activation by neutral Pt3,4 clusters and their ions was studied employing scalar relativistic DFT PBE level of theory. All calculations were carried out using Priroda 6 quantum chemistry program [2]. Methane activation on the Pt3,4 clusters found to proceed in five stages: - formation of the complex of methane and the cluster; - an oxidative addition of the methane's first C-H bond; - migration of the hydrogen atom on the cluster; - rapture of the second C-H bond with methylene-platinum formation; - hydrogen atoms migration to the same platinum atom. The smallest (0.05 kcal/mol) activation energy of an oxidative addition of the methane's first C-H bond is for Pt3 anion, the largest – for Pt4 cation (8.0 kcal/mol). The fourth stage is the rate-limiting step for all the Pt4 clusters, with the highest activation barrier for the cationic cluster (17.1 kcal/mol, that is higher than the energy level of the initial reagents). For the neutral and anionic Pt4 clusters the barrier is slightly lower than the level of initial reagents (22.3 and 23.7 kcal/mol, correspondingly). Hydrogen atoms migration to the same platinum atom in order to make reductive elimination of H2 possible is the limiting stage for anionic and neutral clusters of Pt3 (16.8 and 14.9 kcal/mol). The results obtained allow for explaining of the experimentally observed higher activity of the Pt3 clusters and the inactivity of the Pt4+ cluster. Our calculations were realized using the Joint Supercomputer Center (JSCC). This work was supported by Russian Foundation for Basic Research (grant No 09-03-97013-р_поволжье_а) Reference [1] Adlhart C, Uggerud E., Chem. Comm., 24 (2006) 2581-2582 [2] D.N. Laikov, Chem. Phys. Lett., 461 (2005) 116-120; D.N. Laikov, Chem. Phys. Lett., 281 (1997) 151-156
Aliphatic nitrates and nitrites can decay with explosion in low temperatures. Therefore, the examination of these compounds is important in the practical way. However, alkyl nitrates and nitrites are investigated insufficiently. At present, there are few data about the geometrical and electronic structures of aliphatic nitrates and nitrites by using experimental researches and quantum-chemical methods. A thermal distraction mechanism of aliphatic nitrates and nitrites is not clear. But it is known, the radical mechanism is responsible for the thermal decomposition. Though the radical mechanism becomes unfavorable on high pressure conditions, and the reactions proceeding by the alternative molecular mechanism take place. The consideration of conformational transitions in the non-radical reactions of thermal decomposition for aliphatic nitrates and nitrites. Using ab initio and density functional theory (DFT) methods the influence of conformational transitions in pathway of the non-radical thermal destruction of alkyl nitrates and nitrites have been investigated. General alternative mechanisms of the gas phase monomoleculare thermal decomposition are the process of the nitrous and nitric acid elimination (aliphatic nitrates) and nitrosyl hydride and nitrous acid elimination (aliphatic nitrites). For confirmation the virtual numbers of conformers of elementary alkyl nitrates and nitrites the potentional energy surfaces were done by using B3LYP/6-31G(d) method. By the example of nitrous acid elimination for ethyl nitrate the trans (ΔH°=-153,5 kJ/mole)–gaushe (ΔH°=-152,7 kJ/mole) conformational transitions was observed (B3LYP/6-31G(d)). The basic tendencies in the changes of the geometrical and electronic structures, formation enthalpies and dissociation energies [1] have been analyzed in basic homologous series of alkyl nitrates and nitrites. Calculations were performed using the Gaussian 98 package. In all cases the transition states was provided by the occurrence of a single negative value in a Hessian matrix, while its correlation with the investigation process was provided by descending along the reaction coordinate toward the starting compounds and the reaction products. 1. Mazilov E.; Ogurtsova E.; Shamov A.; Khrapkovskii G. The 39th International Annual Conference of ICT Karlsruhe. 2008, 53,1-10.
Методом функционала плотности изучены механизмы реакций би- и тримолекулярного взаимодействия фосфорорганических соединений (ФОС) - салицилфосфитов с непредельными соединениями (хлораль), которые являются растворителями в этих реакциях. Установлено, что в случае бимолекулярного взаимодействия ФОС с одной молекулой растворителя реакция может протекать по нескольким направлениям с образованием различных продуктов (фосфепинов, циклических и ациклических винилфосфитов). В случае тримолекулярного взаимодействия ФОС с двумя молекулами растворителя продуктами реакции могут быть также пятичленные фосфоланы.
Теоретическое изучение взаимодействия ФОС с одной молекулой растворителя показало, что энергетически более благоприятным каналом является образование фосфепина [1]. Реакция по типу Перкова, с образованием соединений с двойной связью С=С (винилфосфитов), должна протекать при более высоких температурах, что подтверждается экспериментальными данными.
Образование пятичленных фосфоланов протекает в более жестких условиях [2]. Для получения фосфоланов необходимо рассмотреть взаимодействие фосфита с двумя молекулами растворителя [3]. Нами изучены механизмы реакций взаимодействия трис(2,2,2-трифторэтил)фосфита и салицилфосфита с двумя молекулами хлораля, которые могут привести к образованию пятичленных продуктов. Проведен сравнительный анализ реакционной способности этих реакций.
Проведены также расчеты констант ядерного магнитного экранирования, которые сравнены с экспериментальными значениями химических сдвигов.
Для подобного рода бимолекулярных реакций с участием модельных ФОС методами прямой молекулярной динамики установлены временные диапазоны реакционных процессов, которые показали, что такого рода реакции протекают в диапазоне 200 фс.
Работа выполнена при финансировании гранта Президента РФ для государственной поддержки ведущих научных школ НШ-4531.2008.2.
[1] Аминова Р.М., Савостина Л.И.// Хим. физика. 2008. Т.27, №9. С.59.
[2] Коновалова И.В., Бурнаева Л.А., Миронов В.Ф., Логинова И.В., Пудовик А.Н. // Изв. АН СССР Сер. хим. 1990. №12. С. 2876.
[3] Курдюков А.И., Офицеров Е.Н., Урядов В.Г., Миронов В.Ф. // Бутлеровские сообщения. 2005. Т.7. №3. С.8.
В настоящей работе выполнен прецизионный релятивистский неэмпирический расчёт потенциальных кривых основного и нескольких возбуждённых электронных состояний молекулярного катиона PtH+, определены равновесные расстояния, а также рассчитана величина эффективного электрического поля, действующего на электрон. Значение этого поля необходимо для интерпретации результатов планируемого эксперимента по измерению электрического дипольного момента электрона (eЭДМ). Существование eЭДМ и различная его величина предсказывается многими современными фундаментальными физическими теориями, поэтому для их проверки важно его экспериментальное обнаружение, основанное на измерении энергии взаимодействия eЭДМ с внутренним эффективным электрическим полем полярной молекулы, содержащей тяжёлый атом. В таких молекулах могут быть достигнуты значения полей на несколько порядков выше тех, что достижимы в лаборатории. Однако для нахождения самой величины eЭДМ необходимо знать и величину внутреннего поля, которую можно вычислить только методами квантовой химии.
Молекулярный катион PtH+ для подобных исследований был предложен в работе [1]; в этой же работе была сделана оценка значения эффективного электрического поля. Однако, поскольку значение этого поля не может быть измерено экспериментально, мы в настоящей работе выполнили прецизионный расчёт этой характеристики. Для этого была применена методика, аналогичная предложенной нами ранее [2], и состоящая из нескольких этапов. На первом выполняется корреляционный релятивистский расчёт валентной электронной структуры с использованием метода обобщённого релятивистского псевдопотенциала, позволяющего наиболее экономично использовать вычислительные ресурсы, обеспечивая при этом самую высокую точность расчета. Далее восстанавливается остовная структура и вычисляется эффективное электрическое поле, действующее на электрон. Рассчитанное значение этого поля составляет 28 GV/cm, что существенно отличается от оценки в 73 GV/cm, сделанной в работе [1].
Работа поддержана грантом РФФИ 09-03-01034-а. С.Л.В. благодарит за поддержку Правительство Санкт-Петербурга, П.А.Н. благодарит Минобрнауки РФ (Программа Развитие научного потенциала высшей школы, грант № 2.1.1/1136)
[1] Meyer E.R., Bohn J.L., Deskevich M.P. Phys. Rev. A. 73. 062108 (2006)
[2] Titov A.V., Mosyagin N.S., Petrov A.N., Isaev T.A., DeMille D.P. Progr. Theor. Chem. Phys. B~15 253-283 (2006)
In the present paper the structure of the general many-electron wave function F0(r1s1,…,rNsN) with zero z-projection of the total spin (M=0) is examined. This function must describe two independent experiments: the elastic magnetic neutron scattering and the temperature dependence of spin susceptibility of antiferromagnetic (AF) crystals. Let F0 belong to a degenerate manifold containing functions YS0(r1s1,…,rNsN) with both even and odd spins S. Then it is shown [1] that F0 can be spin polarized:
In the present work we show that the elastic magnetic neutron scattering off the target in the state F0 results in the well-known AF Bragg diffraction picture. At the same time, the temperature dependence of the magnetic susceptibility manifests the characteristic AF shape.
Our present results are quite general and can be applied to any periodic quantum many-electron system. As a case study, we investigate elastic magnetic neutron scattering and calculate magnetic susceptibilities for finite chains of one-electron atoms.
This work was supported by RFBR (grant No 09-03-00733).
С помощью программного пакета WIEN2k [1] произведено первопринципное компьютерное моделирование энергии растворения атомарного водорода в ОЦК-железе с суперячейкой из 54 атомов железа. В результате работы были определены основные оптимальные параметры моделирования, необходимые для воспроизведения экспериментальных данных с достаточной точностью: величина Kmax, отвечающая за энергию обрезания, и количество k-точек. Было выяснено, что при использовании экспериментального параметра решетки (5,4168 а.е.) наименьшее значение Kmax, при котором достигается сходимость энергии растворения водорода к экспериментальному значению, составило 5,0 a.e.-1. Наименьшее количество k-точек, необходимое для согласия с экспериментом, оказалось равным 27, однако для большей точности в расчетах использовалось 64 k-точки. Критерием сходимости во всех расчетах задавалась полная энергия и заряд с точностью более 0,0001 Рб и 0,0001 e соответственно.
На основе проведенных оценок было выяснено, что наиболее стабильной позицией атома водорода является тетраэдрическая позиция, что совпадает с экспериментальными данными и рядом недавних работ, например [2]. Энергия растворения водорода в тетраэдрической поре ОЦК-железа составила 0,30 эВ. Октаэдрическая пора оказалась на 0,46 эВ менее стабильной, чем тетраэдрическая. Также была проведена серия расчетов с релаксацией кристаллической решетки. Было определено, что релаксация кристаллической решетки понижает энергию растворения водорода в тетраэдрической позиции до 0,19 эВ, первая координационная сфера водорода испытывает небольшое смещение от атома водорода. Релаксация решетки с водородом в октаэдрической позиции не проводилась.
Данная работа является началом исследования влияния малых примесей переходных металлов, таких как Pd, Ti, V, Cr, Mn, на энергию растворения водорода в железе. Это позволит определить, какие примеси способствуют захвату водорода при изготовлении стали и транспортировке водородного топлива.
Работа поддержана грантом минобрнауки РФ 2.1.1./1776.
[1] K. Schwarz, P. Blaha, G.K.H. Madsen. Electronic structure calculations of solids using the WIEN2k package for material science // Computer Physics Communications, V. 147, P. 71 (2002).
[2] D.E. Jiang, E.A. Carter. Diffusion of interstitial hydrogen into and through bcc Fe from first principles // Phys. Rev. В, V. 70, P. 064102 (2004).
The investigation of the efficiency of conventional SCF algorithm with and without compression of two-electron integrals and their indices has been carried out by compare the CPU user, CPU system, and CPU waiting time of one SCF iteration as well the CPU user and CPU system time of integral calculations in ab initio calculations with both algorithms. The calculations were performed for the fullerene and alanine decapeptide molecules with STO-3G and 3-21SP bases. An analysis of the obtained data shows that the data compression significantly reduces the time of the Fock matrix calculation. It was found also that the reduction of the time scales non-linear with respect to the size of two-electron integral file. Further detail investigation of this effect displays that there are two regimes in data transfer between a hard drive and the main memory of a computer with two quite different data transfer rates. The difference in data transfer for short and long files occurs due to arising conflict in the hard drive cache memory, which reduces the data transfer rate to the theoretical data transfer rate of the computer system bus for long files. Thus, total improvement in Fock matrix calculation reaches not only due to a reduction of the integral file size, but mainly because data compression reduces or even can eliminate the cache conflict in the hard drive cache memory during data transfer from the hard drive to the main computer memory. Thus, the conventional SCF algorithm with the data compression becomes very efficient and permits to carry out large-scale Hartree-Fock calculations. To demonstrate improved performance of the conventional SCF algorithm with data compression a set of large scale Hartree-Fock calculations have performed carried out for some molecules. The largest calculations have been carried out for RNA 433D structure from the PDB data bank with 6080 basis functions formed from 6-31G basis on a workstation with 1 GHz Alpha processor. The two regimes of data transfer observed in the present study gives clear explanation of the mysteriously result reported recently about super-linear scaling with respect to number of nodes in semi-direct parallel SCF algorithm [1].
During the last decade, the possibility to store H2 in the carbon nanostructures has become a subject for numerous studies. An important and extensively explored topic to be mentioned first is the pure carbon nanotubes and fullerenes whose great surface area allows us to believe in their unique sorption properties [1]. Another topic deals with complexes of these objects with light transition atoms, such as Sc or Ti, which can cover the surfaces [2].
In the first case we talk about physical sorption of H2 on the carbon surface. Energy of such interactions is very low, and that does not allow us to use pure C-based materials in the way of H2 storing [3]. In the second case we talk about chemical sorption of H2 on the transition metal layer. It has been shown that up to 4-5 molecules can be bonded by the single atom of Sc or Ti, and energy of this interaction is enough to keep them efficiently [2]. Problem arises when single atoms on the carbon surface start to interact with each other, because energy of this interaction is much higher then with H2. Therefore a real space for the H2 molecules around the metal atoms decreases. It does not allow us to reach required weight capacity of H2 (6.5%) [4]. Early [4] the way to prevent metal associating on the carbon surface has been suggested, which consisted in use the carbon nanomaterials containing of 7-fold (heptagon) and 7-fold (pentagon) rings. Probably, metal atoms interact with these structural parts stronger than with 6-fold (hexagon) rings, that prevents their motion along surface. We've tried to check this idea. Three cluster models of curved carbon sheet with one adsorbed Sc atom were examined by DFT with PBE exchange-correlation potential and plane-wave basis set in the VASP software. One of the clusters consisted of some hexagons and one heptagon, another one also consisted of some hexagons and one pentagon, and the third one consisted of hexagons only. Calculations carried out without periodic boundary conditions. It has been shown that potential barriers of Sc diffusion from heptagon to hexagon and in the reverse direction on the one side of the sheet are equal 0.51 and 0.05 eV, correspondingly, and on the other side of the sheet are equal 0.88 and 0.27 eV. The potential barriers of Sc motion from pentagon to hexagon and back are equal 0.42 and 0.06 eV, correspondingly, and from one hexagon to another one is 0.03 eV in both directions. Equilibrium constants of these processes are equal to 1.8E-8, 2.3E-9, 2.4E-5, and 1. All of the presented data confirm the mentioned idea.Small (from hundreds to thousands atoms) clusters of metal are objects, interesting both in theoretical
and experimental way. Several approaches to description of their properties have emerged since the beginning of intensive
research in 1970's [1]. While they were succesful at explanation of many observed phenomena, some questions
still need further investigation. One such question, important within the context of electrochemistry
and catalysis, is prediction of electronic properties of the clusters with atomic resolution.
Current models mainly fall under the following categories. The first approach consists in usage of ab initio QC methods,
which have proved themselves successful at modeling molecules. Unfortunately, their computational complexity grows at least as the fourth
power of quantity of atoms, making them extremely inefficient at modeling of the clusters of desired sizes. The second way is to use
semiempirical many-body potentials [2], which effectively approximate the energy of electrons within the conductance
band without solving the problem at quantum level. These methods give rather accurate predictions of cluster geometry, but
the information about electronic properties is completely lost. Yet another way to think about small clusters of metal is
so-called shell theory [1]. It correctly describes deformations and abundances of clusters of various sizes, but cannot provide
atomic resolution.
In our work, we use several modifications of the Hückel method to study the clusters. While this method does not take into
account some important effects such as electron correlation and repulsion, it gives satisfactory predictions on the qualitative level
and is several orders of magnitude faster than ab initio methods. Based on tight-binding scheme, it allows to observe several nontrivial
phenomena, which manifest themselves only when electronic structure is examined with atomic resolution.
Distribution of partial atomic charges in clusters with different lattice types is studied. It turns out, that in several
cases small changes of model parameters can lead to drastic difference in observed properties.
Energetically-optimal distribution of components in heterogenous clusters is also investigated. As in some previous
works (e.g. [3]) we observe partial segregation of components with different electronegativity. An interesting result
is that in the case of s.c. lattice the components demonstrate a tendency of arranging themselves in chequer-wise order. When
the quantities of the components in the cluster become same, the NaCl-like structure expands and occupies the whole
cluster. However, in the case of f.c.c. lattice more complex patterns emerge.
Modern
methods of quantum chemistry have achieved significant successes.
Nevertheless, modeling of certain classes of compounds remains
problematic. The main complications are both high computational
complexity of these methods and the lack of a unique way to determine
the ground state with correct asymptotic properties for complex
systems. One of the possible solutions is development of the hybrid
molecular modeling methods.
Our
approach to hybrid molecular modeling is based on the ideas of the
group function approximation, first suggested by McWeeny [1]
and further elaborated in [2].
This approximation lays a solid basis for simultaneous usage of most
appropriate methods for computation of properties of each part of a
complex system and consistent interpretation of the properties of the
system independently of the methods used.
The
CARTESIUS toolkit implements the above mentioned scheme in both
flexible and computationally efficient way. This is achieved by means
of combining cutting-edge C++ techniques for computationally
intensive parts of the code and the full power of Python for the
control interface.
As
a result we have a carefully designed software system, which
possesses both the power of the quantum chemistry codes developed
previously with use of the group function approximation (BF [3],
EHCF [4],
BFSCF[5] etc.) and high potential for further enhancements.
This
work is partially supported by the RFBR through the grant No 07-03-01128.
Literature:
It is well known that vibrational spectra of organic molecules changes upon formation of complexes with transition metals, which is widely used in structural analysis of coordination compounds. The dependence of IR and Raman spectra of transition metal complexes on mode of metal-to-ligand binding, spin and oxidation state of the metal is much less studied. To reveal these spectroscopic effects and separate the spectral changes caused by variation of spin and oxidation state of metal and geometry of the complexes, we applied various functionals of density functional theory (B3LYP, BPW91, OPBE) in combination with several basis sets (6-31+G*, 6-311+G*, cc-pVTZ, LanL2DZ, LACVP). It is shown that B3LYP in combination with 6-31+G* basis set for ligands and LanL2DZ and LACVP ECP basis sets on metal atoms represent a computationally inexpensive approach, which allows to achieve accuracy sufficient for the abovementioned purposes. Possible stable structures of Ni, Mn, Re and Fe complexes with bipyridine and with 1,2-diphosphacyclopentadienide anion with different spin- and oxidation states of metals and with different types of coordination (π, σ) were found by optimization, and the spectra computed for every form were compared with the experimental IR and Raman spectra of the compounds. It is demonstrated that changes in spin- and oxidation states of metal influence both geometry and vibrational spectra of the complexes. Spectral changes are observed not only in low frequency range, corresponding to metal-ligand vibrations, but also in the mid-IR range, where ligand vibrations are active. In particular, dependence of some ligand vibrations on π- or σ-type of their coordination were found for Mn and Re complexes with 1,2-diphosphacyclopentadienide anion, which may be used in analytical applications. Detailed computational analysis show that spectroscopic effects of variation of spin state of metal may be separated from effects caused by changes of geometry of the complexes, which allows using vibrational spectroscopy for diagnostics of metal spin state in coordination compounds.
Previously we developed a series of semiempirical methods based on the NDDO Hamiltonian and the trial wave function in the form of antisymmetrized product of strictly local electron groups (SLG) [1]. These methods are extremely fast, especially when implemented with the atom-atom multipole interaction scheme for long-range Coulomb interactions [2]. The methods rely upon interacting local fragments of the electronic structure. It makes possible to produce a mechanistic approach after a series of approximations [3,4]. Here we deduce a generic molecular-mechanics scheme starting from the local quantum mechanical description of molecular electronic structure. The common molecular mechanics employ ad hoc potential functions with adjusted parameters. The generic molecular mechanics does not require any additional parameterization.
The electronic structure parameters of the SLG method can be divided into two groups: i) density matrix elements for local electron groups (especially, geminals describing two-center two-electron groups); ii) elements of six-parametric SO(4) groups describing hybridization of atoms. The density matrix elements are well transferable [5]. Among the six elements describing the hybridization three describe the form of the hybridization tetrahedron, while the remaining three correspond to its rotation as a whole. The first three parameters are fairly well transferable thus defining the type of the atom in the molecular mechanical sense, while the rotation of the hybridization tetrahedron strongly depends on the environment.
We constructed a series of approximations to the transferable electronic structure parameters. One set of approximations is based on the fixation of the parameters, while the other employs simple corrections to them depending on the environment. The results show that the produced mechanistic scheme well describes the underlying quantum chemical method.
[1] A.M. Tokmachev, A.L. Tchougréeff, J. Phys. Chem. A, 2003, 107, 358-365.
[2] A.M. Tokmachev, A.L. Tchougréeff, J. Phys. Chem. A, 2005, 109, 7613-7620.
[3] A.L. Tchougréeff, A.M. Tokmachev, Int. J. Quantum Chem., 2004, 96, 175-184.
[4] A.M. Tokmachev, A.L. Tchougréeff, J. Comp. Chem., 2005, 26, 491-505.
[5] A.L. Tchougréeff, A.M. Tokmachev, I. Mayer, Int. J. Quantum Chem., 2007, 107, 2539-2555.
It is needless to say anything about the importance of water in everyday life, let alone our environment. Despite numerous studies, however, the properties of water are still poorly understood. One of the major reasons for this is the presence of extended hydrogen-bond networks exhibiting cooperative behavior which are responsible for the anomalous properties of water. In fact, water is a ubiquitous and incredibly complex matter. The use of extremely fast computational procedures becomes indispensable. Here we report the application of the semiempirical method based on strictly local electron groups [1,2] to these problems.
Hydrogen bonds are directed, and the number of possible configurations of hydrogen-bond networks for stable water clusters and elements of gas clathrates is huge. Even if we fix the morphology of the cluster, the number of different structures is on the order of millions. While the standard approach is restricted to the analysis of only a tiny structural part, we are capable, for the first time ever, to carry out exhaustive quantum-chemical analyses of all the cluster structures, that is, to characterize the entire distribution.
Our approach provides us with unique information about the energy, spatial structures and electronic properties of water systems. Using this particular information, one may compute physical and chemical properties of water-based systems, for example order-disorder phase transitions and the details of interaction with other molecules, such as incorporation of molecules into the water clusters and their dissociation. Moreover, the methods give us insights into the origins of the cooperative behavior of water. So far we have studied more than 30 different water systems (from water cages to ice nanotubes; in total about 10 millions of hydrogen-bond configurations), and the results support the conclusion that our fast computational algorithms provide a real breakthrough for the understanding of hydrogen-bond networks.
Acknowledgment. The financial support of this work through the RFBR grant No. 07-03-01128 is gratefully acknowledged.
[1] A.M. Tokmachev, A.L. Tchougréeff, J. Phys. Chem. A, 2003, 107, 358-365.
[2] A.M. Tokmachev, A.L. Tchougréeff, J. Phys. Chem. A, 2005, 109, 7613-7620.
Diversity of carbon modifications determines variety of technological applications of carbon-based materials. One of a new form of carbon is nanoparticles consisted of fullerene-like shells enclosed one inside the other, so-called onion-like carbon (OLC). The OLC structures produced by the ND annealing are jointed into associates covered by continuous corrugated graphitic layers. Recently, OLC have been proposed as shielding systems in wide frequency ranges.1,2 The interaction between external layers of OLC and electric field has a crucial role due to effect of the screening of the core of OLC co by outer shells. To produce the corrugated structure hexagonal graphene net was modulated by cylindrical surface. Different radius of cylinders were obtained and both zigzag and armchair graphite edges were considered. Geometrics such as C-C bonds and the distance between planes were fixed. Unit cell consists of 32 carbon atoms and the AA-stacked models were considered. The calculations of the band structures and the densities of the states of examined structure are presented. We found that distortion of AA-stacked graphitic structure results in appearance of specific peak in the conductive band corresponding to AB-stacked graphite. The changing in the partial densities of states for carbon atoms situated in the different positions of corrugated graphene follow the changing in the sp- hybridization and variation of and the distance between planes. All calculation were done using the pwscf (plane wave – self-consistent field) method with ultrasoft Vanderbilt potential within the Quantum ESPRESSO package. [1]. O. Shenderova, T. Tyler, G. Cunningham, M. Ray, J. Walsh, M. Casulli, S. Hens, G. McGuire, V. Kuznetsov, S. Lipa. “Nanodiamond and onion-like carbon polymer nanocomposites”. Diamond & Related Materials 16, 1213 (2007). [2]. S.A. Maksimenko, V.N. Rodionova, G.Ya. Slepyan, V.A. Karpovich, O. Shenderova, J. Walsh, V.L. Kuznetsov, I.N. Mazov, S.I. Moseenkov, A.V. Okotrub, Ph. Lambin. “Attenuation of electromagnetic waves in onion-like carbon composites”. ”. Diamond & Related Materials 16, 1231 (2007).
Graphene-based nanostructures are under intense investigation now. The next step to advanced materials is grapheme-based nanocomposites. Prediction of material structure is able to improve effectiveness of such materials investigations. The study of possibility of epitaxial growth of different molybdenum sulfides on graphite has been done using semi empirical PM6 calculations [1]. Molybdenum sulfide layers were positioned on graphitic one and rotated in order to check all the possible orientations. The calculations were done using novel PM6 method introduced in MOPAC2009 calculation suit [2].
The data was used to interpret recent experimental results on different molybdenum sulfides particles formation on graphitic surfaces. It was found, that no preferable orientation of Mo2S3 layer on graphitic layer exist. The result is the same as for MoS2, but different from wurtzite phase CdS, which is known to have strong epitaxial preference when growing on graphite [3].
As a result of Mo2S3/graphite composites calculations and separate components the binding energy was determined, in most cases it’s ~20-40 Kcal/mol depending on molybdenum sulfide and graphite layers mutual orientation. Such small value points on weak interaction between components and account for high temperature required for Mo2S3 formation on graphite surface.
Every carbon single-walled nanotube (SWNT) can be generated by first mapping only two nearest-neighbor C atoms onto a surface of a cylinder and then using the rotational and helical symmetry operators to determine the remainder of the tubule. With account of these symmetries, we developed a symmetry-adapted version of a linear augmented cylindrical wave (LACW) method. In this case, the cells contain only two carbon atoms, and the ab initio theory becomes applicable to any SWNT independent of the number of atoms in a translational unit cell [1]. The approximations are made in the sense of muffin-tin potentials and local-density-functional theory only. We have calculated the total band structures and densities of states of the chiral and achiral, semiconducting, semimetallic, and metallic carbon SWNTs up to the (100, 99) tubule containing the 118 804 atoms per translational unit cell. About 150 functions produce convergence of the band structures better then 0.01 eV independent of the number of atoms in the translational unit cell. Moreover, the electronic structure of double-wall carbon nanotubes (DWNT) consisting of two concentric graphene cylinders is calculated in the terms of the LACW method [2]. In this approach, the electronic spectrum of the DWNTs is governed by the free movement of electron in the interatomic space of two cylindrical layers, by electron scattering on the MT spheres, and by electron tunneling between the layers. The electronic structure of SWNTs embedded in a crystal matrix containing structural defects and impurities are investigated using LACW method too [3,4]. A delocalization of the nanotube electrons into the matrix region results in a strong band-structure perturbation. In the case of armchair nanotubes, the delocalization is responsible for a high energy shift of the states and growth of the electron density of states at the Fermi level. For the semiconducting nanotubes, it causes a decay of the minimum energy gap and the formation of a metallic state. This study was supported in part by the Russian Foundation for Basic Research (Grant no. 08-04-00262 and 08-08-90411) and Ukraine National Academy (Grant 0 26-08). 1. P.N. D'yachkov and D.V. Makaev, Phys. Rev. B 76, 195411 (2007). 2. P.N. D'yachkov and D.V. Makaev, Phys. Rev. B 74, 155442 (2006). 3. P.N. D'yachkov and D.V. Makaev, Phys. Rev. B 71, 081101 (2005). 4. P. N. D’yachkov and D.V. Makaev. J. Phys. Chem. Solids. Vol. 69, No 12 (2008).
The electronic structure of the chlorinated fullerene С60Сl30 synthesized using a procedure described in [1] has been investigated by means of x-ray photoelectron (XPS), x-ray emission (XES) and x-ray absorption near-edge structure (XANES) spectroscopy. Interpretation of the experimental spectroscopic data was performed by means of quantum chemical calculation of electronic structure of С60Сl30 molecule of D3d symmetry. The electronic structure of С60Сl30 molecule was calculated using B3LYP method with 6-31G* basis set. The theoretical XPS spectrum of valence band and XES C Kα and Сl L2,3 spectra of С60Сl30 were constructed using the results of quantum-chemical calculations on ground state of the molecule. The theoretical XANES C K and Cl L edge absorption spectra of С60Сl30 and C60 were modeled using the Z + 1 approximation in which a hole on the core level was replaced by an additional proton in the atomic nucleus. Energy of the X-ray C K transition was determined as difference of the Kohn-Shame energies between the C 2p and C 1s levels. Energy of the Cl L transitions was calculated as difference of energies between the Cl 3s, 3d and Cl 2p levels. Intensity of the line corresponding to the X-ray transition was calculated as a sum of squares of coefficients of the contributions of the C 2p and Cl 3s or Cl 3d atomic orbitals (AO) to occupied and unoccupied molecular orbitals (MO). A good agreement between the shapes of measured and calculated x-ray spectra were founded. It was shown that the main peak of the XPS spectrum of valence band is formed mainly by lone pairs of chlorine and the highest occupied MO corresponds to π-electrons of 18-memberted chain of the conjugated C-C bonds of the molecule. Combined analysis of the XPS and XES spectra showed participation of Cl 3d electrons in formation of the C-Cl bonding. Intensity and energy position of main features in the theoretical XANES CK-edge spectrum depend on presence of electron vacancy on core C 1s level. In contrast to C60 the ground state calculation of С60Сl30 molecule gives better agreement with pre-edge region of the experimental XANES C K-edge spectrum than in case of using of the Z+1 approach. [1] S.I. Troyanov, N.B. Shustova, A.A. Popov, L.N. Sidorov, Russ. Chem. Bull. 54 (2005) 1656.
The formation of aromatic hydrocarbon cation-radicals in reaction between molecular oxygen and aromatic hydrocarbons in HF was demonstrated by UV and ESR spectra [1]. However, the exact mechanism of this electron-transfer reaction was not found, and it was uncertain whether the acid transfers a proton to the oxygen ion or stabilizes the M+..O2- complex by HF solvation. We have modeled solvation of singlet and triplet dioxygen by protonated cluster of three hydrogen fluoride molecules using MP2 method with 6-311+G(d,p) basis set. In both cases O2 was bounded with linear HFHFHFH cluster by H-bonds. Upon changing of charge and multiplicity to neutral radical the complex undergoes transposition giving HO2* peroxyl radical enclosed into a cycle formed by HF molecules. Thermodynamics of electron transfer reaction between perylene and dioxygen in HF was estimated at the same computation level. It was shown that this reaction proceeds with ΔG0 = 5.4 kcal/mol for 3O2 and ΔG0 = -19.8 kcal/mol for 1O2. However, the results obtained with MP2/3-21G were better conformed to experimental data. Calculated ΔG0 for triplet oxygen was proved to be -32.9 kcal/mol.
The same electron transfer reaction was studied in the system containing 1,3-butadiene with triplet oxygen solved by (HF)3H+, giving π-complex [trans-C4H6..H+(FH)3..3O2]. Upon butadiene isomerization to cis-form the biradical complex [cis-C4H6+*..(HO2)*..(HF)3] emerges on the same PES. Butadiene cation-radical nature was confirmed by charge and spin density analysis. These results favor the formation of discussed HO2* radical instead of stabilization of the electron-transfer complex by acid solvation. The stabilization of close settled hydrocarbon cation-radical with peroxyl radical in HF medium was demonstrated.
Acknowledgements: We thank the Russian Foundation for Basic Research (Grant No. 08-03-00388-a) and the Program of the Department of Chemistry and Material Sciences of the Russian Academy of Sciences, “Theoretical and experimental study of nature of chemical bonds and of most important chemical reactions and processes”, for financial support.
1. W. Ij Aalbersberg, J. Gaaf and E. L. Mackor, J.Chem.Soc., 1961, p. 905.
The bacterial respiratory di-haem protein Pseudomonas stutzeri cytochrome c4 (cyt c4) offers a prototype target for environmental gating intra-haem electron transfer (ET) which can occur both in homogeneous solution and at electrochemical interfaces. The haem groups are axially coordinated to histidine and methionine and linked to the protein by thioether bonds. The protein can be immobilized on electrode surfaces with either low-potential (N) terminal or the high-potential (C) terminal domain facing the surface. A conspicuous feature of two electron interfacial oxidation (reduction) between the electrode surface and adjacent haem group has been reported in Ref.[1]: the reaction is only possible, when redox processes in the remote haem group proceed solely via intramolecular ET between the haem groups. Data analysis in Ref.[1] gives large values for intramolecular ET rate constants, around 102-103 s-1 for the Cterminal => Nterminal ET process and ca 104 s-1 for the Nterminal => Cterminal ET process. A preliminary analysis (based on a crude formalism) of the electronic coupling in the long-range ET process between the two haem groups in cyt c4 was performed in Ref.[2].
In this work we explore the electronic coupling using large-scale structural dependent density functional calculations to address the electronic structure of the di-haem core of cyt c4 in detail. An original fast method was developed to compute electronic matrix elements for large redox pairs. The electronic transmission coefficient of the intramolecular ET was estimated in the framework of Landau-Zener theory for different orientations of the haeme groups and Fe-Fe distances. The electrostatic contribution to the work term, the inner- and outersphere reorganization energies were calculated as well. Deprotonation of the propionate carboxyl group of one haem-center was found to play an important role leading to a significant increase of the intramoleacular ET rate.
Refs.
Self-assembled monolayers (SAM) have been explored intensively in the recent years which show numerous advanced applications. In particular, SAMs consisting of alkanethiols on the Au(111) surface are in the focus of attention due to their easy preparation, stable and ordered structure [1]. In this work we made an attempt to interpret at molecular level original experimental data on the adsorption of certain alkanethiol isomers (S(CH2)3CH3 - butanethiol, SCH2CH(CH3)2 - 2-methil-1-butanethiol and S(CH3)3 - tert-butanethiol) on the Au(111) electrode surface. The data were obtained using in situ scanning tunneling microscope technique and demonstrate clearly a remarkable difference in the structure of SAMs. The surface lattices of (2√3x3)R30°, (√3x8)R30° and (√7x&7)R19° types were suggested for butanethiol, 2-methil-1-butanethiol and tert-butanethiol, respectively.
The cluster model was employed to investigate the adsorption of single aklanethiol radicals in different sites of Au(111), while the periodical slab model (SIESTA code) was used in density functional calculations of different SAMs. After the optimized geometry of adsorbate has been determined, we employed a computational approach developed recently in Refs.[2, 3] in order to construct STM images (constant current mode). A special attention is paid on the analysis of contribution from different atomic groups of the adsorbed alkanethiols to the resulting STM contrast. The origin of dark and bright contrasts observed in experiment is discussed as well.
Refs.
Electron transfer (ET) processes occurring at electrochemical interfaces are of fundamental interest for theory and have numerous practical applications. Although a general quantum mechanical theory of heterogeneous ET has been already developed (see Ref.[1]), there are still a number of particular unsolved problems. For example, considering a metal electrode we have to deal with a manifold of crossing free energy surfaces (FES) which correspond to different states in electronic band. This might evoke obvious difficulties in calculations of electronic transmission coefficient in intermediate regions of electronic coupling.
In the present work we employed Monte Carlo (MC) simulations to describe ET through a network formed by a family of crossing parabolic FESs which mimic an electrochemical system. Previously a MC technique was successfully used to address similar problems for linear [2] and parabolic [3] free energy surfaces. Both direct and reverse ballistic trajectories were considered in the framefork of Landau-Zener formalism. Pertinent simulation details can be found in Refs.[2, 3]. The model approach devised in this work can be readily extended to redox couples with noticeable intramolecular reorganization (including bond breaking ET).
We report effective electronic transmission coefficients computed as a function of the Landau-Zener factor, density of electronic states, electrode overpotential and temperature. Emphasis is put on exploring the regions of activationless and barierless discharge (in adiabatic and diabatic limits); this is a novel point as compared with results obtained previously [2,3].
Refs.
The modeling of Ln(3+)-water molecules interactions by DFT approach is the aim of this work.
The nonahydrated Ln(3+) cation was studied on UB3P86 theoretical level. Heretofore we’ve shown that the hybrid exchange-correlation functional B3P86 is appropriate to predict the La-O and Lu-O bonds in aqua-ions.
The structural characteristics of Ln(H2O)93+ (Ln = Ce, Pr, Nd, Pm, Sm, Eu) stable aqua-ions were calculated.
Stevens and co-workers (CEP-31) relativistic effective core potential for lanthanides, double-zeta quality basis set for O-, H-atoms were used for calculations. All calculations were made without symmetry constraints. The calculated stationary points on the potential energy surface were characterized by the vibrational frequency analysis. All studied structures are computed in high-spin state approximation.
In preliminary calculation we’ve found that maximal number of water molecules located in first coordination shell of light Ln(3+) cation is nine The tenth water molecule migrates from first coordination shell to second one. It was found that for the nonahydrated structures about one third of tricationic charge was transferred to water molecules. It was explained the charge transfers from water molecule to the s,p,d-orbitals of the studied Ln(3+) ions.
The calculated average R(Ln-O) for Ln(H2O)93+ aqua-complexes were in below (A):
The solvation of Gd(3+) ion in liquid N,N-dimethylformamide was studied. The modeling of Gd(3+)-N,N-dimethylformamide interactions by DFT approach is the aim of this work.
The energetic and structural characteristics of Gd(DMF)93+ and Gd(DMF)83+ stable solvated ions were investigated on USVWN5 theoretical level. Heretofore we’ve shown that the simple local functional SVWN5 is appropriate to predict the lanthanide-oxygen bonds in aqua-ions.
Stevens and co-workers (CEP-4G) relativistic effective core potential for gadolinium, D95V double-zeta quality basis set for O- and N-atoms and single-zeta quality SZ basis set for C- and H-atoms were used for calculations. All calculations were made without symmetry constraints. The calculated stationary points on the potential energy surface were characterized by the vibrational frequency analysis. All studied structures are computed in high-spin state approximation.
In preliminary calculation we’ve found that maximal number of N,N-dimethylformamide molecules located in first coordination shell of Gd(3+) cation is nine since the added tenth N,N-dimethylformamide molecule migrates from first coordination shell to second one. It was found that for the nonasolvated structures about one half of tricationic charge was transferred to N,N-dimethylformamide molecules. It was explained the charge transfers from oxygen atoms of dimethylformamide molecule to the s,p,d-orbitals of the studied Gd(3+) ion.
The calculated average R(Gd-O) and R(Gd-N) distances for Gd(DMF)93+ and Gd(DMF)83+ complexes were in below (A):
Gd(DMF)93+
Nitrogen is an ideal element for substitution of carbon atom in hexagonal graphitic network. X-ray photoelectron and X-ray absorption spectroscopic examination of nitrogen-doped carbon nanotubes has revealed that nitrogen, incorporated in nanotubes, are in three different chemical states at least. Assignment of the spectral maxima to the nitrogen forms was made from the comparison of the experimental data with the results of DFT calculations of nitrogen-containing carbon nanotube models. Geometry of the models was relaxed using B3LYP method (6-31G basis set) included in the Jaquar program package. It was found, that main forms of encapsulated nitrogen are graphtic-like atom (direct substitution of carbon atom for nitrogen one), pyridinic-like atom (location of nitrogen atom on the edge of an atomic vacancy), and molecular nitrogen. Calculations showed that nitrogen molecule is easy rotating inside the carbon nanotube cavity, hence, for explanation of the observed angular dependence of X-ray absorption spectra near the N K-edge we should assume intercalation of molecules between the layers of multi-walled nanotubes and their orientation along a tube axis. To select the structures of nitrogen-doped carbon nanotubes for theoretical calculations of current-voltage dependences, thermodynamic stability of models was investigated. Definition of the most probable mutual arrangement of nitrogen atoms was made for armchair (5,5) tube and zigzag (9,0) tube being close in the diameters. Three-coordinated nitrogen atoms were located: (1) along a tube circumference, (2) along a tube, and (3) at the end tops. Nitrogen atoms were adjusted (ortho-position in a hexagon), located within a carbon atom (meta-position) and two carbon atoms (para-position), and largely separated along a tube circumference. The lowest energy was obtained for the para-position of nitrogen atoms along a circumference of armchair tube and along an axis of zigzag tube. Current-voltage dependences of field electron emission from carbon and nitrogen-doped nanotubes have been calculated using the Fowler-Nordheim equation and details of the measurements. It was shown that doping causes decrease of the field value at which the emission current appears and enhance of the current density. At 2% content of nitrogen in nanotube the best properties are achieved if nitrogen atoms are located at it closed tip, however the energy of this structure is by 0.5 eV higher than the energy of the most stable configuration. Increase of nitrogen concentration from 1% to 2% improves the emission characteristics of nanotubes and for the nanotubes with 4% nitrogen concentration the field emission is close to that expected for the pure carbon nanotube. The theoretical dependences were correlated with the experimental ones.
In this work, we propose a novel approach towards explanation of the electron nature in a framework of the trajectory-wave monism using a further development of optical-mechanical analogy in description of the Physical Reality. In the proposed here theory, we assume that the electron motion is realized along the trajectory, while the trajectory presence is a result of the electron existence itself. Also it is assumed that any electron motion is determined by its wave V(x,t). Coupling between the trajectory and wave motion of the electron is assumed in the developing theory. Following this approach we demonstrate that the propagating electron wave V(x,t) leads the electron trajectory in free space. Also by using a local variation principle for the electron wave coupled with its trajectory we develop a new equation for the electron wave in the hydrogen-like atom. By analytical solution of the obtained equations we give a novel description of the well-known hydrogen-like atom spectrum where the spatial electron trajectories get nonclassical properties which partially similar to the electron properties of the early Bohr theory and quantum mechanics as well as. Here the stationary electron trajectories arise on the two-dimensional surfaces around central nuclear. In the particular case, the surfaces are the spherical surfaces with Bohr radius. Energies of the stationary spherical trajectories coincide with the well-known energies of stationary Bohr orbits. Wave motion of the electron is coupled with the trajectory surface and exists outside of the surface that makes it similar to classical picture of the stationary waves. We also demonstarte that the proposed theory describes very similarly many well-known effects in quantum dynamics of the hydrogen atom, which can take place due to quantum interference the stationary states. In this case, the trajectory surfaces get spatial movement leading thereby to the electrical nostationary currents in the atom. Thus the obtained results describe the trajectory and wave entities of the electron nature in joint corpuscular-wave monism. We also propose an experiment for examination of the presented theory and we discuss its potential possibilities.
A general problem of practical use of polymer films from the organic materials for photovoltaic elements creation is low power conversation efficiency amounting to 6% at presented time [1]. So low value is explained by the causes set, one of them is a small overlap of organic substances and sun light adsorption spectrums [2]. The low intensity of the red light adsorption is being a key moment especially [3].
Porphyrin-fullerene dyads are considered as a perspective material for creating the organic photovoltaic elements. Porphyrin (P) plays an electron donor role, fullerene is electron acceptor. Light radiation induces the charge transfer process from P to F. In this work we are presenting the quantum-chemical calculations results of adsorption spectrums character properties of porphyrin-fullerene dyads with two types of bonding: P and F are bonded covalently (P-F) in one case and bonded by the attracting intermolecular forces without covalent bonds formation (P···F) in another case. DFT method with B3LYP exchange-correlation potential and 6-31G(p,d) atomic basis set was using for calculations. In the beginning the geometry optimization of each structure has been done, and further the excited states calculations of optimized molecules have been performed by the Time-Dependent procedure. It has been shown that wavelengths of radiation inducing the electron transfers and formation of the structure with separated charges have a place in the red region of spectrum (664 and 621 nm for P-F, 689 and 637 nm for P···F). Excited states lifetime is sensibly long and amounts to microseconds (1 and 330 µs for P-F, 63 and 456 µs for P···F). The presented spectrum properties generally are satisfied for potential use of the concerned structures as the photovoltaic elements. Covalent binding of P with F distorts a little the structure of the last one. It leads to the F symmetry decreasing, which is accompanied by the degeneracy losing of molecular orbitals localized on it. Excited state lifetime of the whole dyad decreases as a result. Therefore the dyad chains non-bonded covalently are appropriate to use as the photovoltaic elements. Especially since the structure of their electronic adsorption spectrum is saved generally even by changing the distance between P and F. The negative moment of P···F relatively to P-F is sufficient low intensity of electromagnetic radiation sorption of the wavelengths mentioned above.At the recent time the interest to the systems founded on carbon nanostructures decorated by metal atoms (MA) increases essentially. Carbon nanotubes (CNTs) can be the cells for creation of very thin metal filaments with controllable size [1], which can be used as conductive compounds for molecular nanoelectronic devices. The systems of this type are interesting also as solid state materials for hydrogen storage.
It was shown [2] that single Ti atom sited on the single-walled CNT can bind up to 4 hydrogen molecules, and changing of Ti by Sc allows us to bind up to 5 hydrogen molecules. The problem is that covering of CNTs by transition metals atoms is multi-layer. It leads to decreasing of weight capacity of adsorbed hydrogen up to values non-interesting for the industrial use. Nevertheless, shown results allow us to consider that carbon nanostructures decorated by light transition metals can be effective adsorbents of hydrogen. And now the question about the possibility of formation of even single-layer covering is very important because it provides exactly the maximal sorption capacity, whereas MA aggregating on the CNT surface can decrease the last one essentially [3]. In this work we are presenting the results of quantum-chemical simulations of CNTs (8,0), (9,0) and (10,0) interactions with a few atoms (8-21 respective to 96-121 carbon atoms of unit cells) of transition metals (Sc, Ti, V). All calculations were performed in the VASP package by the DFT method with PBE potential and plane-wave basis set. It was shown that evenness of CNTs covering by the transition metals (distances equality between them) depends on diameters of the first ones. It can be explained by the surface curvature decreasing due to diameter increasing. Since the MA initially were sited symmetrically in the centers of six-fold rings, curvature decreasing has led to decreasing of distances between them. Even covering is formed in the case when obtained metal-metal distances are similar to ones in the corresponding metal clusters. If these distances are longer, MA on the CNT surface aggregate. So, Sc forms much even layer on the CNT (10,0) surface at the time when Ti and V aggregate (Ti in the lesser and V in the greater extents). It is following from the fact that effective atomic radiuses in the Sc-Ti-V order decrease, and as the result the distances between each of them in the compounds decrease either. It means that for formation of even covering by Ti and V it is necessary to use CNT with larger diameters. At the same time it is not possible to define the directions at which additional atoms binding becomes preferably. According to energetic parameters, formation of single or double layer is equiprobable.Теплота перехода является важнейшей характеристикой фазовых переходов первого рода. Впервые в 1762 году Дж. Блэк обнаружил, что при переходе воды в пар поглощается некоторое количество теплоты, названное им латентной теплотой испарения. Несмотря на более чем двухсотлетний период существования понятия теплоты перехода отсутствуют какие-либо аналитические выражения (кроме полученных эмпирически), связывающие теплоту перехода с другими параметрами фазовых превращений. Так, например, в фундаментальной “Физической энциклопедии” [19] статьи, посвященные теплоте испарения, теплоте плавления и т.д., не содержат каких-либо формул, а содержат только таблицы экспериментальных данных. В работе [1] из первого начала термодинамики получены точные выражения для теплоты фазовых переходов первого рода: В работах [2], [3] найдены выражения для теплоты испарения и теплоты плавления. Расчеты теплоты испарения проводились, как при условии, что объем жидкой фазы есть геометрический объем, так и при предположении, что объем жидкой фазы, представляет собой так называемый «свободный объем», т.е. геометрический объем минус объем занимаемый атомами (молекулами). Расчеты, проведенные по второй модели существенно лучше (с точностью до нескольких процентов) согласуются с экспериментальными данными, взятыми из справочника [4]. Хорошее согласие между вычисленными результатами и экспериментальными данными позволяет использовать выражение для теплоты испарения в уравнении Клаузиуса – Клапейрона и получить выражение, связывающее термодинамические параметры в критической точке. В это выражение входит значение «свободного объема» в критической точке, что позволяет получить выражение для объемов атомов (молекул): Предложены некоторые геометрические модели атомов и молекул и сделаны расчеты их линейных параметров, которые хорошо согласуются с общепринятыми значениями. Литература 1. А. А. Собко. Термодинамическое обоснование эвристических выражений для теплоты перехода фазовых превращений первого рода, «Доклады Академии наук» 2007, т.417, №3, с. 326-327. 2. А. А. Собко. Вычисление молярной теплоты испарения, «Доклады Академии наук» 2006, т.407, №3, с. 325-328. 3. А. А. Собко. Вычисление молярной теплоты плавления, «Доклады Академии наук» 2007, т.412, №3, с. 328-333. 4. Н. Б. Варгафтик. Справочник по теплофизическим свойствам газов и жидкостей, М., «Наука», Главная редакция физико-математической литературы, 1972.
Во всех учебниках по квантовой механике в частности [1-2] точные собственные значения уравнения Шредингера находятся для весьма немногих потенциалов, как правило, для прямоугольной ямы конечной и бесконечной глубины, для гармонического осциллятора, кулоновского потенциала и еще для двух-трех финитных потенциалов. Тем временем, задача нахождения собственных значений уравнения Шредингера крайне важна для различных приложений, таких как физика твердого тела и нахождение энергетических уровней молекул. В настоящей работе решается задача получения выражений для определения собственных значений для произвольных финитных потенциалов. Основным аппаратом для получения модифицированного уравнения Шредингера служит Фурье-преобразования. В работе [2] получено уравнение Шредингера в интегральной форме, в котором ядром служит Фурье- образ потенциала. Модификация этого уравнения приводит новому интегральному уравнению Шредингера. Показано, что из модифицированного уравнения Шредингера в интегральной форме получается выражение для единичного уровня в неглубокой потенциальной яме. Результат совпадает с результатом, полученным в [1], что подтверждает эквивалентность полученного уравнения и общепринятого уравнения Шредингера. Предложен метод, позволяющий получить несколько выражений для точного определения собственных значений уравнения Шредингера. Полученные выражения содержат только собственные значения уравнения Шредингера и интегральные формы как с Фурье образами потенциалов, так с самими потенциалами. Для того, чтобы продемонстрировать применение представленных результатов, были получены выражения для определения четных и нечетных уровней в прямоугольной потенциальной яме конечной глубины. Результаты совпадают с результатами, полученными в литературе, в частности с [2]. Литература 1. Ландау Л.Д., Лифшиц Е.М. Квантовая механика т.3. М. , Издательство «Наука» и Главная редакция физико-математической литературы, 1974. 2. Флюгге З. Задачи по квантовой механике т 1. М. , Издательство «Мир», 1974.
Although the structure of molten cryolite compositions has been intensively investigated for a long time using vibrational and NMR spectroscopy, conductivity measurements (see Ref. [1]), some important details remain still unclear so far. First of all, the existence of dimeric (and even more complicated) forms of Al(III) fluorocomplexes, the effect of cations of the structure of cryolite melts, as well as the mechanism of diffusion transport are a matter for discussion. In this work we employed Car-Parrinello Molecular Dynamics (CPMD) and density functional calculations of model clusters to elucidate these problems. A set of test calculations were done to check the accuracy of CPMD level. The simulations were performed for Na+ and Li+ containing melts with three different values of cryolite ratio (CR). The averaged coordination numbers, portions and structure of certain Al(III) fluorocomplexes and their life-times are reported. The electroconductivity of the melts was calculated as a function of CR. The contribution of complexes of different nature to the total electroconductivity is analyzed. The main predictions are compared with those made recently on the basis of a combined spectroscopic and quantum chemical study [2], and with relevant results of classical MD simulations reported in literature [3, 4].
Refs.
The adsorption of a water molecule on Bi(111) surface has been studied in the framework of cluster model for a bismuth metal surface, at the B3LYP/LANL2MB,6-31G(d,p) level. The surface dissociation of water molecule to OH and H species has been predicted to be endothermic. The energy barriers for rotation around the surface normal are low (<2 kJ mol−1). The energy of water adsorption ΔEads has been found to increase in the series “top” < “bridge” < “hollow” ranging from −10 to −28 kJ mol−1, for the “top” and “hollow” sites, respectively. The calculated adsorption energy is comparable with that predicted earlier for liquid Hg surface [1]; this points to similar hydrophilic properties of the both metals. However, energetically preferable site for adsorption differs from computational predictions reported previously for other metal surfaces [1-3]. The adsorption at the “hollow” site gives the strongest binding through a metal image dipole-water molecule dipole interaction due to the lower Pauli repulsion and larger partial charge transfer.
The electrical double layer effects on water adsorption energy and geometry has been addressed by using an external electric field, which generates a positive surface charge density on the metal cluster and reinforces the water-surface interaction. The results obtained have been employed to model the double layer capacitance. The mean field theory combined with the tree-state model have been used to calculate solvent layer capacitance, Cs, which has been found to be equal 15 µC/cm2 and almost constant in a wide range of potentials. Estimated value of metal capacitance, Cm, equals 23 µC/cm2 (for uncharged surface). Data gained have been compared to the known computational [1-4] and experimental [5-6] results and the accordance has been discussed.
Electronic structure of the manganese dimer, Mn2, presents a great challenge for quantum chemistry. Even the spin of its ground electronic state cannot be reliably determined by the DFT methods (see, e.g. [1]). Results of the correlated ab initio calculations, though agree with experiment in the singlet ground state, scatter significantly for the equilibrium distance, binding energy and vibrational frequency [2]. The most accurate interaction potentials obtained by combining CCSD(T) and MRCI approaches produce the vibrational frequencies markedly lower than those determined by matrix isolation spectroscopy [3]. The latter, however, revealed quite significant dependence of the vibrational frequency on the nature of inert matrix (Ar, Kr, Xe) that indicates substantial frequency shift induced by the matrix.
To estimate this effect, molecular dynamics (MD) and Monte-Carlo (MC) simulations for the Mn2@Ar
In agreement with experiment, two trapping sites of the Mn2 in argon were indentified. Both shift the frequency to the red, one by 15, another by 25 cm-1. Being combined with the Mn2 anharmonic frequency, 40 cm-1 [2], it gives the matrix values 55 and 65 cm-1, in close agreement with experimental 59 and 68 cm-1. These results reveal the high accuracy of the ab initio potentials and indicate quite significant compression of the Mn2 in inert matrices. Noteworthy, it should also affect the splitting between the lowest electronic states through the spin-exchange interactions.
The authors thanks MSU Research Computing Center and MSU Department of Computational Mathematics and Cybernetics for providing access to computational resources. The work is supported by Russian Foundation for Basic Research (projects 08-03-00414 and 09-07-12068).
1. S. Yamanaka, T. Ukai, K. Nakata, R. Takeda, M. Shoji, T. Kawakami, T. Takada, K. Yamaguchi. Int. J. Quant. Chem. 107 (2007) 3178.
2. A.A. Buchachenko. Chem. Phys. Lett. 459 (2008) 73; A.A. Buchachenko, G. Chalasinski, M.M. Szczesniak, to be published.
3. K.D. Bier, T.L. Haslett, A.D. Kirkwood, M. Moskovits. J. Phys. Chem. 95 (1991) 2644.
4. R.A. Aziz. J. Chem. Phys. 99 (1993) 4518.
Compounds of type [M(H2O)3]4[H2Mo12VO30
(μ2-OH)10], with M = Ni, Co, Fe, and the H2Mo12VO30(μ2-OH)10 cage of the structure of ε-Keggin had been discovered by Koegerler et al. [1]. Their magneto-optical behavior is rather intriguing: having applied the magnetic field, a marked decrease appears on the magneto-optical response curve of Ni-compound at energy 1.95 eV, which originally had unknown nature. In addition its optical conductivity and reflectance spectra show the presence of two absorption bands at lower energies (0.8-0.9 and 1.6 eV).
Appreciated the closeness of the d-shell excitation energies in hexaaquanickel cation with those found from optical conductivity spectrum and the similarity between the structures of closest environment of the nickel ions in the above Ni-compound (M = Ni) and in its hexaaquacomplex we have calculated the d-d-spectrum of Ni-compound by means of EHCF method [2]. These calculations showed that the energies of the first two spin-allowed transitions (at 0.9 and 1.6 eV) fairly coincide with those observed in the absorption, optical conductivity and reflectance spectra. The first spin-forbidden transition has a bit higher energy than it is observed on magneto-optical response spectrum, which nonetheless allows us to interpret the observed feature as a modification of the intensity of the spin-forbidden transition in the magnetic field.
The Ni-compound also possess unusual magnetic properties resulted in nonequidistant steps on its magnetization curve which cannot be explained by means of the Heisenberg model even complemented with anisotropic corrections and biquadratic terms. Phenomenologically the field dependence of the magnetization of the above Ni-compound can be described [1] in an assumption of strong nonuniform field-dependency of the spin-spin interaction constant. In order clarify this point we studied electronic structure of the superexchange paths between nonpaired electron centers to magnetic behavior of the molecule we investigated electronic structure of the [M(H2O)3]4[H2Mo12
VO30( μ2-OH)10] cage and established localisation of highest occupied MOs on the Mo atoms, which comprise O- Mo2V-O bridging motifs between the Ni atoms. The influence of protonation on the MO composition had been found so that only twice protonated groups O-Mo2V(μ2-OH)2-O are probably involved in the superexchange.
This work has been supported by the RFBR through the grants ## 07-03-01128, 08-03-00414,
09-03-92425-CE.
Using ab initio methods we have studied structure and and conformational dynamics of the methyl oxiranyl ketone molecule (MOXK) in the ground S0 and lowest excited (T1, S1) electronic states.
According to the results, obtained by the RHF, MP2, B3LYP computational methods with Pople (up to the 6-311+G(2d,2p)) and Dunning (up to the cc-pVTZ) basis sets, in the S0 electronic state there are two stable “cis” and “trans” conformations. Conformer energy difference was found to be 690 cm-1, “trans” conformer is more stable.
We calculated one- (1D) and two- (2D) dimensional sections of the MOXK PES by the oxirane and methyl rotation coordinates (using MP2/6-311+G(2d,2p) method). We should note that on the 2D torsion-torsion PES section of the MOXK there are three minima, corresponding to the “cis” and three minima corresponding to the “trans” conformer. On the PES of the MOXK there are two types of the saddle points corresponding to the barriers to the rotation of the oxirane group (2300 and 1300 cm-1, MP2/cc-pVTZ, relative to the “trans” conformer) and saddle points corresponding to the methyl rotation barriers for the “cis” conformer (320 cm-1, relative to the cis conformer) and for the trans conformer (180 cm-1, relative to the trans conformer).
The excitation of the MOXK to the T1 and S1 electronic states leads to the dramatic structural changes: pyramidal distortion of the carbonyl fragment, rotation of the oxirane fragment and small rotation of the methyl group.
In the excited electronic states there are six stable conformations of the MOXK (out-of-plane angle for the C=O bond is ±40°, the oxirane fragment rotation angle is ≈60°, ≈180°, ≈310°, the methyl top rotation angle is near ≈60° for all the conformers). According to CASPT2/aug-cc-pVDZ calculations in the T1 electronic state the conformer energy difference lies in the range from 144 to 430 cm-1, in the S1 electronic state – from 220 to 420 cm-1.
Using various ab initio methods we have studied structure and conformational dynamics of the isomer (with Cs symmetry) of the dioxiranyl ketone molecule (DOXK) in the ground S0 and lowest excited (T1, S1) electronic states.
The RHF, MP2, B3LYP calculations with Pople (up to the 6-311+G(2d,2p)) and Dunning (up to the cc-pVTZ) basis sets demonstrated that in the S0 electronic state there are two stable “cis-trans” and “gauche-antigauche”conformations of the DOXK. For the MP2/cc-pVTZ method the conformer energy difference was found to be 380 cm-1, “gauche-antigauche” conformer is more stable.
For the DOXK molecule in the S0 state two large amplitude motions are possible: rotations of the two oxirane groups. So we calculated one- (1D) and two (2D) sections of the PES using MP2/6-311+G(2d,2p). On the 2D torsion-torsion section of the DOXK PES we observed two minima of the “cis-trans” and two minima of the “gauche-antigauche” conformers and the region of the sterically strained structures with the energy up to the 6000 cm-1.
The excitation of the DOXK to the T1 and S1 electronic states leads to the pyramidalization of the carbonyl fragment and rotation of the oxirane rings. In the excited states we have to consider three large-amplitude motions: two ring rotations and inversion. The analysis of the 1D and 2D sections by torsion and inversion coordinates (CASPT2/6-31G*) demonstrate that in the T1 and S1 states there are three conformers with oxirane rotation angles: 190°, 50°; 310°,170°; 330°,10° and inversion angles 30°, -30°, 10°. In the T1 electronic state the conformer differences are 170, 0, 900 cm-1 (CASPT2/6-31+G*).
Using 1D and 2D DOXK PES sections were obtained torsion and inversion transition energies in the anharmonic approaches of the various dimensions. Analysis of the 2D vibrational wave functions enables to make a conclusion that in the some PES regions there is a strong coupling of the low-frequency motions.