This abstract is devoted to the description of problems in the calculation of observables in the method of coupled clusters. To date, one can often find statements in the literature that this method is the gold standard for calculating the energy of the ground state of molecular systems containing several tens of atoms.
The first part is devoted to a general overview of the fundamentals of the method and the current state of affairs. The problem of dimensional consistency, the introduction of an exponential ansatz, and the derivation of working equations of the method are discussed. The application of modern hot topics in the field of development of computational approaches is described: quantum computing and the use of ML techniques. The development of the method towards f12 and EOM implementations is shown, as well as the orbital localization technique to reduce the computational complexity of the problem.
The second part is devoted to the problem of calculating the properties of molecular systems. Since the initial construction of the coupled cluster method does not imply the calculation of the wave function, in practice, to calculate the properties, the linear response technique is used to obtain the density matrices of the required order. The main approaches to the calculation of these mathematical objects and their analysis are described.
In the last part presents the original results obtained in our scientific group. A method for calculating the working expressions for the arbitrary-order coupled cluster methods is shown for both the amplitudes of the excitation operator and the coefficients for calculating the single-particle density matrix. The procedure for numerical optimization of the calculation algorithm through the calculation of intermediate expressions is described. The use of a two-particle density matrix for the analysis of the completeness of the basis in the calculation of van der Waals systems is demonstrated.
The author is grateful to the Russian Science Foundation for the financial support under Project 22-23-01180.