ABSTRACT
The single-reference coupled-cluster method has proven very effective in the ab initio description of atomic and molecular systems, but its successful application is limited to states dominated by a single Slater determinant, which is used as the reference. In cases where several determinants are important in the wave function expansion, i.e., we have to deal with nondynamic correlation effects, a multi-reference version of the coupled-cluster method is required. The multi-reference coupled-cluster approaches are based on the effective Hamiltonian formulation providing a two-step procedure, in which dynamic correlation effects can be efficiently evaluated by the wave operator, while nondynamic correlation contributions are given by diagonalization of the effective Hamiltonian in the final step. There are two classical multi-reference coupled-cluster formulations. In this paper, the focus is on the so-called Fock-space coupled-cluster method in its basic version with one- and two-particle operators in the exponent. Computational schemes using this truncation of the cluster operator have been successfully applied in calculations in one- and two-valence sectors of the Fock space. In this paper, we show that the approach can be easily extended and effectively employed in the three-valence sector calculations.
ABSTRACT
The exponential parametrization of the wave function used in the coupled-cluster approaches has proven very successful in the ab initio description of atomic and molecular systems. This concerns first of all the single-reference version of the method that is designed for states dominated by a single Slater determinant. Usually, the coupled-cluster methods with one- and two-body excitation operators in the exponent form the basic computational schemes. The inclusion of three-body effects in the cluster operator to increase the accuracy of the results is numerically expensive, so their approximate evaluation is rather used in practice. In the case of the single-reference coupled-cluster approach, the problem of approximate evaluation of three-body effects in the cluster operator has been well studied, and computational schemes of both noniterative and iterative nature have been proposed. The situation is different in the case of multireference coupled-cluster methods which are required to describe open shell and quasidegenerate states. The multireference approaches in their standard effective Hamiltonian formulations are more complicated and less frequently used in routine calculations; however, one of them, the so-called Fock-space coupled-cluster method, becomes very effective if reformulated within the intermediate Hamiltonian framework. Both the basic version of the method with one- and two-body clusters and the extended one that includes up to three-body operators in the exponent are implemented. The latter approach provides more accurate results, but its relatively high numerical cost limits its applicability. For this reason, going beyond the basic scheme with one- and two-body clusters through an approximate evaluation of the impact of three-body clusters is of great interest. In the paper, we investigate different ways of approximate inclusion of the three-body effects in the Fock-space coupled-cluster method designated for excitation energy calculations.
ABSTRACT
The intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculate vertical excitation energies (EEs) for some molecular systems. The calculations are performed for several small molecules, such as H2O, N2, and CO, and for larger systems, such as C2H4, C4H6, and C6H6. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and model spaces are employed permitting a comparison of the calculated vertical EEs with the experimental data.
