The intermediate Hamiltonian Fock-space coupled-cluster method with approximate evaluation of the three-body effects

Intermediate Hamiltonian Fock-space coupled-cluster theory for excitation energies, double ionization potentials, and double electron attachments with spin–orbit coupling

The intermediate Hamiltonian Fock-space coupled-cluster methods at the singles and doubles level (IHFSCCSD) for excitation energies in the (1p, 1h) sector, double ionization potentials in the (0p, 2h) sector, and double electron attachments in the (2p, 0h) sector of the Fock space are implemented based on the CCSD method with spin–orbit coupling (SOC) included in the post-Hartree–Fock treatment using a closed-shell reference in this work. The active space is chosen to contain those orbitals that have the largest contribution to principal ionized or electron-attached states obtained from the equation-of-motion coupled-cluster calculations. Both time-reversal symmetry and spatial symmetry are exploited in the implementation. Our results show that the accuracy of IHFSCCSD results is closely related to the active space, and the sufficiency of the active space can be assessed from the percentage of transitions within the active space. In addition, unreasonable results may be encountered when the ionized or electron-attached states with a somewhat larger contribution from double excitations are included to determine the active space and cluster operators in the (0p, 1h) or (1p, 0h) sector of the Fock space. A larger active space may be required to describe SO splitting reliably than that in the scalar-relativistic calculations in some cases. The IHFSCCSD method with SOC developed in this work can provide reliable results for heavy-element systems when a sufficient active space built upon the principal ionization potential/electron affinity states is adopted.

Extension of the Fock-space coupled-cluster method with singles and doubles to the three-valence sector

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.

Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations

The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.