Excitation energies of closed-shell systems based on the equation-of-motion (EOM) coupled-cluster theory at the singles and doubles (CCSD) level with spin-orbit coupling (SOC) included in the post-Hartree-Fock treatment are implemented in the present work. SOC can be included in both the CC and EOM steps (EOM-SOC-CCSD) or only in the EOM part (SOC-EOM-CCSD). The latter approach is an economical way to account for SOC effects, but excitation energies with this approach are not size-intensive. When the unlinked term in the latter approach is neglected (cSOC-EOM-CCSD), size-intensive excitation energies can be obtained. Time-reversal symmetry and spatial symmetry are exploited to reduce the computational effort. Imposing time-reversal symmetry results in a real matrix representation for the similarity-transformed Hamiltonian, which facilitates the requirement of time-reversal symmetry for new trial vectors in Davidson's algorithm. Results on some closed-shell atoms and molecules containing heavy elements show that EOM-SOC-CCSD can provide excitation energies and spin-orbit splittings with reasonable accuracy. On the other hand, the SOC-EOM-CCSD approach is able to afford accurate estimates of SOC effects for valence electrons of systems containing elements up to the fifth row, while cSOC-EOM-CCSD is less accurate for spin-orbit splittings of transitions involving p1/2 spinors, even for Kr.

Orbital-optimized third-order Møller-Plesset perturbation theory and its spin-component and spin-opposite scaled variants: Application to symmetry breaking problems J. Chem. Phys. 135, 224103 (2011) Interaction energies of large clusters from many-body expansion J. Chem. Phys. 135, 224102 (2011) Local pair natural orbitals for excited states J. Chem. Phys. 135, 214106 (2011) Effect of microhydration on the guanidiniumbenzene interaction J. Chem. Phys. 135, 214301 (2011) Dispersion interactions in density-functional theory: An adiabatic-connection analysis J. Chem. Phys. 135, 194109 (2011) Additional information on J. Chem. Phys. In the present work, we report exploitation of spatial symmetry in calculations of ground state energy and analytic first derivatives of closed-shell molecules based on our previously developed coupledcluster (CC) approach with spin-orbit coupling. Both time-reversal symmetry and spatial symmetry for D 2h and its subgroups are exploited in the implementation. The symmetry of a certain spin case for the amplitude, intermediate, or density matrix is determined by the symmetry of the corresponding spin functions and the direct product decomposition method is employed in computations involving these quantities. The reduction in computational effort achieved through the use of spatial symmetry is larger than the order of the molecular single point group. Symmetry exploitation renders application of the CC approaches with spin-orbit coupling to larger closed-shell molecules containing heavy elements with high accuracy.

We report implementation of the equation of motion coupled-cluster approach for ionized states (EOMIP-CC) with spin-orbit coupling (SOC) using closed-shell state as reference in this work. Ionization potentials (IPs) are calculated in the ionized 1h and 2h1p space with EOM at the CC singles (CCS) as well as the CC singles and doubles levels (CCSD). In this EOMIP-CC approach, SOC is included either in both the CC and EOM steps or only in the EOM step. It should be noted that IPs provided by the EOMIP-CC approach with SOC included only in the EOM step are not size-intensive. Time-reversal symmetry and spatial symmetry are exploited for D(2h) and its subgroups to reduce computational effort. All these approaches have been shown to be able to afford acceptable estimates for SOC splittings. The EOMIP-CCSD with SOC included only in the EOM step can provide reasonable IPs for systems containing up to 5th row elements. On the other hand, the EOMIP-CCS approach with SOC included in both CC and EOM steps could not predict a bounded (2)∑(g) (+) state for I(2) (+) and should be used with care.