Treating spin-orbit coupling at different levels in equation-of-motion coupled-cluster calculations

ABSTRACT

Spin–orbit coupling (SOC) in EOM-CCSD calculations can be treated in SCF step (SOC-EOM-CCSD), in both the CCSD and EOM steps (EOM-CCSD(SOC)), only in the EOM step (EOM(SOC)-CCSD) or perturbatively (pSOC-EOM-CCSD). In this work, we report implementation of pSOC-EOM-CCSD based on the EOM(SOC)-CCSD program by directly calculating the SOC matrix between two states without using the transition density matrix. Computational cost of pSOC-EOM-CCSD can be further reduced particularly for excited states by using only the r-amplitudes (rpSOC-EOM-CCSD). Accuracy of EOM-CCSD(SOC) is evaluated by comparing its results with those of SOC-EOM-CCSD for heavy and superheavy elements. Highly accurate results are obtained with EOM-CCSD(SOC) for elements up to the sixth-row, and reasonable results are achieved for superheavy elements when contribution of the 7p_1/2 spinor to the involved occupied orbitals is insignificant. Performance of EOM(SOC)-CCSD, and (r)pSOC-EOM-CCSD is investigated by comparing their results with those of EOM-CCSD(SOC). According to our results, EOM(SOC)-CCSD is not necessarily more accurate than the perturbative methods and should not be used. Difference between rpSOC-EOM-CCSD and pSOC-EOM-CCSD is small and rpSOC-EOM-CCSD is an economical and reliable method in treating SOC effects particularly for excited states for systems containing elements up to the fifth row.

GRAPHICAL ABSTRACT

KEYWORDS:

• Equation-of-motion coupled-cluster theory
• spin-orbit coupling
• relativistic effects

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 21973063 and 21703020].