Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling

ABSTRACT

Development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) together with pilot applications are reported. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. To demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO${}^{+}$ is reported.

GRAPHICAL ABSTRACT

KEYWORDS:

• Relativistic effects
• exact two-component theory
• spin–orbit coupling
• actinide spectroscopy
• mean field spin orbit approach

Acknowledgments

Lan Cheng would like to thank Jürgen Gauss for his support and many stimulating discussions. This work has been supported by the Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0020317. All computations in this work were carried out using Maryland Advanced Research Computing Center (MARCC).

Disclosure statement

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

Additional information

Funding

This work has been supported by the Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0020317.