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General Framework for Calculating Spin–orbit Couplings Using Spinless One-Particle Density Matrices: Theory and Application to the Equation-of-Motion Coupled-Cluster Wave Functions

preprint
submitted on 01.05.2019 and posted on 03.05.2019 by Pavel Pokhilko, Evgeny Epifanovsky, Anna I. Krylov
Standard implementations of non-relativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms =0 triplets), however, matrix elements for all components are necessary for calculations of experimentally relevant spin-dependent quantities. To circumvent explicit calculations of all multiplet components, we employ Wigner–Eckart’s theorem. Applied to a reduced one-particle transition density matrix computed for a single multiplet component, Wigner–Eckart’s theorem generates all other spin–orbit matrix elements. In addition to computational efficiency, this approach also resolves the phase issue arising within Born–Oppenheimer’s separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculations of spin–orbit couplings using equation-of-motion coupled-cluster wave functions is presented. The two-electron contributions are included via the mean-field spin–orbit treatment. Intrinsic issues of constructing spin–orbit mean-field operators for open-shell references are discussed and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

Funding

DE-SC0018910

History

Email Address of Submitting Author

pokhilko@usc.edu

Institution

University of Southern California

Country

USA

ORCID For Submitting Author

0000-0001-5754-9836

Declaration of Conflict of Interest

No conflict of interest

Licence

Exports