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Title: 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

Abstract

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner–Eckart’s theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin–orbit matrix elements by applying Wigner–Eckart’s theorem to a reduced one-particle transition density matrix computed for a single multiplet component. 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 calculation of spin–orbit couplings using equation-of-motion coupled-cluster wave functions are 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.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Univ. of Southern California, Los Angeles, CA (United States)
  2. Q-Chem, Inc., Pleasanton, CA (United States)
  3. Univ. of Southern California, Los Angeles, CA (United States); Johannes Gutenberg Univ., Mainz (Germany)
Publication Date:
Research Org.:
Univ. of Southern California, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1613024
Alternate Identifier(s):
OSTI ID: 1542533
Grant/Contract Number:  
SC0018910
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 3; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Chemistry; Physics; Magnetic materials; Relativistic effects; Transition metals; Coupled-cluster methods; Wigner-Eckart theorem; Density-matrix

Citation Formats

Pokhilko, Pavel, Epifanovsky, Evgeny, and Krylov, Anna I. 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. United States: N. p., 2019. Web. doi:10.1063/1.5108762.
Pokhilko, Pavel, Epifanovsky, Evgeny, & Krylov, Anna I. 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. United States. https://doi.org/10.1063/1.5108762
Pokhilko, Pavel, Epifanovsky, Evgeny, and Krylov, Anna I. Mon . "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". United States. https://doi.org/10.1063/1.5108762. https://www.osti.gov/servlets/purl/1613024.
@article{osti_1613024,
title = {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},
author = {Pokhilko, Pavel and Epifanovsky, Evgeny and Krylov, Anna I.},
abstractNote = {Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner–Eckart’s theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin–orbit matrix elements by applying Wigner–Eckart’s theorem to a reduced one-particle transition density matrix computed for a single multiplet component. 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 calculation of spin–orbit couplings using equation-of-motion coupled-cluster wave functions are 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.},
doi = {10.1063/1.5108762},
journal = {Journal of Chemical Physics},
number = 3,
volume = 151,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
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Cited by: 9 works
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Figures / Tables:

FIG. 1 FIG. 1: The workflow of the present algorithm (shown by green arrows), Fedorov’s scheme (red arrows), and the approach implemented in Molcas (blue arrows). Here, the WE label denotes the application of Wigner–Eckart’s theorem. In our scheme, we start from one transition density matrix, extract the triplet part, construct themore » spinless density, and then form three reduced matrix elements. In the Molcas scheme, the spinless transition density matrix is built directly from spin manifolds ||IS⟩ and ||I′S′⟩, also known as “tensor” states. In Fedorov’s scheme, the reduced matrix elements are computed from three matrix elements.« less

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