Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

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]
+ Show Author Affiliations
  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.
Copy to clipboard
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
Copy to clipboard
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.
Copy to clipboard
@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 = {Mon Jul 15 00:00:00 EDT 2019},
month = {Mon Jul 15 00:00:00 EDT 2019}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5108762
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 37 works
Citation information provided by
Web of Science

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
All figures and tables (9 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

DFT spin–orbit coupling between singlet and triplet excited states: A case of psoralen compounds
journal, April 2010

Multireference coupled-cluster theory: The easy way
journal, March 2011

  • Musiał, Monika; Perera, Ajith; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 134, Issue 11
  • DOI: 10.1063/1.3567115

Molecular Electronic-Structure Theory
book, August 2000

On the Origin of Spin‐Hamiltonian Parameters
journal, March 1965

  • McWeeny, R.
  • The Journal of Chemical Physics, Vol. 42, Issue 5
  • DOI: 10.1063/1.1696183

Charge localization and Jahn–Teller distortions in the benzene dimer cation
journal, August 2008

  • Pieniazek, Piotr A.; Bradforth, Stephen E.; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 129, Issue 7
  • DOI: 10.1063/1.2969107

An extension of the coupled cluster formalism to excited states (I)
journal, January 1981

A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: Application to transition metal L-edge X-ray absorption spectroscopy
journal, May 2013

  • Roemelt, Michael; Maganas, Dimitrios; DeBeer, Serena
  • The Journal of Chemical Physics, Vol. 138, Issue 20
  • DOI: 10.1063/1.4804607

First-principles calculations of zero-field splitting parameters
journal, July 2006

  • Ganyushin, Dmitry; Neese, Frank
  • The Journal of Chemical Physics, Vol. 125, Issue 2
  • DOI: 10.1063/1.2213976

An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling
journal, April 2018

  • Liu, Junzi; Cheng, Lan
  • The Journal of Chemical Physics, Vol. 148, Issue 14
  • DOI: 10.1063/1.5023750

A mean-field spin-orbit method applicable to correlated wavefunctions
journal, March 1996

Resolving the Notorious Case of Conical Intersections for Coupled Cluster Dynamics
journal, September 2017

Ab Initio Potential Energy Surface and Vibrational−Rotational Energy Levels of X 2 Σ + CaOH
journal, October 2002

  • Koput, Jacek; Peterson, Kirk A.
  • The Journal of Physical Chemistry A, Vol. 106, Issue 41
  • DOI: 10.1021/jp026283u

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
journal, September 2014

Tools for Predicting the Nature and Magnitude of Magnetic Anisotropy in Transition Metal Complexes: Application to Co(II) Complexes
journal, August 2016

Triplet state. Its radiative and nonradiative properties
journal, January 1968

Calculation of electronic g-tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin-orbit operators
journal, April 2002

  • Kaupp, Martin; Reviakine, Roman; Malkina, Olga L.
  • Journal of Computational Chemistry, Vol. 23, Issue 8
  • DOI: 10.1002/jcc.10049

First principles approach to the electronic structure, magnetic anisotropy and spin relaxation in mononuclear 3d-transition metal single molecule magnets
journal, April 2015

  • Atanasov, Mihail; Aravena, Daniel; Suturina, Elizaveta
  • Coordination Chemistry Reviews, Vol. 289-290
  • DOI: 10.1016/j.ccr.2014.10.015

Internal and external heavy-atom effects on phosphorescence radiative lifetimes calculated using a mean-field spin–orbit Hamiltonian
journal, August 1999

New implementation of high-level correlated methods using a general block tensor library for high-performance electronic structure calculations
journal, July 2013

  • Epifanovsky, Evgeny; Wormit, Michael; Kuś, Tomasz
  • Journal of Computational Chemistry, Vol. 34, Issue 26
  • DOI: 10.1002/jcc.23377

Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods
journal, January 2018

  • Faraji, Shirin; Matsika, Spiridoula; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 148, Issue 4
  • DOI: 10.1063/1.5009433

Stability of polyatomic molecules in degenerate electronic states - I—Orbital degeneracy
journal, July 1937

  • Jahn, H. A.; Teller, E.
  • Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 161, Issue 905, p. 220-235
  • DOI: 10.1098/rspa.1937.0142

Spin-Vibronic Mechanism for Intersystem Crossing
journal, March 2018

Can coupled-cluster theory treat conical intersections?
journal, July 2007

  • Köhn, Andreas; Tajti, Attila
  • The Journal of Chemical Physics, Vol. 127, Issue 4
  • DOI: 10.1063/1.2755681

Equation of motion coupled cluster method for electron attachment
journal, March 1995

  • Nooijen, Marcel; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 102, Issue 9
  • DOI: 10.1063/1.468592

Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals
journal, January 2018

  • Liu, Junzi; Shen, Yue; Asthana, Ayush
  • The Journal of Chemical Physics, Vol. 148, Issue 3
  • DOI: 10.1063/1.5009177

Analytic evaluation of the nonadiabatic coupling vector between excited states using equation-of-motion coupled-cluster theory
journal, September 2009

  • Tajti, Attila; Szalay, Péter G.
  • The Journal of Chemical Physics, Vol. 131, Issue 12
  • DOI: 10.1063/1.3232011

Spin-orbit multireference multistate perturbation theory
journal, September 2001

Advanced aspects of ab initio theoretical optical spectroscopy of transition metal complexes: Multiplets, spin-orbit coupling and resonance Raman intensities
journal, February 2007

  • Neese, Frank; Petrenko, Taras; Ganyushin, Dmitry
  • Coordination Chemistry Reviews, Vol. 251, Issue 3-4
  • DOI: 10.1016/j.ccr.2006.05.019

Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to g-tensors
journal, July 2015

  • Roemelt, Michael
  • The Journal of Chemical Physics, Vol. 143, Issue 4
  • DOI: 10.1063/1.4927432

Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton
journal, April 1999

  • Wilson, Angela K.; Woon, David E.; Peterson, Kirk A.
  • The Journal of Chemical Physics, Vol. 110, Issue 16
  • DOI: 10.1063/1.478678

Magnetic Interactions in Molecules and Highly Correlated Materials: Physical Content, Analytical Derivation, and Rigorous Extraction of Magnetic Hamiltonians
journal, September 2013

  • Malrieu, Jean Paul; Caballol, Rosa; Calzado, Carmen J.
  • Chemical Reviews, Vol. 114, Issue 1
  • DOI: 10.1021/cr300500z

The coupled-cluster revolution
journal, November 2010

Spin-Forbidden Channels in Reactions of Unsaturated Hydrocarbons with O( 3 P)
journal, December 2018

  • Pokhilko, Pavel; Shannon, Robin; Glowacki, David
  • The Journal of Physical Chemistry A, Vol. 123, Issue 2
  • DOI: 10.1021/acs.jpca.8b10225

Spin-orbit coupling in molecules: Chemistry beyond the adiabatic approximation
journal, July 2003

  • Fedorov, Dmitri G.; Koseki, Shiro; Schmidt, Michael W.
  • International Reviews in Physical Chemistry, Vol. 22, Issue 3
  • DOI: 10.1080/0144235032000101743

Magnetic anisotropy barrier for spin tunneling in Mn 12 O 12 molecules
journal, October 1999

Spin-orbit coupling and intersystem crossing in molecules: Spin-orbit coupling
journal, July 2011

  • Marian, Christel M.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2
  • DOI: 10.1002/wcms.83

Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method
journal, November 1994

  • Stanton, John F.; Gauss, Jürgen
  • The Journal of Chemical Physics, Vol. 101, Issue 10
  • DOI: 10.1063/1.468022

Termstruktur und Zeemaneffekt der Multipletts
journal, December 1923

Spin-orbit coupling constants from coupled-cluster response theory
journal, January 2000

  • Christiansen, Ove; Gauss, Jürgen; Schimmelpfennig, Bernd
  • Physical Chemistry Chemical Physics, Vol. 2, Issue 5
  • DOI: 10.1039/a908995k

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations
journal, August 2015

  • Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella
  • The Journal of Chemical Physics, Vol. 143, Issue 6
  • DOI: 10.1063/1.4927785

Termstruktur und Zeemaneffekt der Multipletts
journal, December 1923

Computation of one and two electron spin-orbit integrals
journal, October 1988

  • King, Harry F.; Furlani, Thomas R.
  • Journal of Computational Chemistry, Vol. 9, Issue 7
  • DOI: 10.1002/jcc.540090707

Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations
journal, December 2011

  • Helgaker, Trygve; Coriani, Sonia; Jørgensen, Poul
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr2002239

Jahn–Teller distortions in the electronically excited states of sym -triazine
journal, April 2009

Combining spin-adapted open-shell TD-DFT with spin–orbit coupling
journal, December 2013

Excited state coupled cluster methods: Excited state coupled cluster methods
journal, November 2011

  • Sneskov, Kristian; Christiansen, Ove
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 4
  • DOI: 10.1002/wcms.99

Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc–Zn
journal, August 2005

  • Balabanov, Nikolai B.; Peterson, Kirk A.
  • The Journal of Chemical Physics, Vol. 123, Issue 6
  • DOI: 10.1063/1.1998907

A study of the relative importance of one and two-electron contributions to spin–orbit coupling
journal, April 2000

  • Fedorov, Dmitri G.; Gordon, Mark S.
  • The Journal of Chemical Physics, Vol. 112, Issue 13
  • DOI: 10.1063/1.481136

Conical and glancing Jahn-Teller intersections in the cyclic trinitrogen cation
journal, June 2006

  • Mozhayskiy, Vadim A.; Babikov, Dmitri; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 124, Issue 22
  • DOI: 10.1063/1.2204602

Quantum computing in molecular magnets
journal, April 2001

  • Leuenberger, Michael N.; Loss, Daniel
  • Nature, Vol. 410, Issue 6830
  • DOI: 10.1038/35071024

Electronic structure of the 1,3,5-tridehydrobenzene triradical in its ground and excited states
journal, June 2003

  • Slipchenko, Lyudmila V.; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 118, Issue 21
  • DOI: 10.1063/1.1569845

Perturbative calculation of spin-orbit splittings using the equation-of-motion ionization-potential coupled-cluster ansatz
journal, November 2008

  • Klein, Kerstin; Gauss, Jürgen
  • The Journal of Chemical Physics, Vol. 129, Issue 19
  • DOI: 10.1063/1.3013199

Spin-forbidden chemistry within the Breit-Pauli approximation
journal, September 1992

Q-Chem: an engine for innovation: Q-Chem: an engine for innovation
journal, November 2012

  • Krylov, Anna I.; Gill, Peter M. W.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 3
  • DOI: 10.1002/wcms.1122

Quantum Mechanics of One- and Two-Electron Atoms
book, January 1957

Zero-field splittings from density functional calculations: Analysis and improvement of known methods
journal, May 2011

  • Schmitt, Sebastian; Jost, Patrick; van Wüllen, Christoph
  • The Journal of Chemical Physics, Vol. 134, Issue 19
  • DOI: 10.1063/1.3590362

Slow Magnetic Relaxation in a High-Spin Iron(II) Complex
journal, February 2010

  • Freedman, Danna E.; Harman, W. Hill; Harris, T. David
  • Journal of the American Chemical Society, Vol. 132, Issue 4
  • DOI: 10.1021/ja909560d

First-principles calculations of magnetic circular dichroism spectra
journal, March 2008

  • Ganyushin, Dmitry; Neese, Frank
  • The Journal of Chemical Physics, Vol. 128, Issue 11
  • DOI: 10.1063/1.2894297

General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: Theory, implementation, and benchmarks
journal, May 2012

  • Bernard, Yves A.; Shao, Yihan; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 136, Issue 20
  • DOI: 10.1063/1.4714499

Coupled-cluster theory and its equation-of-motion extensions: Coupled-cluster theory
journal, July 2011

  • Bartlett, Rodney J.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 1
  • DOI: 10.1002/wcms.76

Spin–orbit coupling constants in a multiconfiguration linear response approach
journal, February 1992

  • Vahtras, Olav; Ågren, Hans; Jo/rgensen, Poul
  • The Journal of Chemical Physics, Vol. 96, Issue 3
  • DOI: 10.1063/1.462063

Spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions
journal, November 2000

  • Berning, Andreas; Schweizer, Marcus; Werner, Hans-Joachim
  • Molecular Physics, Vol. 98, Issue 21
  • DOI: 10.1080/00268970009483386

Relativistic quantum chemistry: the multiconfigurational approach
journal, January 2004

  • Roos, Bj�rn O.; Malmqvist, Per-�ke
  • Physical Chemistry Chemical Physics, Vol. 6, Issue 11
  • DOI: 10.1039/b401472n

Double spin-flip approach within equation-of-motion coupled cluster and configuration interaction formalisms: Theory, implementation, and examples
journal, January 2009

  • Casanova, David; Slipchenko, Lyudmila V.; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 130, Issue 4
  • DOI: 10.1063/1.3066652

Theory of spin‐orbit coupling. Application to singlet–triplet interaction in the trimethylene biradical
journal, June 1985

  • Furlani, Thomas R.; King, Harry F.
  • The Journal of Chemical Physics, Vol. 82, Issue 12
  • DOI: 10.1063/1.448967

Analytic gradients for the spin-conserving and spin-flipping equation-of-motion coupled-cluster models with single and double substitutions
journal, June 2005

  • Levchenko, Sergey V.; Wang, Tao; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 122, Issue 22
  • DOI: 10.1063/1.1877072

Use of 2h and 3h−p-like coupled-cluster Tamm–Dancoff approaches for the equilibrium properties of ozone
journal, August 2003

  • Sattelmeyer, Kurt W.; Schaefer III, Henry F.; Stanton, John F.
  • Chemical Physics Letters, Vol. 378, Issue 1-2
  • DOI: 10.1016/s0009-2614(03)01181-3

Spin-orbit coupling in the first and second transition series
journal, January 1961

Einige Folgerungen aus der Schr�dingerschen Theorie f�r die Termstrukturen
journal, July 1927

Direct Observation of Quantum Coherence in Single-Molecule Magnets
text, January 2008

Quantum Computing in Molecular Magnets
text, January 2000

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Spin-flip methods in quantum chemistry
    journal, January 2020

    • Casanova, David; Krylov, Anna I.
    • Physical Chemistry Chemical Physics, Vol. 22, Issue 8
    • DOI: 10.1039/c9cp06507e

    Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets
    journal, January 2020

    • Pokhilko, Pavel; Izmodenov, Daniil; Krylov, Anna I.
    • The Journal of Chemical Physics, Vol. 152, Issue 3
    • DOI: 10.1063/1.5138643
      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      FIG. 1 (p. 7)figure
      FIG. 2 (p. 9)figure
      TABLE I (p. 9)table
      TABLE II (p. 9)table
      FIG. 3 (p. 10)figure
      TABLE III (p. 10)table
      TABLE IV (p. 10)table
      TABLE V (p. 11)table
      TABLE VI (p. 11)table
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: