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Title: Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

Abstract

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg (1997). This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H2O)6]2+ and [Fe(NH3)6]2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple-ζ basis set predicts the spin splittings of [Fe(H2O)6]2+ and [Fe(NH3)6]2+ to be –35.7 andmore » –17.1 kcal mol–1, respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Beijing Normal Univ., Beijing (China); Emory Univ., Atlanta, GA (United States)
  2. Emory Univ., Atlanta, GA (United States)
Publication Date:
Research Org.:
Emory Univ., Atlanta, GA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1852064
Grant/Contract Number:  
SC0016004
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 155; Journal Issue: 11; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; electronic correlation; chemical processes; energy economics; complete-active space self-consistent field; perturbation theory; diatomic molecule; geometrical optics; corrections; renormalization and regularization; coupled-cluster methods

Citation Formats

Li, Chenyang, and Evangelista, Francesco A. Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics. United States: N. p., 2021. Web. doi:10.1063/5.0059362.
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Li, Chenyang, & Evangelista, Francesco A. Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics. United States. https://doi.org/10.1063/5.0059362
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Li, Chenyang, and Evangelista, Francesco A. Mon . "Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics". United States. https://doi.org/10.1063/5.0059362. https://www.osti.gov/servlets/purl/1852064.
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@article{osti_1852064,
title = {Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics},
author = {Li, Chenyang and Evangelista, Francesco A.},
abstractNote = {We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg (1997). This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H2O)6]2+ and [Fe(NH3)6]2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple-ζ basis set predicts the spin splittings of [Fe(H2O)6]2+ and [Fe(NH3)6]2+ to be –35.7 and –17.1 kcal mol–1, respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.},
doi = {10.1063/5.0059362},
journal = {Journal of Chemical Physics},
number = 11,
volume = 155,
place = {United States},
year = {Mon Sep 20 00:00:00 EDT 2021},
month = {Mon Sep 20 00:00:00 EDT 2021}
}
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  • DOI: 10.1063/1.1867332

Spin–phonon coupling and dynamic zero-field splitting contributions to spin conversion processes in iron(II) complexes
journal, May 2020

  • Higdon, Nicholas J.; Barth, Alexandra T.; Kozlowski, Patryk T.
  • The Journal of Chemical Physics, Vol. 152, Issue 20
  • DOI: 10.1063/5.0006361

An exponential multireference wave-function Ansatz
journal, August 2005

  • Hanrath, Michael
  • The Journal of Chemical Physics, Vol. 123, Issue 8
  • DOI: 10.1063/1.1953407

Driven similarity renormalization group for excited states: A state-averaged perturbation theory
journal, March 2018

  • Li, Chenyang; Evangelista, Francesco A.
  • The Journal of Chemical Physics, Vol. 148, Issue 12
  • DOI: 10.1063/1.5019793

Benchmarks and Reliable DFT Results for Spin Gaps of Small Ligand Fe(II) Complexes
journal, March 2018

  • Song, Suhwan; Kim, Min-Cheol; Sim, Eunji
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 5
  • DOI: 10.1021/acs.jctc.7b01196

Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly
journal, May 2011

  • Hanauer, Matthias; Köhn, Andreas
  • The Journal of Chemical Physics, Vol. 134, Issue 20
  • DOI: 10.1063/1.3592786

Second-order perturbation theory with a CASSCF reference function
journal, July 1990

  • Andersson, Kerstin.; Malmqvist, Per Aake.; Roos, Bjoern O.
  • The Journal of Physical Chemistry, Vol. 94, Issue 14
  • DOI: 10.1021/j100377a012

Orthogonally spin‐adapted single‐reference coupled‐cluster formalism: Linear response calculation of static properties
journal, April 1995

  • Kondo, A. E.; Piecuch, P.; Paldus, J.
  • The Journal of Chemical Physics, Vol. 102, Issue 16
  • DOI: 10.1063/1.469365

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

Additional global internal contraction in variations of multireference equation of motion coupled cluster theory
journal, April 2013

  • Demel, Ondřej; Datta, Dipayan; Nooijen, Marcel
  • The Journal of Chemical Physics, Vol. 138, Issue 13
  • DOI: 10.1063/1.4796523

Basis-set convergence of correlated calculations on water
journal, June 1997

  • Helgaker, Trygve; Klopper, Wim; Koch, Henrik
  • The Journal of Chemical Physics, Vol. 106, Issue 23
  • DOI: 10.1063/1.473863

Accurate singlet–triplet gaps in biradicals via the spin averaged anti-Hermitian contracted Schrödinger equation
journal, April 2021

  • Boyn, Jan-Niklas; Mazziotti, David A.
  • The Journal of Chemical Physics, Vol. 154, Issue 13
  • DOI: 10.1063/5.0045007

Third-order multireference perturbation theory The CASPT3 method
journal, October 1996

Toward subchemical accuracy in computational thermochemistry: Focal point analysis of the heat of formation of NCO and [H,N,C,O] isomers
journal, June 2004

  • Schuurman, Michael S.; Muir, Steven R.; Allen, Wesley D.
  • The Journal of Chemical Physics, Vol. 120, Issue 24
  • DOI: 10.1063/1.1707013
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