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Title: Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

Abstract

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

Authors:
ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry, Kenneth S. Pitzer Center for Theoretical Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Div.
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1779239
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 16; Journal Issue: 3; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Hait, Diptarka, and Head-Gordon, Martin. Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory. United States: N. p., 2020. Web. doi:10.1021/acs.jctc.9b01127.
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Hait, Diptarka, & Head-Gordon, Martin. Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory. United States. https://doi.org/10.1021/acs.jctc.9b01127
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Hait, Diptarka, and Head-Gordon, Martin. Tue . "Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory". United States. https://doi.org/10.1021/acs.jctc.9b01127. https://www.osti.gov/servlets/purl/1779239.
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@article{osti_1779239,
title = {Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory},
author = {Hait, Diptarka and Head-Gordon, Martin},
abstractNote = {We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.},
doi = {10.1021/acs.jctc.9b01127},
journal = {Journal of Chemical Theory and Computation},
number = 3,
volume = 16,
place = {United States},
year = {Tue Feb 04 00:00:00 EST 2020},
month = {Tue Feb 04 00:00:00 EST 2020}
}
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An Efficient Variational Principle for the Direct Optimization of Excited States
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  • Zhao, Luning; Neuscamman, Eric
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 8
  • DOI: 10.1021/acs.jctc.6b00508

Reference Energies for Double Excitations
journal, January 2019

  • Loos, Pierre-François; Boggio-Pasqua, Martial; Scemama, Anthony
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 3
  • DOI: 10.1021/acs.jctc.8b01205

Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
journal, January 2005

  • Weigend, Florian; Ahlrichs, Reinhart
  • Physical Chemistry Chemical Physics, Vol. 7, Issue 18, p. 3297-3305
  • DOI: 10.1039/b508541a

Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations
journal, January 2019

  • Hait, Diptarka; Rettig, Adam; Head-Gordon, Martin
  • Physical Chemistry Chemical Physics, Vol. 21, Issue 39
  • DOI: 10.1039/c9cp04452c

Excitation energies in density functional theory: An evaluation and a diagnostic test
journal, January 2008

  • Peach, Michael J. G.; Benfield, Peter; Helgaker, Trygve
  • The Journal of Chemical Physics, Vol. 128, Issue 4
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Communication: Adjusting charge transfer state energies for configuration interaction singles: Without any parameterization and with minimal cost
journal, April 2012

  • Liu, Xinle; Fatehi, Shervin; Shao, Yihan
  • The Journal of Chemical Physics, Vol. 136, Issue 16
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Excitation energies and Stokes shifts from a restricted open-shell Kohn-Sham approach
journal, April 2013

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A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches
journal, April 2014

  • Sharada, Shaama Mallikarjun; Bell, Alexis T.; Head-Gordon, Martin
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Non-orthogonal configuration interaction with single substitutions for the calculation of core-excited states
journal, July 2018

  • Oosterbaan, Katherine J.; White, Alec F.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 149, Issue 4
  • DOI: 10.1063/1.5023051

Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ω B97M(2) double hybrid density functional
journal, June 2018

  • Mardirossian, Narbe; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 148, Issue 24
  • DOI: 10.1063/1.5025226

Lack of Hohenberg-Kohn Theorem for Excited States
journal, October 2004

A generalized variational principle with applications to excited state mean field theory
preprint, January 2019

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals [Supplemental Data]
fileset, June 2017

  • Head-Gordon, Martin; Mardirossian, Narbe
  • figshare-Supplementary information for journal article at DOI: 10.1080/00268976.2017.1333644, 10 files
  • DOI: 10.6084/m9.figshare.5132923

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals [Supplemental Data]
fileset, June 2017

  • Head-Gordon, Martin; Mardirossian, Narbe
  • figshare-Supplementary information for journal article at DOI: 10.1080/00268976.2017.1333644, 10 files
  • DOI: 10.6084/m9.figshare.5132923
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    An Overview of Self-Consistent Field Calculations Within Finite Basis Sets
    journal, March 2020

    An overview of self-consistent field calculations within finite basis sets
    text, January 2019

    An Overview of Self-Consistent Field Calculations Within Finite Basis Sets
    journal, March 2020

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