skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations

Abstract

Linear response time dependent density functional theory (TDDFT), which builds upon configuration interaction singles (CIS) and TD-Hartree–Fock (TDHF), is the most widely used class of excited state quantum chemistry methods and is often employed to study photochemical processes. This paper studies the behavior of the resulting excited state potential energy surfaces beyond the Coulson–Fischer (CF) point in single bond dissociations, when the optimal reference determinant is spin-polarized. Many excited states exhibit sharp kinks at the CF point, and connect to different dissociation limits via a zone of unphysical concave curvature. In particular, the unrestricted MS = 0 lowest triplet T1 state changes character, and does not dissociate into ground state fragments. The unrestricted MS = ±1 T1 CIS states better approximate the physical dissociation limit, but their degeneracy is broken beyond the CF point for most single bond dissociations. On the other hand, the MS = ±1 T1 TDHF states reach the asymptote too soon, by merging with the ground state from the CF point onwards. Use of local exchange–correlation functionals causes MS = ±1 T1 TDDFT states to resemble their unphysical MS = 0 counterpart. The 2 orbital, 2-electron model system of minimal basis H2 is analytically treated tomore » understand the origin of these issues, revealing that the lack of double excitations is at the root of these remarkable observations. In conclusion, the behavior of excited state surfaces is also numerically examined for species like H2, NH3, C2H6 and LiH in extended basis sets.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Univ. of California, Berkeley, CA (United States). Kenneth S. Pitzer Center for Theoretical Chemistry
  2. Univ. of California, Berkeley, CA (United States). Kenneth S. Pitzer Center for Theoretical Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1605256
Alternate Identifier(s):
OSTI ID: 1566251
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Chemistry Chemical Physics. PCCP (Print)
Additional Journal Information:
Journal Name: Physical Chemistry Chemical Physics. PCCP (Print); Journal Volume: 21; Journal Issue: 39; Journal ID: ISSN 1463-9076
Publisher:
Royal Society of Chemistry
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Hait, Diptarka, Rettig, Adam, and Head-Gordon, Martin. Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations. United States: N. p., 2019. Web. https://doi.org/10.1039/c9cp04452c.
Hait, Diptarka, Rettig, Adam, & Head-Gordon, Martin. Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations. United States. https://doi.org/10.1039/c9cp04452c
Hait, Diptarka, Rettig, Adam, and Head-Gordon, Martin. Thu . "Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations". United States. https://doi.org/10.1039/c9cp04452c. https://www.osti.gov/servlets/purl/1605256.
@article{osti_1605256,
title = {Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations},
author = {Hait, Diptarka and Rettig, Adam and Head-Gordon, Martin},
abstractNote = {Linear response time dependent density functional theory (TDDFT), which builds upon configuration interaction singles (CIS) and TD-Hartree–Fock (TDHF), is the most widely used class of excited state quantum chemistry methods and is often employed to study photochemical processes. This paper studies the behavior of the resulting excited state potential energy surfaces beyond the Coulson–Fischer (CF) point in single bond dissociations, when the optimal reference determinant is spin-polarized. Many excited states exhibit sharp kinks at the CF point, and connect to different dissociation limits via a zone of unphysical concave curvature. In particular, the unrestricted MS = 0 lowest triplet T1 state changes character, and does not dissociate into ground state fragments. The unrestricted MS = ±1 T1 CIS states better approximate the physical dissociation limit, but their degeneracy is broken beyond the CF point for most single bond dissociations. On the other hand, the MS = ±1 T1 TDHF states reach the asymptote too soon, by merging with the ground state from the CF point onwards. Use of local exchange–correlation functionals causes MS = ±1 T1 TDDFT states to resemble their unphysical MS = 0 counterpart. The 2 orbital, 2-electron model system of minimal basis H2 is analytically treated to understand the origin of these issues, revealing that the lack of double excitations is at the root of these remarkable observations. In conclusion, the behavior of excited state surfaces is also numerically examined for species like H2, NH3, C2H6 and LiH in extended basis sets.},
doi = {10.1039/c9cp04452c},
journal = {Physical Chemistry Chemical Physics. PCCP (Print)},
number = 39,
volume = 21,
place = {United States},
year = {2019},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM)
journal, December 2008

  • Gilbert, Andrew T. B.; Besley, Nicholas A.; Gill, Peter M. W.
  • The Journal of Physical Chemistry A, Vol. 112, Issue 50
  • DOI: 10.1021/jp801738f

Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number
journal, October 2018


Troubleshooting time-dependent density-functional theory for photochemical applications: Oxirane
journal, October 2007

  • Cordova, Felipe; Doriol, L. Joubert; Ipatov, Andrei
  • The Journal of Chemical Physics, Vol. 127, Issue 16
  • DOI: 10.1063/1.2786997

A long-range-corrected time-dependent density functional theory
journal, May 2004

  • Tawada, Yoshihiro; Tsuneda, Takao; Yanagisawa, Susumu
  • The Journal of Chemical Physics, Vol. 120, Issue 18
  • DOI: 10.1063/1.1688752

Reliable Prediction with Tuned Range-Separated Functionals of the Singlet–Triplet Gap in Organic Emitters for Thermally Activated Delayed Fluorescence
journal, July 2015

  • Sun, Haitao; Zhong, Cheng; Brédas, Jean-Luc
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 8
  • DOI: 10.1021/acs.jctc.5b00431

Holomorphic Hartree–Fock Theory: An Inherently Multireference Approach
journal, December 2015

  • Burton, Hugh G. A.; Thom, Alex J. W.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 1
  • DOI: 10.1021/acs.jctc.5b01005

Non-orthogonal configuration interaction for the calculation of multielectron excited states
journal, March 2014

  • Sundstrom, Eric J.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 140, Issue 11
  • DOI: 10.1063/1.4868120

Second‐order perturbation theory with a complete active space self‐consistent field reference function
journal, January 1992

  • Andersson, Kerstin; Malmqvist, Per‐Åke; Roos, Björn O.
  • The Journal of Chemical Physics, Vol. 96, Issue 2
  • DOI: 10.1063/1.462209

Double excitations within time-dependent density functional theory linear response
journal, April 2004

  • Maitra, Neepa T.; Zhang, Fan; Cave, Robert J.
  • The Journal of Chemical Physics, Vol. 120, Issue 13
  • DOI: 10.1063/1.1651060

How Accurate Is Density Functional Theory at Predicting Dipole Moments? An Assessment Using a New Database of 200 Benchmark Values
journal, March 2018

  • Hait, Diptarka; Head-Gordon, Martin
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 4
  • DOI: 10.1021/acs.jctc.7b01252

Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory
journal, July 1996


Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
journal, December 1982


Stability conditions and nuclear rotations in the Hartree-Fock theory
journal, November 1960


Communication: Configuration interaction singles has a large systematic bias against charge-transfer states
journal, August 2011

  • Subotnik, Joseph E.
  • The Journal of Chemical Physics, Vol. 135, Issue 7
  • DOI: 10.1063/1.3627152

Self‐consistent molecular orbital methods. XVIII. Constraints and stability in Hartree–Fock theory
journal, April 1977

  • Seeger, Rolf; Pople, John A.
  • The Journal of Chemical Physics, Vol. 66, Issue 7
  • DOI: 10.1063/1.434318

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


Toward a systematic molecular orbital theory for excited states
journal, January 1992

  • Foresman, James B.; Head-Gordon, Martin; Pople, John A.
  • The Journal of Physical Chemistry, Vol. 96, Issue 1
  • DOI: 10.1021/j100180a030

Constrained Density Functional Theory
journal, November 2011

  • Kaduk, Benjamin; Kowalczyk, Tim; Van Voorhis, Troy
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200148b

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


Conical intersections and double excitations in time-dependent density functional theory
journal, March 2006

  • Levine, Benjamin G.; Ko, Chaehyuk; Quenneville, Jason
  • Molecular Physics, Vol. 104, Issue 5-7
  • DOI: 10.1080/00268970500417762

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals
journal, April 2017


Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules
journal, November 2005

  • Dreuw, Andreas; Head-Gordon, Martin
  • Chemical Reviews, Vol. 105, Issue 11
  • DOI: 10.1021/cr0505627

A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach
journal, May 1980


Generalized Kohn-Sham schemes and the band-gap problem
journal, February 1996


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
  • DOI: 10.1063/1.2831900

Excited-State Electronic Structure with Configuration Interaction Singles and Tamm–Dancoff Time-Dependent Density Functional Theory on Graphical Processing Units
journal, May 2011

  • Isborn, Christine M.; Luehr, Nathan; Ufimtsev, Ivan S.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 6
  • DOI: 10.1021/ct200030k

Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals
journal, September 1969

  • Hehre, W. J.; Stewart, R. F.; Pople, J. A.
  • The Journal of Chemical Physics, Vol. 51, Issue 6
  • DOI: 10.1063/1.1672392

A long-range correction scheme for generalized-gradient-approximation exchange functionals
journal, August 2001

  • Iikura, Hisayoshi; Tsuneda, Takao; Yanai, Takeshi
  • The Journal of Chemical Physics, Vol. 115, Issue 8
  • DOI: 10.1063/1.1383587

How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry
journal, January 2018

  • Hait, Diptarka; Head-Gordon, Martin
  • Physical Chemistry Chemical Physics, Vol. 20, Issue 30
  • DOI: 10.1039/C8CP03569E

Many-electron self-interaction error in approximate density functionals
journal, November 2006

  • Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
  • The Journal of Chemical Physics, Vol. 125, Issue 20
  • DOI: 10.1063/1.2403848

Density-Functional Theory for Time-Dependent Systems
journal, March 1984


Toward reliable density functional methods without adjustable parameters: The PBE0 model
journal, April 1999

  • Adamo, Carlo; Barone, Vincenzo
  • The Journal of Chemical Physics, Vol. 110, Issue 13
  • DOI: 10.1063/1.478522

Hartree–Fock solutions as a quasidiabatic basis for nonorthogonal configuration interaction
journal, September 2009

  • Thom, Alex J. W.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 131, Issue 12
  • DOI: 10.1063/1.3236841

Inhomogeneous Electron Gas
journal, November 1964


A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions
journal, January 2017

  • Goerigk, Lars; Hansen, Andreas; Bauer, Christoph
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 48
  • DOI: 10.1039/C7CP04913G

Prediction of Excited-State Energies and Singlet–Triplet Gaps of Charge-Transfer States Using a Restricted Open-Shell Kohn–Sham Approach
journal, June 2016

  • Hait, Diptarka; Zhu, Tianyu; McMahon, David P.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 7
  • DOI: 10.1021/acs.jctc.6b00426

Failure of time-dependent density functional theory for excited state surfaces in case of homolytic bond dissociation
journal, August 2008


On the calculation of Δ S ˆ 2 for electronic excitations in time-dependent density-functional theory
journal, April 2017


Overcoming Low Orbital Overlap and Triplet Instability Problems in TDDFT
journal, September 2012

  • Peach, Michael J. G.; Tozer, David J.
  • The Journal of Physical Chemistry A, Vol. 116, Issue 39
  • DOI: 10.1021/jp308662x

Time-dependent density functional theory within the Tamm–Dancoff approximation
journal, December 1999


Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration
journal, October 2013

  • Cui, Yao; Bulik, Ireneusz W.; Jiménez-Hoyos, Carlos A.
  • The Journal of Chemical Physics, Vol. 139, Issue 15
  • DOI: 10.1063/1.4824905

XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule
journal, April 1949

  • Coulson, C. A.; Fischer, I.
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 303
  • DOI: 10.1080/14786444908521726

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

Stability analysis for solutions of the closed shell Kohn–Sham equation
journal, June 1996

  • Bauernschmitt, Rüdiger; Ahlrichs, Reinhart
  • The Journal of Chemical Physics, Vol. 104, Issue 22
  • DOI: 10.1063/1.471637

Influence of Triplet Instabilities in TDDFT
journal, October 2011

  • Peach, Michael J. G.; Williamson, Matthew J.; Tozer, David J.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 11
  • DOI: 10.1021/ct200651r

Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H 2
journal, March 2019

  • Hait, Diptarka; Rettig, Adam; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 150, Issue 9
  • DOI: 10.1063/1.5080122

Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange
journal, August 2003

  • Dreuw, Andreas; Weisman, Jennifer L.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 119, Issue 6
  • DOI: 10.1063/1.1590951

A doubles correction to electronic excited states from configuration interaction in the space of single substitutions
journal, March 1994


The second-order approximate coupled cluster singles and doubles model CC2
journal, September 1995


Time-Dependent Density Functional Theory
journal, June 2004


Configuration interaction based on constrained density functional theory: A multireference method
journal, October 2007

  • Wu, Qin; Cheng, Chiao-Lun; Van Voorhis, Troy
  • The Journal of Chemical Physics, Vol. 127, Issue 16
  • DOI: 10.1063/1.2800022

Inhomogeneous Electron Gas
journal, March 1973