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

Title: An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation

Abstract

The accurate prediction of singlet and triplet excitation energies is an area of intense research of significant fundamental interest and critical for many applications. Most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiel’s set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relative to higher level theories. Lastly, we find that BSE-TDA calculations built on effective DFT starting points, such as those utilizing optimally tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.

Authors:
 [1];  [1];  [2];  [3]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States); Univ. Paris-Saclay, Gif-sur-Yvette (France)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States); Kavli Energy Nanosciences Inst. at Berkeley, Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1543834
Alternate Identifier(s):
OSTI ID: 1361875
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 19; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Chemistry; Physics

Citation Formats

Rangel, Tonatiuh, Hamed, Samia M., Bruneval, Fabien, and Neaton, Jeffrey B. An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation. United States: N. p., 2017. Web. doi:10.1063/1.4983126.
Rangel, Tonatiuh, Hamed, Samia M., Bruneval, Fabien, & Neaton, Jeffrey B. An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation. United States. doi:10.1063/1.4983126.
Rangel, Tonatiuh, Hamed, Samia M., Bruneval, Fabien, and Neaton, Jeffrey B. Fri . "An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation". United States. doi:10.1063/1.4983126. https://www.osti.gov/servlets/purl/1543834.
@article{osti_1543834,
title = {An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation},
author = {Rangel, Tonatiuh and Hamed, Samia M. and Bruneval, Fabien and Neaton, Jeffrey B.},
abstractNote = {The accurate prediction of singlet and triplet excitation energies is an area of intense research of significant fundamental interest and critical for many applications. Most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiel’s set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relative to higher level theories. Lastly, we find that BSE-TDA calculations built on effective DFT starting points, such as those utilizing optimally tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.},
doi = {10.1063/1.4983126},
journal = {Journal of Chemical Physics},
number = 19,
volume = 146,
place = {United States},
year = {2017},
month = {5}
}

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

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Charge-Transfer-Like π→π* Excitations in Time-Dependent Density Functional Theory: A Conundrum and Its Solution
journal, July 2011

  • Kuritz, Natalia; Stein, Tamar; Baer, Roi
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 8
  • DOI: 10.1021/ct2002804

A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules
journal, June 2015

  • Bruneval, Fabien; Hamed, Samia M.; Neaton, Jeffrey B.
  • The Journal of Chemical Physics, Vol. 142, Issue 24
  • DOI: 10.1063/1.4922489

Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
journal, May 2016

  • Rangel, Tonatiuh; Hamed, Samia M.; Bruneval, Fabien
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 6
  • DOI: 10.1021/acs.jctc.6b00163

Recent Advances in Singlet Fission
journal, April 2013


Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues
journal, March 1985


Improving the TDDFT calculation of low-lying excited states for polycyclic aromatic hydrocarbons using the Tamm–Dancoff approximation
journal, January 2007

  • Wang, Yi-Lei; Wu, Guo-Shi
  • International Journal of Quantum Chemistry, Vol. 108, Issue 3
  • DOI: 10.1002/qua.21510

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of GW Methods
journal, January 2016

  • Knight, Joseph W.; Wang, Xiaopeng; Gallandi, Lukas
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 2
  • DOI: 10.1021/acs.jctc.5b00871

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


Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules II: Non-Empirically Tuned Long-Range Corrected Hybrid Functionals
journal, January 2016

  • Gallandi, Lukas; Marom, Noa; Rinke, Patrick
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 2
  • DOI: 10.1021/acs.jctc.5b00873

Origin and TDDFT Benchmarking of the Plasmon Resonance in Acenes
journal, October 2013

  • Guidez, Emilie B.; Aikens, Christine M.
  • The Journal of Physical Chemistry C, Vol. 117, Issue 41
  • DOI: 10.1021/jp4059033

A TDDFT study of the lowest excitation energies of polycyclic aromatic hydrocarbons
journal, July 2003


molgw 1: Many-body perturbation theory software for atoms, molecules, and clusters
journal, November 2016

  • Bruneval, Fabien; Rangel, Tonatiuh; Hamed, Samia M.
  • Computer Physics Communications, Vol. 208
  • DOI: 10.1016/j.cpc.2016.06.019

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

Application of the Green’s functions method to the study of the optical properties of semiconductors
journal, December 1988


Ab Initio Calculations of the Quasiparticle and Absorption Spectra of Clusters: The Sodium Tetramer
journal, July 1995


The Larger Acenes: Versatile Organic Semiconductors
journal, January 2008


Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory
journal, March 2009

  • Stein, Tamar; Kronik, Leeor; Baer, Roi
  • Journal of the American Chemical Society, Vol. 131, Issue 8
  • DOI: 10.1021/ja8087482

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


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

Fast and Accurate Electronic Excitations in Cyanines with the Many-Body Bethe–Salpeter Approach
journal, February 2014

  • Boulanger, Paul; Jacquemin, Denis; Duchemin, Ivan
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 3
  • DOI: 10.1021/ct401101u

A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes
journal, December 2009

  • Hajgató, B.; Szieberth, D.; Geerlings, P.
  • The Journal of Chemical Physics, Vol. 131, Issue 22
  • DOI: 10.1063/1.3270190

High Accuracy Many-Body Calculational Approaches for Excitations in Molecules
journal, January 2001


Singlet Exciton Fission Photovoltaics
journal, April 2013

  • Lee, Jiye; Jadhav, Priya; Reusswig, Philip D.
  • Accounts of Chemical Research, Vol. 46, Issue 6
  • DOI: 10.1021/ar300288e

Influence of the Non-Hermitean Splitting Terms on Excitonic Spectra
journal, January 1970


A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
journal, July 2004

  • Yanai, Takeshi; Tew, David P.; Handy, Nicholas C.
  • Chemical Physics Letters, Vol. 393, Issue 1-3, p. 51-57
  • DOI: 10.1016/j.cplett.2004.06.011

Benchmarking the Bethe–Salpeter Formalism on a Standard Organic Molecular Set
journal, June 2015

  • Jacquemin, Denis; Duchemin, Ivan; Blase, Xavier
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 7
  • DOI: 10.1021/acs.jctc.5b00304

Classification of Spectra of Cata‐Condensed Hydrocarbons
journal, May 1949

  • Platt, John R.
  • The Journal of Chemical Physics, Vol. 17, Issue 5
  • DOI: 10.1063/1.1747293

Comment on “Significance of the highest occupied Kohn-Sham eigenvalue”
journal, December 1997


A new implementation of the second‐order polarization propagator approximation (SOPPA): The excitation spectra of benzene and naphthalene
journal, October 1996

  • Packer, Martin J.; Dalskov, Erik K.; Enevoldsen, Thomas
  • The Journal of Chemical Physics, Vol. 105, Issue 14
  • DOI: 10.1063/1.472430

A complete active space valence bond method with nonorthogonal orbitals
journal, December 1997

  • Hirao, Kimihiko; Nakano, Haruyuki; Nakayama, Kenichi
  • The Journal of Chemical Physics, Vol. 107, Issue 23
  • DOI: 10.1063/1.475300

Gap renormalization of molecular crystals from density-functional theory
journal, August 2013


Optoelectronic and Excitonic Properties of Oligoacenes: Substantial Improvements from Range-Separated Time-Dependent Density Functional Theory
journal, November 2010

  • Wong, Bryan M.; Hsieh, Timothy H.
  • Journal of Chemical Theory and Computation, Vol. 6, Issue 12
  • DOI: 10.1021/ct100529s

Quasiparticle Spectra from a Nonempirical Optimally Tuned Range-Separated Hybrid Density Functional
journal, November 2012


Progress in Time-Dependent Density-Functional Theory
journal, May 2012


Basis set effects on coupled cluster benchmarks of electronically excited states: CC3, CCSDR(3) and CC2
journal, February 2010

  • Silva-Junior, Mario R.; Sauer, Stephan P. A.; Schreiber, Marko
  • Molecular Physics, Vol. 108, Issue 3-4
  • DOI: 10.1080/00268970903549047

A well-tempered density functional theory of electrons in molecules
journal, January 2007

  • Livshits, Ester; Baer, Roi
  • Physical Chemistry Chemical Physics, Vol. 9, Issue 23
  • DOI: 10.1039/b617919c

A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency
journal, August 2002

  • Weigend, Florian
  • Physical Chemistry Chemical Physics, Vol. 4, Issue 18
  • DOI: 10.1039/b204199p

Advances in methods and algorithms in a modern quantum chemistry program package
journal, January 2006

  • Shao, Yihan; Molnar, Laszlo Fusti; Jung, Yousung
  • Phys. Chem. Chem. Phys., Vol. 8, Issue 27
  • DOI: 10.1039/b517914a

Koopmans-compliant functionals and their performance against reference molecular data
journal, August 2014


Combining long-range configuration interaction with short-range density functionals
journal, August 1997


Performance of SOPPA-based methods in the calculation of vertical excitation energies and oscillator strengths
journal, March 2015


Charge-Transfer Versus Charge-Transfer-Like Excitations Revisited
journal, June 2015

  • Moore, Barry; Sun, Haitao; Govind, Niranjan
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 7
  • DOI: 10.1021/acs.jctc.5b00335

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

Time-Dependent Density-Functional Description of the 1 L a State in Polycyclic Aromatic Hydrocarbons: Charge-Transfer Character in Disguise?
journal, April 2011

  • Richard, Ryan M.; Herbert, John M.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 5
  • DOI: 10.1021/ct100607w

Transition moments and dynamic polarizabilities in a second order polarization propagator approach
journal, December 1980

  • Nielsen, Egon S.; Jo/rgensen, Poul; Oddershede, Jens
  • The Journal of Chemical Physics, Vol. 73, Issue 12
  • DOI: 10.1063/1.440119

0–0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/ GW formalisms for 80 Real-Life Compounds
journal, October 2015

  • Jacquemin, Denis; Duchemin, Ivan; Blase, Xavier
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 11
  • DOI: 10.1021/acs.jctc.5b00619

Benchmarks of electronically excited states: Basis set effects on CASPT2 results
journal, November 2010

  • Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A.
  • The Journal of Chemical Physics, Vol. 133, Issue 17
  • DOI: 10.1063/1.3499598

Density Functional Theory with Correct Long-Range Asymptotic Behavior
journal, February 2005


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

Prediction of charge-transfer excitations in coumarin-based dyes using a range-separated functional tuned from first principles
journal, December 2009

  • Stein, Tamar; Kronik, Leeor; Baer, Roi
  • The Journal of Chemical Physics, Vol. 131, Issue 24
  • DOI: 10.1063/1.3269029

Benchmarking the Starting Points of the GW Approximation for Molecules
journal, December 2012

  • Bruneval, Fabien; Marques, Miguel A. L.
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 1
  • DOI: 10.1021/ct300835h

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

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

Communication: Orbital instabilities and triplet states from time-dependent density functional theory and long-range corrected functionals
journal, October 2011

  • Sears, John S.; Koerzdoerfer, Thomas; Zhang, Cai-Rong
  • The Journal of Chemical Physics, Vol. 135, Issue 15
  • DOI: 10.1063/1.3656734

Excited-State Studies of Polyacenes: A Comparative Picture Using EOMCCSD, CR-EOMCCSD(T), Range-Separated (LR/RT)-TDDFT, TD-PM3, and TD-ZINDO
journal, October 2011

  • Lopata, K.; Reslan, R.; Kowalska, M.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 11
  • DOI: 10.1021/ct2005165

Electronic excitations: density-functional versus many-body Green’s-function approaches
journal, June 2002


Benchmark of Bethe-Salpeter for Triplet Excited-States
journal, February 2017

  • Jacquemin, Denis; Duchemin, Ivan; Blondel, Aymeric
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 2
  • DOI: 10.1021/acs.jctc.6b01169

Electron-Hole Excitations in Semiconductors and Insulators
journal, September 1998


An efficient polarization propagator approach to valence electron excitation spectra
journal, June 1995

  • Trofimov, A. B.; Schirmer, J.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 28, Issue 12
  • DOI: 10.1088/0953-4075/28/12/003

Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals
journal, April 2012

  • Kronik, Leeor; Stein, Tamar; Refaely-Abramson, Sivan
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 5
  • DOI: 10.1021/ct2009363

Exact differential equation for the density and ionization energy of a many-particle system
journal, November 1984


Integral approximations for LCAO-SCF calculations
journal, October 1993


Koopmans’ springs to life
journal, December 2009

  • Salzner, Ulrike; Baer, Roi
  • The Journal of Chemical Physics, Vol. 131, Issue 23
  • DOI: 10.1063/1.3269030

    Works referencing / citing this record:

    The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges
    journal, January 2018

    • Blase, Xavier; Duchemin, Ivan; Jacquemin, Denis
    • Chemical Society Reviews, Vol. 47, Issue 3
    • DOI: 10.1039/c7cs00049a

    The Bethe–Salpeter formalism with polarisable continuum embedding: reconciling linear-response and state-specific features
    journal, January 2018

    • Duchemin, Ivan; Guido, Ciro A.; Jacquemin, Denis
    • Chemical Science, Vol. 9, Issue 19
    • DOI: 10.1039/c8sc00529j

    Ab initio modelling of local interfaces in doped organic semiconductors
    journal, January 2020

    • Valencia, Ana M.; Guerrini, Michele; Cocchi, Caterina
    • Physical Chemistry Chemical Physics, Vol. 22, Issue 6
    • DOI: 10.1039/c9cp06655a

    Implicit and explicit host effects on excitons in pentacene derivatives
    journal, March 2018

    • Charlton, R. J.; Fogarty, R. M.; Bogatko, S.
    • The Journal of Chemical Physics, Vol. 148, Issue 10
    • DOI: 10.1063/1.5017285

    On the possibility of singlet fission in crystalline quaterrylene
    journal, May 2018

    • Wang, Xiaopeng; Liu, Xingyu; Cook, Cameron
    • The Journal of Chemical Physics, Vol. 148, Issue 18
    • DOI: 10.1063/1.5027553

    Communication: A hybrid Bethe–Salpeter/time-dependent density-functional-theory approach for excitation energies
    journal, September 2018

    • Holzer, Christof; Klopper, Wim
    • The Journal of Chemical Physics, Vol. 149, Issue 10
    • DOI: 10.1063/1.5051028

    All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals
    journal, January 2020

    • Liu, Chi; Kloppenburg, Jan; Yao, Yi
    • The Journal of Chemical Physics, Vol. 152, Issue 4
    • DOI: 10.1063/1.5123290

    Many-body perturbation theory for understanding optical excitations in organic molecules and solids
    journal, March 2018


    Screening mixing GW/Bethe–Salpeter approach for triplet states of organic molecules
    journal, September 2018


    Bethe–Salpeter equation for absorption and scattering spectroscopy: implementation in the exciting code
    journal, August 2019

    • Vorwerk, Christian; Aurich, Benjamin; Cocchi, Caterina
    • Electronic Structure, Vol. 1, Issue 3
    • DOI: 10.1088/2516-1075/ab3123