On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies
Abstract
The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionization energies obtained from total energy difference calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement withmore »
- Authors:
-
- Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
- Theory and Simulation of Condensed Matter, King’s College London, The Strand, London WC2R 2LS (United Kingdom)
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)
- Publication Date:
- OSTI Identifier:
- 22415794
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 19; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; BENCHMARKS; BENZENE; COMPARATIVE EVALUATIONS; CORRECTIONS; DENSITY FUNCTIONAL METHOD; ELECTRONS; HARTREE-FOCK METHOD; IONIZATION; MOLECULES; PERTURBATION THEORY; PROPAGATOR
Citation Formats
McKechnie, Scott, Booth, George H., Cohen, Aron J., Cole, Jacqueline M., E-mail: jmc61@cam.ac.uk, and Argonne National Laboratory, 9700 S Cass Avenue, Argonne, Illinois 60439. On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies. United States: N. p., 2015.
Web. doi:10.1063/1.4921037.
McKechnie, Scott, Booth, George H., Cohen, Aron J., Cole, Jacqueline M., E-mail: jmc61@cam.ac.uk, & Argonne National Laboratory, 9700 S Cass Avenue, Argonne, Illinois 60439. On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies. United States. https://doi.org/10.1063/1.4921037
McKechnie, Scott, Booth, George H., Cohen, Aron J., Cole, Jacqueline M., E-mail: jmc61@cam.ac.uk, and Argonne National Laboratory, 9700 S Cass Avenue, Argonne, Illinois 60439. 2015.
"On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies". United States. https://doi.org/10.1063/1.4921037.
@article{osti_22415794,
title = {On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies},
author = {McKechnie, Scott and Booth, George H. and Cohen, Aron J. and Cole, Jacqueline M., E-mail: jmc61@cam.ac.uk and Argonne National Laboratory, 9700 S Cass Avenue, Argonne, Illinois 60439},
abstractNote = {The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionization energies obtained from total energy difference calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.},
doi = {10.1063/1.4921037},
url = {https://www.osti.gov/biblio/22415794},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 19,
volume = 142,
place = {United States},
year = {Thu May 21 00:00:00 EDT 2015},
month = {Thu May 21 00:00:00 EDT 2015}
}
Works referenced in this record:
PW86-PW91 density functional calculation of vertical ionization potentials: Some implications for present-day functionals
journal, January 2000
- Shapley, Warwick A.; Chong, Delano P.
- International Journal of Quantum Chemistry, Vol. 81, Issue 1
Jahn-Teller Effects in Molecular Cations Studied by Photoelectron Spectroscopy and Group Theory
journal, August 2009
- Wörner, Hans Jakob; Merkt, Frédéric
- Angewandte Chemie International Edition, Vol. 48, Issue 35
Long-range corrected functionals satisfy Koopmans' theorem: Calculation of correlation and relaxation energies
journal, January 2013
- Kar, Rahul; Song, Jong-Won; Hirao, Kimihiko
- Journal of Computational Chemistry, Vol. 34, Issue 11
Electron propagator theory: an approach to prediction and interpretation in quantum chemistry: Electron propagator theory
journal, September 2012
- Ortiz, Joseph Vincent
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 2
Application and Testing of Diagonal, Partial Third-Order Electron Propagator Approximations
book, January 2001
- Ferreira, Antonio M.; Seabra, Gustavo; Dolgounitcheva, O.
- Understanding Chemical Reactivity
Practical Aspects of Computational Chemistry III
book, January 2014
- Leszczynski, Jerzy; Shukla, Manoj K.
The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals
journal, July 2007
- Zhao, Yan; Truhlar, Donald G.
- Theoretical Chemistry Accounts, Vol. 120, Issue 1-3
Orbital energies and Koopmans' theorem in open-shell Hartree-Fock theory
journal, February 1972
- Dodds, J. L.; McWeeny, R.
- Chemical Physics Letters, Vol. 13, Issue 1
Computational methods for the one-particle green's function
journal, April 1984
- von Niessen, W.; Schirmer, J.; Cederbaum, L. S.
- Computer Physics Reports, Vol. 1, Issue 2
How to determine vertical ionization potentials from photoelectron spectra
journal, January 1975
- Schwarz, W. H. Eegen
- Journal of Electron Spectroscopy and Related Phenomena, Vol. 6, Issue 5
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
An experimental and theoretical study of the valence shell photoelectron spectrum of the benzene molecule
journal, November 1997
- Baltzer, P.; Karlsson, L.; Wannberg, B.
- Chemical Physics, Vol. 224, Issue 1
Challenges for Density Functional Theory
journal, December 2011
- Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
- Chemical Reviews, Vol. 112, Issue 1
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
More π Electrons Make a Difference: Emergence of Many Radicals on Graphene Nanoribbons Studied by Ab Initio DMRG Theory
journal, December 2012
- Mizukami, Wataru; Kurashige, Yuki; Yanai, Takeshi
- Journal of Chemical Theory and Computation, Vol. 9, Issue 1
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields
journal, November 1994
- Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.
- The Journal of Physical Chemistry, Vol. 98, Issue 45, p. 11623-11627
Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies
journal, May 2003
- Zhan, Chang-Guo; Nichols, Jeffrey A.; Dixon, David A.
- The Journal of Physical Chemistry A, Vol. 107, Issue 20
Vertical Ionization Energies of Free Radicals and Electron Detachment Energies of Their Anions: A Comparison of Direct and Indirect Methods Versus Experiment
journal, July 2014
- Pérez-González, Adriana; Galano, Annia; Ortiz, J. V.
- The Journal of Physical Chemistry A, Vol. 118, Issue 31
Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation
journal, October 2011
- Peverati, Roberto; Truhlar, Donald G.
- The Journal of Physical Chemistry Letters, Vol. 2, Issue 21
Assessment of density functional methods with correct asymptotic behavior
journal, January 2013
- Tsai, Chen-Wei; Su, Yu-Chuan; Li, Guan-De
- Physical Chemistry Chemical Physics, Vol. 15, Issue 21
The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies
journal, January 2013
- Baerends, E. J.; Gritsenko, O. V.; van Meer, R.
- Physical Chemistry Chemical Physics, Vol. 15, Issue 39
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
Interpretation of the Kohn–Sham orbital energies as approximate vertical ionization potentials
journal, February 2002
- Chong, D. P.; Gritsenko, O. V.; Baerends, E. J.
- The Journal of Chemical Physics, Vol. 116, Issue 5
Benchmark theoretical study of the ionization threshold of benzene and oligoacenes
journal, August 2003
- Deleuze, M. S.; Claes, L.; Kryachko, E. S.
- The Journal of Chemical Physics, Vol. 119, Issue 6
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
On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell‐Type Expansion Using Quantum‐Field Theoretical Methods
journal, December 1966
- Čížek, Jiří
- The Journal of Chemical Physics, Vol. 45, Issue 11
Koopmans’ theorem in the ROHF method: Canonical form for the Hartree-Fock Hamiltonian
journal, November 2006
- Plakhutin, B. N.; Gorelik, E. V.; Breslavskaya, N. N.
- The Journal of Chemical Physics, Vol. 125, Issue 20
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
Tests of functionals for systems with fractional electron number
journal, April 2007
- Vydrov, Oleg A.; Scuseria, Gustavo E.; Perdew, John P.
- The Journal of Chemical Physics, Vol. 126, Issue 15
Systematic optimization of long-range corrected hybrid density functionals
journal, February 2008
- Chai, Jeng-Da; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 128, Issue 8
On Koopmans’ theorem in density functional theory
journal, November 2010
- Tsuneda, Takao; Song, Jong-Won; Suzuki, Satoshi
- The Journal of Chemical Physics, Vol. 133, Issue 17
Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory
journal, May 2012
- Yang, Weitao; Cohen, Aron J.; Mori-Sánchez, Paula
- The Journal of Chemical Physics, Vol. 136, Issue 20
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples
journal, February 1982
- Purvis, George D.; Bartlett, Rodney J.
- The Journal of Chemical Physics, Vol. 76, Issue 4
An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations
journal, December 1988
- Scuseria, Gustavo E.; Janssen, Curtis L.; Schaefer, Henry F.
- The Journal of Chemical Physics, Vol. 89, Issue 12
Is coupled cluster singles and doubles (CCSD) more computationally intensive than quadratic configuration interaction (QCISD)?
journal, April 1989
- Scuseria, Gustavo E.; Schaefer, Henry F.
- The Journal of Chemical Physics, Vol. 90, Issue 7
Density‐functional thermochemistry. III. The role of exact exchange
journal, April 1993
- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652
Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections
journal, April 2012
- Lin, You-Sheng; Tsai, Chen-Wei; Li, Guan-De
- The Journal of Chemical Physics, Vol. 136, Issue 15
Partial third‐order quasiparticle theory: Comparisons for closed‐shell ionization energies and an application to the Borazine photoelectron spectrum
journal, May 1996
- Ortiz, J. V.
- The Journal of Chemical Physics, Vol. 104, Issue 19
A non-Dyson third-order approximation scheme for the electron propagator
journal, September 1998
- Schirmer, J.; Trofimov, A. B.; Stelter, G.
- The Journal of Chemical Physics, Vol. 109, Issue 12
Extension of many-body theory and approximate density functionals to fractional charges and fractional spins
journal, September 2013
- Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J.
- The Journal of Chemical Physics, Vol. 139, Issue 10
Fractional charge perspective on the band gap in density-functional theory
journal, March 2008
- Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
- Physical Review B, Vol. 77, Issue 11
Insights into Current Limitations of Density Functional Theory
journal, August 2008
- Cohen, A. J.; Mori-Sanchez, P.; Yang, W.
- Science, Vol. 321, Issue 5890
Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules
journal, October 1981
- Bartlett, R. J.
- Annual Review of Physical Chemistry, Vol. 32, Issue 1
CurlySMILES: a chemical language to customize and annotate encodings of molecular and nanodevice structures
journal, January 2011
- Drefahl, Axel
- Journal of Cheminformatics, Vol. 3, Issue 1
Jahn-Teller effects in molecular cations studied by photoelectron spectroscopy and group theory
text, January 2009
- Wörner, Hans Jakob; Merkt, Frédéric
- ETH Zurich
Fractional charge perspective on the band-gap in density-functional theory
text, January 2007
- Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
- arXiv
Assessment of density functional methods with correct asymptotic behavior
text, January 2012
- Tsai, Chen-Wei; Su, Yu-Chuan; Li, Guan-De
- arXiv
Works referencing / citing this record:
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journal, June 2019
- Valadbeigi, Younes; Vianello, Robert
- Journal of Physical Organic Chemistry, Vol. 32, Issue 10
Assignment of photoelectron spectra of intramolecular silicon complexes: 1-vinyl- and 1-phenylsilatranes
journal, January 2018
- Belogolova, Elena F.; Doronina, Evgeniya P.; Sidorkin, Valery F.
- Physical Chemistry Chemical Physics, Vol. 20, Issue 41
Polypyrrole derivatives for optoelectronic applications: a DFT study on the influence of side groups
journal, January 2019
- Coleone, Alex Pifer; Lascane, Leonardo Gois; Batagin-Neto, Augusto
- Physical Chemistry Chemical Physics, Vol. 21, Issue 32
Accurate density functional prediction of molecular electron affinity with the scaling corrected Kohn–Sham frontier orbital energies
journal, October 2017
- Zhang, DaDi; Yang, Xiaolong; Zheng, Xiao
- Molecular Physics, Vol. 116, Issue 7-8
Micropollutant Oxidation Studied by Quantum Chemical Computations: Methodology and Applications to Thermodynamics, Kinetics, and Reaction Mechanisms
journal, March 2019
- Tentscher, Peter R.; Lee, Minju; von Gunten, Urs
- Accounts of Chemical Research, Vol. 52, Issue 3
The LDA-1/2 method applied to atoms and molecules
text, January 2018
- Pela, Ronaldo Rodrigues; Gulans, Andris; Draxl, Claudia
- arXiv