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Title: 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 » 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.« less

Authors:
 [1];  [2];  [3];  [1];  [4]
  1. Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
  2. Theory and Simulation of Condensed Matter, King’s College London, The Strand, London WC2R 2LS (United Kingdom)
  3. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)
  4. (United States)
Publication Date:
OSTI Identifier:
22415794
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 19; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
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. doi: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. Thu . "On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies". United States. doi: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},
journal = {Journal of Chemical Physics},
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}
}
  • 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 (HF), second-order Møller-Plesset perturbation theory (MP2) 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 ionizationmore » energies obtained from total energy diff 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.« less
  • Cited by 6
  • The simplified energy functional of Harris has given results of useful accuracy for systems well outside the limits of weakly interacting fragments for which the method was originally proposed. In the present study, we discuss the source of the frequent good agreement of the Harris energy with full Kohn-Sham self-consistent results. A procedure is described for extending the applicability of the scheme to more strongly interacting systems by going beyond the frozen-atom fragment approximation. A gradient-force expression is derived, based on the Harris functional, which accounts for errors in the fragment charge representation. Results are presented for some diatomic molecules,more » illustrating the points of this study.« less
  • In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO{sub 2}{sup 2+} molecule excitation energies and geometries of states originating from excitation from the {sigma}{sub u}, {sigma}{sub g}, {pi}{sub u}, and {pi}{sub g} orbitals to the nonbonding 5f{sub {delta}} and 5f{sub {phi}} have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCF/CASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFT/MRCI method. Excellent agreement between allmore » nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFT/MRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied {sigma}{sub u} orbital are symmetric while that arising from excitations out of the {pi}{sub u} orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.« less
  • A systematic assessment of theoretical methods applicable to the accurate characterization of catalytic cycles of homogeneous catalysts for H2 oxidation and evolution is reported. For these catalysts, H2 bond breaking or formation involve di-hydrogen, di-hydride, hydride-proton, and di-proton complexes. The key elementary steps have heterolytic character. In the context of Density Functional Theory (DFT) we investigated the use of functionals in the generalized gradient approximation (GGA) as well as hybrid functionals. We compared the results with wavefunction theories based on perturbation theory (MP2 and MP4) and on coupled-cluster expansions (CCSD and CCSD(T)). Our findings suggest that DFT results based onmore » Perdew functionals are in semi-quantitative agreement with the CCSD(T) results, with deviations of a few kcal/mol only. On the other hand, the B3LYP functional is not even in qualitative agreement with CCSD[T]. Surprisingly the MP2 results are found to be extremely poor, a finding that we attribute to the limited treatment in MP2 theory of dynamic electron correlation effects in Ni(0) oxidation state. This material is based upon work supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences.« less