# 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)
- (United States)

- 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. 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},

issn = {0021-9606},

number = 19,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}