### Abstract

We report a test of 30 density functionals, including several recent ones, for their predictions of 69 singlet-to-singlet excitation energies of 11 molecules. The reference values are experimental results collected by Caricato for 30 valence excitations and 39 Rydberg excitations. All calculations employ time-dependent density functional theory in the adiabatic, linear-response approximation. As far as reasonable, all of the assignments are performed by essentially the same protocol as used by Caricato, and this allows us to merge our mean unsigned errors (MUEs) with the ones they calculated for both density functional and wave function methods. We find 21 of the 30 density functionals calculated here have smaller MUEs for the 30 valence states than what they obtained (0.47 eV) for the state-of-the-art EOM-CCSD wave function. In contrast, for all of density functionals the MUE for 39 Rydberg states is larger than that (0.11 eV) of EOM-CCSD. Merging the 30 density functionals calculated here with the 26 calculated by Caricato makes a set of 56 density functionals. Averaging the unsigned errors over both the valence excitations and the Rydberg excitations, none of the 56 density functionals shows a lower mean unsigned error than that (0.27 eV) of EOM-CCSD. Nevertheless, two functionals are successful in having an overall mean unsigned error of 0.30 eV, and another nine are moderately successful in having overall mean unsigned errors in the range 0.32-0.36 eV. Successful or moderately successful density functionals include seven hybrid density functionals with 41 to 54 Hartree-Fock exchange, and four range-separated hybrid density functionals in which the percentage of Hartree-Fock exchange increases from 0 to 19 at small interelectronic separation to 65-100 at long range.

Original language | English |
---|---|

Article number | 244104 |

Journal | Journal of Chemical Physics |

Volume | 137 |

Issue number | 24 |

DOIs | |

Publication status | Published - Dec 28 2012 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*137*(24), [244104]. https://doi.org/10.1063/1.4769078

**Performance of recent and high-performance approximate density functionals for time-dependent density functional theory calculations of valence and Rydberg electronic transition energies.** / Isegawa, Miho; Peverati, Roberto; Truhlar, Donald G.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 137, no. 24, 244104. https://doi.org/10.1063/1.4769078

}

TY - JOUR

T1 - Performance of recent and high-performance approximate density functionals for time-dependent density functional theory calculations of valence and Rydberg electronic transition energies

AU - Isegawa, Miho

AU - Peverati, Roberto

AU - Truhlar, Donald G.

PY - 2012/12/28

Y1 - 2012/12/28

N2 - We report a test of 30 density functionals, including several recent ones, for their predictions of 69 singlet-to-singlet excitation energies of 11 molecules. The reference values are experimental results collected by Caricato for 30 valence excitations and 39 Rydberg excitations. All calculations employ time-dependent density functional theory in the adiabatic, linear-response approximation. As far as reasonable, all of the assignments are performed by essentially the same protocol as used by Caricato, and this allows us to merge our mean unsigned errors (MUEs) with the ones they calculated for both density functional and wave function methods. We find 21 of the 30 density functionals calculated here have smaller MUEs for the 30 valence states than what they obtained (0.47 eV) for the state-of-the-art EOM-CCSD wave function. In contrast, for all of density functionals the MUE for 39 Rydberg states is larger than that (0.11 eV) of EOM-CCSD. Merging the 30 density functionals calculated here with the 26 calculated by Caricato makes a set of 56 density functionals. Averaging the unsigned errors over both the valence excitations and the Rydberg excitations, none of the 56 density functionals shows a lower mean unsigned error than that (0.27 eV) of EOM-CCSD. Nevertheless, two functionals are successful in having an overall mean unsigned error of 0.30 eV, and another nine are moderately successful in having overall mean unsigned errors in the range 0.32-0.36 eV. Successful or moderately successful density functionals include seven hybrid density functionals with 41 to 54 Hartree-Fock exchange, and four range-separated hybrid density functionals in which the percentage of Hartree-Fock exchange increases from 0 to 19 at small interelectronic separation to 65-100 at long range.

AB - We report a test of 30 density functionals, including several recent ones, for their predictions of 69 singlet-to-singlet excitation energies of 11 molecules. The reference values are experimental results collected by Caricato for 30 valence excitations and 39 Rydberg excitations. All calculations employ time-dependent density functional theory in the adiabatic, linear-response approximation. As far as reasonable, all of the assignments are performed by essentially the same protocol as used by Caricato, and this allows us to merge our mean unsigned errors (MUEs) with the ones they calculated for both density functional and wave function methods. We find 21 of the 30 density functionals calculated here have smaller MUEs for the 30 valence states than what they obtained (0.47 eV) for the state-of-the-art EOM-CCSD wave function. In contrast, for all of density functionals the MUE for 39 Rydberg states is larger than that (0.11 eV) of EOM-CCSD. Merging the 30 density functionals calculated here with the 26 calculated by Caricato makes a set of 56 density functionals. Averaging the unsigned errors over both the valence excitations and the Rydberg excitations, none of the 56 density functionals shows a lower mean unsigned error than that (0.27 eV) of EOM-CCSD. Nevertheless, two functionals are successful in having an overall mean unsigned error of 0.30 eV, and another nine are moderately successful in having overall mean unsigned errors in the range 0.32-0.36 eV. Successful or moderately successful density functionals include seven hybrid density functionals with 41 to 54 Hartree-Fock exchange, and four range-separated hybrid density functionals in which the percentage of Hartree-Fock exchange increases from 0 to 19 at small interelectronic separation to 65-100 at long range.

UR - http://www.scopus.com/inward/record.url?scp=84872014575&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872014575&partnerID=8YFLogxK

U2 - 10.1063/1.4769078

DO - 10.1063/1.4769078

M3 - Article

C2 - 23277925

AN - SCOPUS:84872014575

VL - 137

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 24

M1 - 244104

ER -