Vertical ionization potential benchmarks from Koopmans prediction of Kohn-Sham theory with long-range corrected (LC) functional

Kimihiko Hirao; Han-Seok Bae; Jong-Won Song; Bun Chan

doi:10.1088/1361-648X/ac54e3

Vertical ionization potential benchmarks from Koopmans prediction of Kohn-Sham theory with long-range corrected (LC) functional

J Phys Condens Matter. 2022 Mar 7;34(19). doi: 10.1088/1361-648X/ac54e3.

Authors

Kimihiko Hirao^{1

2}, Han-Seok Bae³, Jong-Won Song³, Bun Chan⁴

Affiliations

¹ Fukui Institute for Fundamental Chemistry, Kyoto University, Takano, Nishihiraki-cho 34-4, Sakyo-ku, Kyoto, 606-8103, Japan.
² RIKEN Center for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, 650-0047, Japan.
³ Department of Chemistry Education, Daegu University, Gyeongsan, 113-8656, Korea.
⁴ Graduate School of Engineering, Nagasaki University, Bunkyo 1-14, Nagasaki 852-8521, Japan.

PMID: 35158348
DOI: 10.1088/1361-648X/ac54e3

Abstract

The Kohn-Sham density functional theory (KS-DFT) with the long-range corrected (LC) functional is applied to the benchmark dataset of 401 valence ionization potentials (IPs) of 63 small molecules of Chong, Gritsenko and Baerends (the CGB set). The vertical IP of the CGB set are estimated as negative orbital energies within the context of the Koopmans' prediction using the LCgau-core range-separation scheme in combination with PW86-PW91 exchange-correlation functional. The range separation parameterμof the functional is tuned to minimize the error of the negative HOMO orbital energy from experimental IP. The results are compared with literature data, includingab initioIP variant of the equation-of-motion coupled cluster theory with singles and doubles (IP-EOM-CCSD), the negative orbital energies calculated by KS-DFT with the statistical averaging of orbital potential, and those with the QTP family of functionals. The optimally tuned LC functional performs better than other functionals for the estimation of valence level IP. The mean absolute deviations (MAD) from experiment and from IP-EOM-CCSD are 0.31 eV (1.77%) and 0.25 eV (1.46%), respectively. LCgau-core performs quite well even with fixedμ(not system-dependent). Aμvalue around 0.36 bohr^-1gives MAD of 0.40 eV (2.42%) and 0.33 eV (1.96%) relative to experiment and IP-EOM-CCSD, respectively. The LCgau-core-PW86-PW91 functional is an efficient alternative to IP-EOM-CCSD and it is reasonably accurate for outer valence orbitals. We have also examined its application to core ionization energies of C(1s), N(1s), O(1s) and F(1s). The C(1s) core ionization energies are reproduced reasonably [MAD of 46 cases is 0.76 eV (0.26%)] but N(1s), O(1s) and F(1s) core ionization energies are predicted less accurately.

Keywords: Kohn–Sham theory; Koopmans’ theorem; density functional theory (DFT); ionization potential; long-range corrected functional; optimally tuned range separation parameter.