The core ionization energies calculated by delta SCF and Slater's transition state theory

Kimihiko Hirao; Takahito Nakajima; Bun Chan; Ho-Jin Lee

doi:10.1063/5.0140032

The core ionization energies calculated by delta SCF and Slater's transition state theory

J Chem Phys. 2023 Feb 14;158(6):064112. doi: 10.1063/5.0140032.

Authors

Kimihiko Hirao¹, Takahito Nakajima², Bun Chan³, Ho-Jin Lee⁴

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 Graduate School of Engineering, Nagasaki University, Bunkyo 1-14, Nagasaki 852-8521, Japan.
⁴ Department of Natural Sciences, Southwest Tennessee Community College, Memphis, Tennessee 38015, USA.

PMID: 36792520
DOI: 10.1063/5.0140032

Abstract

The core ionization energies of the second-period and third-period elements are studied by ΔSCF and Slater's transition state (STS) theory by using Hartree-Fock (HF) and Kohn-Sham (KS) approximations. Electron correlation increases the estimated core ionization energies, while the self-interaction error (SIE) decreases them, especially for the third-period elements and is a more significant factor. As a result, while HF lacks electron correlation, it is free of SIE and reasonably predicts the core ionization energies. The core ionization energies calculated by HF STS are very close to those calculated by HF ΔSCF, showing that STS reasonably describes the relaxation of the core hole. The core ionization energies calculated by KS are particularly sensitive to the SIE of the functional used, with functionals having less SIE yielding more accurate ΔSCF core ionization energies. Consequently, BH&HLYP gives better results than B3LYP and LC-BOP since BH&HLYP is the hybrid functional with high proportion of the exact HF exchange. Although the core ionization energies are underestimated by ΔSCF due to SIE, STS gives larger core ionization energies than ΔSCF due to a concave behavior of the error curves of STS, which is also related to SIE. The mean absolute deviations of STS relative to ΔSCF, and relative to the experiment, are almost constant regardless of the nuclei among the element in the second period, and likewise among those in the third period. The systematic nature suggests that shifting the STS core ionization energies may be useful. We propose the shifted STS (1) for reproducing ΔSCF values, and the shifted STS (2) to reproduce the observed ones for KS calculations. Both schemes work quite well. The calculated results of KS ΔSCF and STS vary depending on the functional. However, the variation of each species' shifted STS (2) is very small, and all shifted STS (2) values are close to the observed ones. As the shifted STS require only one SCF calculation, they are simple and practical for predicting the core ionization energies.