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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. [ABSTRACT FROM AUTHOR]

The core ionization energies of second‐ and third‐period elements of the molecules C2H5NO2, SiF4, Si(CH3)4, PF3, POF3, PSF3, CS2, OCS, SO2, SO2F2, CH3Cl, CFCl3, SF5Cl, and Cl3PS are calculated by using Hartree‐Fock (HF), and Kohn‐Sham (KS) with BH&HLYP, B3LYP, and LC‐BOP functionals. We used ΔSCF, Slater's transition state (STS), and two previously proposed shifted STS (1) and shifted STS (2) methods, which have been developed. The errors of ΔSCF and STS come mainly from the self‐interaction errors (SIE) and can be corrected with a shifting scheme. In this study, we used the shifting parameters determined for each atom. The shifted STS (1) reproduces ΔSCF almost perfectly with mean absolute deviations (MAD) of 0.02 eV. While ΔSCF and STS vary significantly depending on the functional used, the variation of shifted STS (2) is small, and all shifted STS (2) values are close to the observed ones. The deviations of the shifted STS (2) from the experiment are 0.24 eV (BH&HLYP), 0.19 eV (B3LYP), and 0.23 eV (LC‐BOP). These results further support the use of shifted STS methods for predicting the core ionization energies. [ABSTRACT FROM AUTHOR]

We generalize Slater's transition state concept by deriving systematic higher-order transition state approximations. Numerical validation is performed by the calculation of transition energies for various excitations, including core, valence, and charge-transfer excitations, at Hartree–Fock and Kohn–Sham density functional theory levels. All higher-order transition state approximations introduced in this study accurately reproduce the results from delta self-consistent-field calculations. In particular, we demonstrate that the third-order generalized transition state (GTS3) approximation is a promising alternative to the original, owing to a good balance between the accuracy and computational cost. We also demonstrate that accurate and reliable results can be obtained with a low computational cost by combining the GTS3 approximation with the transition potential scheme. [ABSTRACT FROM AUTHOR]

We have extended Slater's transition state concept for the approximation of the difference in total energies of the initial and final states by three orbital energies of initial, final, and half-way Slater's transition states of the system. Numerical validation was performed with the ionization energies for H2O, CO, and pyrrole by calculation using Hartree–Fock (HF) and Kohn–Sham (KS) theories with the B3LYP and LCgau-core-BOP functionals. The present extended method reproduces full ΔSCF very accurately for all occupied orbitals obtained with HF and for valence orbitals obtained with KS. KS core orbitals have some errors due to the self-interaction errors, but the present method significantly improves the core electron binding energies. In its current form, the newly derived theory may not yet be practically useful, but it is simple and conceptually useful for gaining improved understanding of SCF-type orbital theories. [ABSTRACT FROM AUTHOR]

Several different types of density functional theory (DFT) exchange correlation functionals were applied to a periodic boundary condition (PBC) system [carbon monoxide (CO) adsorbed on Cu(111): CO/Cu(111)] and the differences in the results calculated using these functionals were compared. The exchange correlation functionals compared were those of Perdew–Burke–Ernzerhof (PBE) and those of long-range corrected density functional theory (LC-DFT), such as LC-ωPBE(2Gau) and LC-BLYP(2Gau). Solid state properties such as the partial density of states were calculated in order to elucidate the detailed adsorption mechanisms and back-bonding peculiar to the CO/Cu(111) system. In addition, our benchmark analysis of the correlations among the orbitals of CO and Cu metal using LC-DFT reasonably was in line with the experimentally observed adsorption site. The computation time was reasonable, and other numerical results were found to agree well with the experimental results and also with the theoretical results of other researchers. This suggests that the long-range Hartree–Fock exchange integral should be included to correctly predict the electronic nature of PBC systems. [ABSTRACT FROM AUTHOR]