Representation of Kohn–Sham free atom eigenfunctions by Slater‐type orbitals

Slater‐type orbitals are applied to represent the numerically obtained Kohn–Sham eigenfunction of free atom. The algorithm evaluating the nonlinear expansion coefficients of this approximation is described. Standard iterative solution of Kohn–Sham equation to obtain the nonlinear expansion coefficients is avoided and replaced by the projection method. First, the eigenfunction is obtained in the B‐spline space based on the Galerkin formulation of the finite element method. Then, based on the density functional theory, the conditions are formulated, which leads to the set of nonlinear equations. The proposed algorithm is general and can be applied for any atomic Kohn–Sham eigenfunction. As an examplary application of the proposed algorithm, the set of nonlinear equations is derived for occupied states of N, Al, Ga, and In atoms. The expansion coefficients, obtained for these atoms, are evaluated numerically by Newton procedure and listed in the tables. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Variation of parameters in Becke‐3 hybrid exchange‐correlation functional

We have investigated the consequences of varying the three parameters in Becke's hybrid exchange‐correlation functional, which includes five contributions: Hartree–Fock exchange, local exchange, Becke's gradient exchange correction, local correlation, and some form of gradient correlation correction. Our primary focus was upon obtaining orbital energies with magnitudes that are reasonable approximations to the electronic ionization potentials; however, we also looked at the effects on molecular geometries and atomization enthalpies. A total of 12 parameter combinations was considered for each of three different gradient correlation corrections: the Lee–Yang–Parr, the Perdew‐86, and the Perdew–Wang 91. Five molecules were included in the study: HCN, N₂, N₂O, F₂O, and H₂O. For comparison, a Hartree–Fock calculation was also carried out for each of these. The 6‐31+G** basis set was used throughout this work. We found that the ionization potential estimates can be greatly improved (to much better than Hartree–Fock levels) by increasing the Hartree–Fock exchange contribution at the expense of local exchange. In itself, this also introduces major errors in the atomization enthalpies. However, this can be largely or even completely counteracted by reducing or eliminating the role of the gradient exchange correction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 227–238, 2000     

关于零和二人有限计策问题(英文)

令［ａｉｊ］ｍ ×ｎ是二人零和对策的支付矩阵．本文研究局中人１ 用“计策”获取最大支付ａ＝ ｍ ａｘ｛ａｉｊ｜１≤ｉ≤ｍ ,１≤ｊ≤ｎ｝的问题     

Calculation of core-level electron spectra of ionic liquids

On the example of 40 ion pairs (5 cations times 8 anions), this study demonstrates how the core-level binding energy values can be calculated and used to plot theoretical spectra at low computational cost using density functional theory methods. Three approaches for obtaining the binding energy values are based on delta Kohn–Sham (ΔKS) calculations, 1s KS orbital energies, and atomic charges. The ΔKS results show reasonable agreement with the available experimental X-ray photoelectron data. The 1s KS orbital energies correlate well with the ΔKS results. Atomic charge correlation with ΔKS is improved by accounting for the charges of neighboring atoms. Assignment of binding energies to atoms and the applicability of the mentioned methods to model systems of ionic liquids are discussed.     

Existence of minimizers for Kohn–Sham models in quantum chemistry

This article is concerned with the mathematical analysis of the Kohn–Sham and extended Kohn–Sham models, in the local density approximation (LDA) and generalized gradient approximation (GGA) frameworks. After recalling the mathematical derivation of the Kohn–Sham and extended Kohn–Sham LDA and GGA models from the Schrödinger equation, we prove that the extended Kohn–Sham LDA model has a solution for neutral and positively charged systems. We then prove a similar result for the spin-unpolarized Kohn–Sham GGA model for two-electron systems, by means of a concentration-compactness argument.     

Determination of the ionic radii by means of the Kohn–Sham potential: Identification of the chemical potential

Under the Kohn–Sham theory, we examine solutions for the equations δT_S/δρ(r) = 0 and δT_S/δρ(r) = ν_KS(r) that link the chemical potential of the electronic system with the effective Kohn–Sham potential through μ = ν_KS(r) + δT_S/δρ. For single ions, we identify the chemical potential with the eigenvalue of the frontier orbital when the atom is in the limit of full ionization. For the case of cations, the chemical potential is found above ?(I + A)/2 and has the property of grouping ions with the same chemical characteristics. For the anion instead, the chemical potential is fixed at the ionization energy. By solving the above equations numerically, two radial points called r_? and r₊ are obtained and compared with the Shannon–Prewitt ionic radius. Moreover, we found for the halide series, that r_? is numerically equivalent to rm, the radii where the electrostatic potential has its minimum, but shows different behavior upon charge variation. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

PSIXAS: A Psi4 plugin for efficient simulations of X-ray absorption spectra based on the transition-potential and Δ-Kohn–Sham method

Near edge X-ray absorption fine structure (NEXAFS) spectra and their pump-probe extension (PP-NEXAFS) offer insights into valence- and core-excited states. We present PSIXAS, a recent implementation for simulating NEXAFS and PP-NEXAFS spectra by means of the transition-potential and the Δ-Kohn–Sham method. The approach is implemented in form of a software plugin for the Psi4 code, which provides access to a wide selection of basis sets as well as density functionals. We briefly outline the theoretical foundation and the key aspects of the plugin. Then, we use the plugin to simulate PP-NEXAFS spectra of thymine, a system already investigated by others and us. It is found that larger, extended basis sets are needed to obtain more accurate absolute resonance positions. We further demonstrate that, in contrast to ordinary NEXAFS simulations, where the choice of the density functional plays a minor role for the shape of the spectrum, for PP-NEXAFS simulations the choice of the density functional is important. Especially hybrid functionals (which could not be used straightforwardly before to simulate PP-NEXAFS spectra) and their amount of “Hartree-Fock like” exact exchange affects relative resonance positions in the spectrum.