A mesh-free convex approximation scheme for Kohn–Sham density functional theory

Density functional theory developed by Hohenberg, Kohn and Sham is a widely accepted, reliable ab initio method. We present a non-periodic, real space, mesh-free convex approximation scheme for Kohn–Sham density functional theory. We rewrite the original variational problem as a saddle point problem and discretize it using basis functions which form the Pareto optimum between competing objectives of maximizing entropy and minimizing the total width of the approximation scheme. We show the utility of the approximation scheme in performing both all-electron and pseudopotential calculations, the results of which are in good agreement with literature.     

Kohn–Sham potentials by an inverse Kohn–Sham equation and accuracy assessment by virial theorem

In the recent study, the authors have proposed an integral equation for solving the inverse Kohn–Sham problem. In the present paper, the integral equation is numerically solved for one-dimensional model of a He atom and an H₂ molecule in the electronic ground states. For this purpose, we propose an iterative solution algorithm avoiding the inversion of the kernel of the integral equation. To quantify the numerical accuracy of the calculated exchange-correlation potentials, we evaluate the exchange and correlation energies based on the virial theorem as well as the reproduction of the exact ground-state electronic energy. The results demonstrate that the numerical solutions of our integral equation for the inverse Kohn–Sham problem are accurate enough in reproducing the Kohn–Sham potential and in satisfying the virial theorem.     

Kohn-Sham Density Matrix and the Kernel Energy MethodSCI北大核心CSCD

The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.