Numerical Analysis of Finite Dimensional Approximations of Kohn-Sham Models

TL;DR

This paper analyzes finite dimensional approximations of Kohn-Sham models, proving their convergence and error estimates, supported by numerical simulations on molecular systems.

Contribution

It provides the first rigorous proof of convergence and error bounds for finite dimensional Kohn-Sham approximations in electronic structure calculations.

Findings

Finite dimensional approximations converge to the true solutions.

A priori error estimates are derived for energies and solutions.

Numerical simulations validate the theoretical results.

Abstract

In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error estimates for ground state energies and solutions. We also provide numerical simulations for several molecular systems that support our theory.