Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals

TL;DR

This paper introduces a new class of iterative schemes for solving the Kohn-Sham equations in density functional theory that guarantees exponential convergence without orthogonalization, improving computational efficiency.

Contribution

The authors propose and analyze orthogonality-preserving iteration schemes that ensure convergence without orthogonalization, with practical methods for selecting optimal time step sizes.

Findings

Schemes guarantee exponential convergence to Kohn-Sham orbitals.

Numerical experiments validate the theoretical convergence and efficiency.

Method avoids orthogonalization, reducing computational cost.

Abstract

To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose and analyze a class of iteration schemes for the discretized Kohn- Sham Density Functional Theory model, with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals exponentially without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given properly. In addition, we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.