Direct Minimization for Ensemble Electronic Structure Calculations

TL;DR

This paper introduces a direct optimization method for ensemble density functional theory calculations, improving efficiency by simultaneously optimizing orbitals and occupation numbers while respecting constraints.

Contribution

It presents a novel simultaneous optimization scheme for orbitals and occupation numbers on the Stiefel manifold, enhancing computational performance in electronic structure calculations.

Findings

Simultaneous optimization outperforms sequential methods.

The approach maintains constraints on occupation numbers.

Performance improvements demonstrated in computational experiments.

Abstract

We consider a direct optimization approach for ensemble density functional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel manifold into account and we present an optimization scheme for the occupation numbers that ensures that the constraints remain satisfied. We also compare sequential and simultaneous quasi-Newton and nonlinear conjugate gradient optimization procedures, and demonstrate that simultaneous optimization of the electronic orbitals and occupation numbers improve performance compared to the sequential approach.