Robust Mixing for Ab-Initio Quantum Mechanical Calculations

TL;DR

This paper introduces a robust multisecant Broyden method for solving self-consistent field equations in ab-initio quantum mechanics, demonstrating improved convergence over existing techniques, especially in challenging cases.

Contribution

It proposes a novel multisecant Broyden method tailored for quantum mechanical calculations, enhancing robustness and efficiency in solving Kohn-Sham equations.

Findings

Outperforms existing methods in convergence speed

Effective on challenging and pathological cases

Requires minimal parameter tuning

Abstract

We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broydens second method for solving the self-consistent field equations of Kohn-Sham density functional theory. The algorithm is robust, requires relatively little finetuning and appears to outperform the current state of the art, converging for cases that defeat many other methods. We compare our technique to the conventional methods for problems ranging from simple to nearly pathological.