FEAST fundamental framework for electronic structure calculations: Reformulation and solution of the muffin-tin problem

TL;DR

This paper introduces a fundamental FEAST-based framework for electronic structure calculations that directly addresses the muffin-tin problem, offering accurate, scalable solutions without traditional approximations.

Contribution

It reformulates the muffin-tin eigenvalue problem within the FEAST framework, providing a new exact and scalable approach for electronic structure calculations.

Findings

Successfully applied to molecular systems

Achieves accurate results without pseudopotentials

Demonstrates scalability and efficiency

Abstract

In a recent article [1], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the "black-box" solver as a fundamental modeling framework which can naturally address the original numerical complexity of the electronic structure problem as formulated by Slater in 1937 [2]. The non-linear eigenvalue problem arising from the muffin-tin decomposition of the real-space domain is first derived and then reformulated to be solved exactly within the FEAST framework. This new framework is presented as a fundamental and practical solution for performing both accurate and scalable electronic structure calculations, bypassing the various issues of using traditional approaches such as linearization and pseudopotential techniques. A finite element implementation of this FEAST framework along with simulation results for various molecular systems are also presented and discussed.