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

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.

20 pages, 7 figures

References in corpus (4)

• A Density Matrix-based Algorithm for Solving Eigenvalue Problems
• All-electron density functional theory and time-dependent density functional theory with high-order finite elements
• An Efficient and Robust Technique for Achieving Self Consistency in Electronic Structure Calculations
• Spectral-based Propagation Schemes for Time-Dependent Quantum Systems with Application to Carbon Nanotubes

Cited by in corpus (4)

• Non-linear eigensolver-based alternative to traditional SCF methods
• A New Highly Parallel Non-Hermitian Eigensolver
• Universal nature of collective plasmonic excitations in finite 1-D carbon-based nanostructures
• Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver