New Algebraic Formulation of Density Functional Calculation

TL;DR

This paper introduces a new algebraic, basis-set independent matrix formulation for density functional theories, simplifying the development and implementation of ab initio computational methods.

Contribution

It presents a novel formalism that streamlines the creation and sharing of new ab initio techniques through simple algebraic derivations.

Findings

Provides a basis-set independent matrix framework for density functional calculations.

Facilitates rapid development and implementation of new ab initio methods.

Details efficient algorithms and computational kernels for high-performance computing.

Abstract

This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to the derivation and transcription of a few lines of algebra. This new framework enables us to concisely demystify the inner workings of fully functional, highly efficient modern ab initio codes and to give complete instructions for the construction of such for calculations employing arbitrary basis sets. Within this framework, we also discuss in full detail a variety of leading-edge ab initio techniques, minimization algorithms, and highly efficient computational kernels for use with scalar as well as shared and distributed-memory supercomputer architectures.