A proposal to first principles electronic structure calculation: Symbolic-Numeric method

TL;DR

This paper introduces a symbolic-numeric method for first principles electronic structure calculations that simplifies solving Hartree-Fock equations by transforming them into polynomial forms using Grobner bases, eliminating iterative procedures.

Contribution

It presents a novel approach combining symbolic computation and polynomial transformation to perform electronic structure calculations without iterative self-consistent methods.

Findings

Transforms Hartree-Fock equations into polynomial forms

Simplifies numerical procedures for electronic structure calculations

Enables solving inverse and optimization problems in a unified framework

Abstract

This study proposes an approach toward the first principles electronic structure calculation with the aid of symbolic-numeric solving. The symbolic computation enables us to express the Hartree-Fock-Roothaan equation and the molecular integrals in analytic forms and approximate them as a set of polynomial equations. By use of the Grobner bases technique, the polynomial equations are transformed into other ones which have identical roots. The converted equations take more convenient forms which will simplify numerical procedures, from which we can derive necessary physical properties in order, in an a la carte way. This method enables us to solve the electronic structure calculation, the optimization of any kind, or the inverse problem as a forward problem in a unified way, in which there is no need for iterative self-consistent procedures with trials and errors.