Algebraic Density Functionals

TL;DR

This paper introduces a systematic algebraic approach for calculating density functionals and Kohn-Sham potentials by encoding density and energy into polynomials and eliminating degrees of freedom, with numerical examples demonstrating the method.

Contribution

It presents a novel algebraic formalism for deriving density functionals and potentials through polynomial encoding and elimination techniques.

Findings

Formalism successfully applied to numerical examples

Provides a systematic strategy for density functional calculation

Enhances understanding of polynomial-based density functional methods

Abstract

A systematic strategy for the calculation of density functionals (DFs) consists in coding informations about the density and the energy into polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham potentials (KSPs) are then obtained by standard elimination procedures of such degrees of freedom between the polynomials. Numerical examples illustrate the formalism.