Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory

TL;DR

This paper develops and analyzes atomistic-to-continuum coupling methods for a simplified one-dimensional density functional theory model, providing rigorous error estimates for the proposed approaches.

Contribution

It introduces and rigorously analyzes atomistic-to-continuum coupling mechanisms for a toy density functional theory model, focusing on boundary dependence and error bounds.

Findings

First-order error estimates for coupling mechanisms

Dependence of atomistic subproblem on boundary conditions

Rigorous mathematical analysis of coupling accuracy

Abstract

We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling mechanisms for this atomistic model, paying special attention to the dependence of the atomistic subproblem on the atomistic region boundary and the boundary conditions. We rigorously prove first-order error estimates for two related coupling mechanisms.