On assessing the accuracy of defect free energy computations

TL;DR

This paper provides a rigorous error analysis for coarse-graining defect-formation free energy in atomistic systems, establishing convergence rates and reducing computational costs with explicit examples and simulations.

Contribution

It introduces a novel error analysis framework for coarse-graining defect energies and constructs efficient coarse-grained models with proven convergence properties.

Findings

Established the thermodynamic limit for defect-formation free energy.

Derived explicit convergence rates for coarse-grained energies.

Validated results through harmonic potential examples and numerical simulations.

Abstract

We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the same rate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.