An analysis of the field theoretic approach to the quasi-continuum method

TL;DR

This paper analyzes the field theoretic approach to the quasi-continuum method using orbital-free density functional theory, providing formal justification for coarse-graining and deriving homogenized equations for electronic fields under deformation.

Contribution

It offers a formal justification for coarse-graining in the quasi-continuum method and derives homogenized equations for electronic fields in deformed regions.

Findings

Validated the coarse-graining approach via perturbation and multiple scale analysis.

Derived homogenized equations for electronic fields under smooth deformation.

Estimated cell-size effects on defect energy calculations.

Abstract

Using the orbital-free density functional theory as a model theory, we present an analysis of the field theoretic approach to quasi-continuum method. In particular, by perturbation method and multiple scale analysis, we provide a formal justification for the validity of the coarse-graining of various fields, which is central to the quasi-continuum reduction of field theories. Further, we derive the homogenized equations that govern the behavior of electronic fields in regions of smooth deformations. Using Fourier analysis, we determine the far-field solutions for these fields in the presence of local defects, and subsequently estimate cell-size effects in computed defect energies.