On the identification and finite element treatment of macroscopic stress in Kohn–Sham density functional theory

Abstract

The macroscopic stress formulation for periodic systems in Kohn–Sham density functional theory is critically examined. The identification of the stress through the partial variation of the energy with respect to cell deformation is cast in a strictly large deformation context. The nature of the non-uniqueness in the stress expression which emanates from this variation is extensively discussed. The possible lack of symmetry in this expression is highlighted and the conditions under which different expressions deliver the same tensorial value are derived. These observations are demonstrated through a finite element framework that is validated towards energy, force and stress calculations.