Metric Tensor Formulation of Strain in Density-Functional Perturbation Theory

摘要

The direct calculation of the elastic and piezoelectric tensors of solids canbe accomplished by treating homogeneous strain within the framework ofdensity-functional perturbation theory. By formulating the energy functional inreduced coordinates, we show that the strain perturbation enters only throughmetric tensors, and can be treated in a manner exactly paralleling thetreatment of other perturbations. We present an analysis of the strainperturbation of the plane-wave pseudopotential functional, including theinternal strain terms necessary to treat the atomic-relaxation contributions.Procedures for computationally verifying these expressions by comparison withnumerical derivatives of ground-state calculations are described andillustrated.