metric tensor dft

1 Metric Tensor Formulation of Strain in Density-F unctional Perturbation Theory D. R. Hamann, 1,2,3 Xifan Wu, 1 Karin M. Rabe, 1 and David Vanderbilt 1 1 Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019 2 Bell Laboratories, Lucent Technologies, Murray Hill, NJ, 07974 3 Mat-Sim Research LLC, P. O. Box 742, Murray Hill, NJ, 07974 ABSTRACT The direct calculation of the elastic and piezoelectric tensors of solids can be ac- complished by treating homogeneous strain within the framework of d ensity-functional perturbation theory. By formulating the energy f unctional in reduced coordinates, we show that the strain perturbation enters only through metric tensors, and c an be treated in a manner exactly paralleling the t reatment of other perturbations. We present an analysis of the strain perturbation of the plane-wave pseudopotential functional, including the in- ternal strain terms necessary to treat the atomic-relaxation contributions. Procedures for computationally verifying these expressions by comparison with numerical derivatives of ground-state calculations are described and illustrated. PACS numbers: 71.15.-m, 62.20.Dc, 77.65.Bn, 71.15.Mb

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