Band-structure perturbations in strained crystals

A perturbation method has been developed in the modified-plane-wave formalism to calculate first-order splitting and shifting of electronic energy levels for fcc crystals under hydrostatic, tetragonal, and trigonal strains. Numerical results for Cu for the $\Gamma$, $X$, and $L$ symmetry points are given. The hydrostatic results are compared with the difference calculation of Davis et al. The tetragonal and trigonal results are compared with those of Juras and Segall who performed both a perturbation and a difference calculation. Reasonable agreement with these other calculations is obtained. For the shear cases the numerical ratios of appropriate shifts are in excellent agreement with the ratios predicted from symmetry calculations alone. A representative case involving a second-order correction due to mixing between close-lying levels is included.