Elasticity effects in electronic structure calculations with periodic boundary conditions

We investigate the effects of elastic interactions between defects in electronic structure calculations with periodic boundary conditions. Our approach, building on the work of Toshio Mura [Proc. Roy. Soc. 280 (1964) 1383], is based on the distortion tensor and the topology of the defects and does not involve evaluating sums of long-range functions. We construct solutions in a straight-forward way that makes them easily applied to electronic structure calculations. The results explain how to interpret volume changes in systems with periodic boundary conditions. We also show that the periodicity may be chosen in such a way as to minimize the elastic effects of the boundary condition.