We have derived and implemented the theory for directly computing the contribution to the stress tensor ${\sigma }_{\alpha \beta }$ from exchange and correlation effects when using the screened exchange method in Kohn-Sham density functional theory (DFT). The method is also applicable when using related functionals such as Hartree-Fock or exact exchange. This paves the way for full geometric relaxation of a crystal structure when using such functionals, without the need for expensive numerical differentiation. The theory is derived in reciprocal space, appropriate for plane-wave based calculations, and has been implemented within an efficient, and fully parallel, DFT code. As a simple demonstration of the validity of this method we calculate the variation in stress as both hydrostatic and shear strains are applied to silicon when using screened exchange.

• Received 18 January 2006

DOI:https://doi.org/10.1103/PhysRevB.73.125120