The accuracy of density functional theory (DFT) calculations depends on the ability of the exchange-correlation (XC) functional to describe inter-electron interactions. A proper description of exchange is important in this context and most modern XC functionals include some degree of exact exchange (EE). The non-local nature exchange operator makes evaluating EE computationally demanding in periodic DFT calculations that use planewave basis sets. Methods for reducing this expense often limit the number of orbital pairs included when evaluating EE by only evaluating EE using pairs of localized states within a certain distance of one another or truncating the Coulomb operator. We have developed a method for calculating EE in periodic systems that uses non-orthogonal generalized Wannier functions (NGWFs) as basis functions. The NGWFs are Fourier series representations of atom-centered basis functions. Unlike conventional planewave calculations, where each planewave is assigned a variational parameter, the Fourier coefficients defining the NGWFs are fixed and each NGWF is assigned a variational coefficient. This approach drastically reduces the number of variational parameters and permits the use of efficient direct diagonalization methods. Tests show the NGWF method is orders of magnitude faster than conventional methods for calculating EE in periodic systems and yields results of similar accuracy. We have recently improved the NGWF method to achieve linear scaling without truncating operators or neglecting integrals.
Ongoing efforts in this area include improving the performance of this method, extending the abilities of the NGWF calculations to permit geometry optimizations, frequency calculations and dynamic correlation via perturbation theory, and ultimately developing and NGWF code that can be distributed for general use among computational chemists.