Formulation and Implementation of Density Functional Embedding Theory using Products of Basis Functions

The representation of embedding potential in using products of AO basis functions has been developed in the context of density functional embedding theory (DFET). The formalism allows to treat pseudopotential and all-electron calculations on the same footing and enables simple transfer of the embedding potential in the compact matrix form. In addition, a simple cost-reduction procedure for basis set and potential reduction has been proposed. The theory has been implemented for the condensed-phase and molecular systems using Gaussian and Plane Waves (GPW) and Gaussian and Augmented Plane Waves (GAPW) formalisms and tested for proton transfer reactions in the cluster and the condensed phase. The computational scaling of the embedding potential optimization is similar to this of hybrid DFT with a significantly reduced prefactor and allows for large-scale applications.