Paramaterizing DFT functionals to recover GW energetics

Density functional theory is the most commonly used electronic structure method to predict the structure of various systems, but DFT loses its predictive power in examining strongly correlated systems. The GW approximation of many-body perturbation theory more accurately captures electron correlation, but its much higher computational expense limits its application. We seek to parameterize a DFT functional based on GW data that is able to recover the more accurate GW results at DFT's lower computational cost. The functional is trained for a given material by a global optimization scheme that determines optimum parameters for existing DFT functionals. The resulting functional is a material-specific DFT functional that recovers the energetics and density coming out of GW data. We validate on a series of molecular examples and solids how well this optimization performs for data that were not included in the original training set. Subsequently, we will use these functionals to optimize geometries and get access to quantities that may be too expensive to be evaluated in GW itself.