Novel approaches to spectral properties of correlated electron materials: From generalized Kohn-Sham theory to screened exchange dynamical mean field theory

The most intriguing properties of emergent materials are typically consequences of highly correlated quantum states of their electronic degrees of freedom. Describing those materials from first principles remains a challenge for modern condensed matter theory. Here, we review, apply and discuss novel approaches to spectral properties of correlated electron materials, assessing current day predictive capabilities of electronic structure calculations. In particular, we focus on the recent Screened Exchange Dynamical Mean-Field Theory scheme and its relation to generalized Kohn-Sham theory. These concepts are illustrated on the transition metal pnictide BaCo$_2$As$_2$ and elemental zinc and cadmium.