Status in calculating electronic excited states in transition metal oxides from first principles

Characterization of excitations in transition metal oxides is a crucial step in the development of these materials for photonic and optoelectronic applications. However, many transition metal oxides are considered to be strongly correlated materials, and their complex electronic structure is challenging to model with many established quantum mechanical techniques. We review state-of-the-art first-principles methods to calculate charged and neutral excited states in extended materials, and discuss their application to transition metal oxides. We briefly discuss developments in density functional theory (DFT) to calculate fundamental band gaps, and introduce time-dependent DFT, which can model neutral excitations. Charged excitations can be described within the framework of many-body perturbation theory based on Green's functions techniques, which predominantly employs the GW approximation to the self-energy to facilitate a feasible solution to the quasiparticle equations. We review the various implementations of the GW approximation and evaluate each approach in its calculation of fundamental band gaps of many transition metal oxides. We also briefly review the related Bethe-Salpeter equation (BSE), which introduces an electron-hole interaction between GW-derived quasiparticles to describe accurately neutral excitations. Embedded correlated wavefunction theory is another framework used to model localized neutral or charged excitations in extended materials. Here, the electronic structure of a small cluster is modeled within correlated wavefunction theory, while its coupling to its environment is represented by an embedding potential. We review a number of techniques to represent this background potential, including electrostatic representations and electron density-based methods, and evaluate their application to transition metal oxides.