Accurate solid-state electronic and optical excitations
from non-empirical (time-dependent) density functional theory

Accurate prediction of the electronic structure of molecules and solids, entirely within density
functional theory (DFT), has been a long-standing challenge in computational materials science.
Specifically, the accurate prediction of band gaps has long been believed to be outside the reach
of DFT. Optimal tuning has emerged as a highly accurate method for predicting fundamental
gaps of molecules by enforcing the ionization potential (IP) theorem – an exact condition in
DFT. Unfortunately, this approach breaks down for periodic solids, where the delocalized nature
of electronic orbitals causes the IP theorem to be trivially satisfied and thus of no predictive
value.
Throughout my PhD we developed a simple, computationally inexpensive, and fully non-
empirical method for solid-state band gap predictions. The approach introduces an ansatz that
generalizes the IP theorem to the removal of charge from a localized Wannier orbital. I will
present applications of the method to three-dimensional solids, notably simple semiconductors
and insulators, halide perovskites, and metal oxides. Our results demonstrate quantitative
accuracy in band gaps and optical absorption spectra with respect to experiment and a
comparable level of accuracy to many-body perturbation theory. I will also show that the method
performs consistently well for systems of increasing size across all length scales, highlighting its
robustness. In particular, it yields accurate results for one-dimensional molecular chains, from
the monomer limit to the infinite polymer limit. Finally, I will discuss and analyze the
foundations of optimal tuning via localized orbitals from a theoretical perspective, laying a
rigorous justification for the ansatz, hitherto used without proof.