Orbital-optimized density functional calculations of excited electronic states: Recent advances and perspectives

Abstract

Orbital-optimized (OO) density functional calculations provide a time-independent, variational route to electronic excitations, alternative to presently widely used time-dependent density functional theory (TDDFT) approaches. As the orbitals are optimized in a state specific way, these methods can provide a balanced description of excited states with different character, thereby overcoming several limitations of practical implementations of TDDFT. Driven by recent developments in algorithms for obtaining excited states as saddle points on the electronic energy surface, OO methods have attracted increasing interest, maturing into an active and rapidly expanding area of research. Here, the theoretical foundations of the approach are clarified and an overview of recent methodological developments in excited-state orbital optimization is provided. An overview of methods for treating open-shell singlet excited states and current approaches for computing transition properties and spectra is also provided. Finally, recent applications to molecular Rydberg, charge-transfer, and core excitations are reviewed, with the aim of assessing the present accuracy and range of applicability of OO density functional calculations with common exchange and correlation functionals.