Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane Wave Basis Set

TL;DR

This paper introduces a variational orbital optimization method for calculating excited electronic states using density functionals, applicable with real space grid or plane wave basis sets, and capable of handling complex excited states with improved convergence.

Contribution

The authors develop a novel direct orbital optimization approach for excited states that works with both KS and orbital-density dependent functionals, including self-interaction corrections, and demonstrates enhanced convergence and accuracy.

Findings

Successfully computed charge-transfer excitations in nitrobenzene and CO.

Applied the method to metal-to-ligand charge-transfer states of an Fe(II) complex.

Analyzed the impact of self-interaction correction on various excited states.

Abstract

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density dependent functionals (ODD) including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate $\pi^\ast$ orbitals where the importance of complex orbitals is illustrated. An application of the method to several metal-to-ligand charge-transfer and metal-centred excited states of an Fe$^{\rm II}$ photosensitizer complex is described and the results compared to reported experimental estimates. The method is also used to study the effect of Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.