Variational density functional calculations of excited states via direct optimization

TL;DR

This paper introduces a direct optimization method for variational density functional calculations of excited states, improving robustness and convergence over traditional SCF approaches, and demonstrates its effectiveness on various molecular systems.

Contribution

A novel direct optimization approach using a maximum overlap method for excited states in density functional theory, enhancing convergence and accuracy.

Findings

The method converges faster and more reliably than SCF strategies.

It successfully calculates a conical intersection without fractional occupations.

Self-interaction correction improves excited state accuracy.

Abstract

The development of variational density functional theory approaches to excited electronic states is impeded by limitations of the commonly used self-consistent field (SCF) procedure. A method based on a direct optimization approach as well as the maximum overlap method is presented and the performance compared with previously proposed SCF strategies. Excited-state solutions correspond to saddle points of the energy as a function of the electronic degrees of freedom. The approach presented here makes use of a preconditioner determined with the help of the maximum overlap method to guide the convergence on a target nth-order saddle point. The method is found to be more robust and to converge faster than previously proposed SCF approaches for a set of 89 excited states of molecules. A limited-memory formulation of the symmetric rank-one method for updating the inverse Hessian is found to give the best performance. A conical intersection for the carbon monoxide molecule is calculated without resorting to fractional occupation numbers. Calculations on excited states of the hydrogen atom and a doubly excited state of the dihydrogen molecule using a self-interaction corrected functional are presented. For these systems, the self-interaction correction is found to improve the accuracy of density functional calculations of excited states.