Analytical expression for the excited-state force from density-functional perturbation theory

Abstract

We provide an analytical expression for the energy gradient of electronically excited states within the combined time-dependent density-functional theory and the dynamical density-response formalism, called the Casida formalism. This is achieved by obtaining the nuclear coordinate derivatives of the Kohn-Sham eigenvalues and orbitals through density-functional perturbation theory (DFPT). The DFPT-based method was found successfully applied to obtain potential energy surfaces of small molecules (${\text{N}}_{2}$ and $\text{CO}$) and conduct a molecular dynamics simulation of a benzene molecule, thereby revealing the slow convergence problem associated with the singular matrix appearing in DFPT.