Plane wave/pseudopotential implementation of excited state gradients in density functional linear response theory: a new route via implicit differentiation

TL;DR

This paper introduces a novel method for calculating excited state nuclear forces in TDDFT using plane wave basis sets and implicit differentiation, enabling accurate force computations for molecules.

Contribution

It develops and implements an implicit differentiation approach for excited state gradients within plane wave TDDFT, focusing on nonadiabatic couplings and orbital energy gradients.

Findings

Gradients converge rapidly with increasing active orbital subspace.

Method accurately computes excited state forces for H2 and N2 molecules.

Implementation demonstrates efficiency in plane wave pseudopotential codes.

Abstract

This work presents the formalism and implementation of excited state nuclear forces within density functional linear response theory (TDDFT) using a plane wave basis set. An implicit differentiation technique is developed for computing nonadiabatic coupling between Kohn-Sham molecular orbital wavefunctions as well as gradients of orbital energies which are then used to calculate excited state nuclear forces. The algorithm has been implemented in a plane wave/pseudopotential code taking into account only a reduced active subspace of molecular orbitals. It is demonstrated for the H$_2$ and N$_2$ molecules that the analytical gradients rapidly converge to the exact forces when the active subspace of molecular orbitals approaches completeness.