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

This work presents the formalism and implementation of excited state nuclear forces within density functional linear response theory using a plane wave basis set. An implicit differentiation technique is developed for computing nonadiabatic coupling between Kohn-Sham molecular orbital wave functions 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.