Evaluation of Pulay forces due to change in overlap of subspace-projection orbitals in constrained DFT: Application in calculation of reorganization energy of adsorbed molecule

Total energy of a constrained DFT calculation depends on population of subspace(s). When such subspace is defined in terms of orbitals localized on host atoms, ionic translations change the overlap of corresponding projection orbitals generating unconventional Pulay terms. We derive an exact expression for such Pulay terms maintaining non-orthogonality of projection orbitals. The corrected forces are implemented in the linear scaling DFT code ONETEP and, in conjunction with constrained DFT, are used to calculate the reorganization energy of a pentacene molecule adsorbed on a graphene flake. We show that subspace population depends on the choice of projection orbitals centred on a given set of host atoms and that non-orthogonal Wannier functions offer more precise results compared to pseudo-atomic orbitals. Our calculations of reorganization energy, performed by including ensemble DFT, correction for periodic boundary conditions and dispersion corrections show that, in general, reorganization energy of an adsorbed pentacene is lower than that of one in gas phase. This is consistent with effect of steric hindrance.