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Pulay terms arise in the Hellman-Feynman forces in electronic structurecalculations when one employs a basis set made of localized orbitals that movewith their host atoms. If the total energy of the system depends on a subspacepopulation defined in terms of the localized orbitals across multiple atoms,then unconventional Pulay terms will emerge due to the variation of the orbitalnonorthogonality with ionic translation. Here, we derive the required exactexpressions for such terms, which cannot be eliminated by orbitalorthonormalization. We have implemented these corrected ionic forces within thelinear-scaling density functional theory (DFT) package ONETEP, and have usedconstrained DFT to calculate the reorganization energy of a pentacene moleculeadsorbed on a graphene flake. The calculations are performed by includingensemble DFT, corrections for periodic boundary conditions, and empirical Vander Waals interactions. For this system we find that tensorially invariantpopulation analysis yields an adsorbate subspace population that is very closeto integer-valued when based upon nonorthogonal Wannier functions, and also butless precisely when using pseudoatomic functions. Thus, orbitals can provide avery effective population analysis for constrained DFT. Our calculations showthat the reorganization energy of the adsorbed pentacene is typically lowerthan that of pentacene in the gas phase. We attribute this effect to sterichindrance.

physical review. b./physical review. b

Wannier-function-based constrained DFT with nonorthogonality-correcting  Pulay forces in application to the reorganization effects in  graphene-adsorbed pentacene