# Wannier-function-based constrained DFT with nonorthogonality-correcting Pulay forces in application to the reorganization effects in graphene-adsorbed pentacene. (arXiv:1802.01669v2 [cond-mat.mtrl-sci] UPDATED)

Pulay terms arise in the Hellman-Feynman forces in electronic structure

calculations when one employs a basis set made of localized orbitals that move

with their host atoms. If the total energy of the system depends on a subspace

population defined in terms of the localized orbitals across multiple atoms,

then unconventional Pulay terms will emerge due to the variation of the orbital

nonorthogonality with ionic translation. Here, we derive the required exact

expressions for such terms, which cannot be eliminated by orbital

orthonormalization. We have implemented these corrected ionic forces within the

linear-scaling density functional theory (DFT) package ONETEP, and have used

constrained DFT to calculate the reorganization energy of a pentacene molecule

adsorbed on a graphene flake. The calculations are performed by including

ensemble DFT, corrections for periodic boundary conditions, and empirical Van

der Waals interactions. For this system we find that tensorially invariant

population analysis yields an adsorbate subspace population that is very close

to integer-valued when based upon nonorthogonal Wannier functions, and also but

less precisely when using pseudoatomic functions. Thus, orbitals can provide a

very effective population analysis for constrained DFT. Our calculations show

that the reorganization energy of the adsorbed pentacene is typically lower

than that of pentacene in the gas phase. We attribute this effect to steric

hindrance.