Derivation of the Supermolecular Interaction Energy from the Monomer Densities in the Density Functional Theory

Abstract

The density functional theory (DFT) interaction energy of a dimer is rigorously derived from the monomer densities. To this end, the supermolecular energy bifunctional is formulated in terms of mutually orthogonal sets of orbitals of the constituent monomers. The orthogonality condition is preserved in the solution of the Kohn-Sham equations through the Pauli blockade method. Numerical implementation of the method provides interaction energies which agree with those obtained from standard supermolecular calculations within less than 0.1~\% error for three example functionals: Slater-Dirac, PBE0 and B3LYP, and for two model van der Waals dimers: Ne$_2$ and (C$_2$H$_4$)$_2$, and two model H-bond complexes: (HF)$_2$ and (NH$_3$)$_2$.