The reference-geometry Harris-Foulkes (RGHF) approach has been used to model high-order terms within the expansion of multi-dimensional potential energy surfaces (PES) as needed within the calculation of accurate vibrational frequencies beyond the harmonic approximation. The key step of this method is a localization of the electron density to the atoms of the molecule at a given reference structure and a subsequent transfer of these atom-centered partial densities to the atom positions of distorted structures. This concept has been used to evaluate the 3-mode coupling terms of a multi-mode expansion of the PES as arising in the Watson Hamiltonian. Systematic benchmark calculations for vibrational frequencies obtained from vibrational configuration interaction (VCI) theory have been performed in order to study the effects of this approximation on the fundamental modes of a test suite of 28 molecules.

We present a method which uses the results of a molecular Kohn-Sham calculation at a reference geometry to approximate the energy at many different geometries. The Kohn-Sham electron density of the reference geometry is decomposed into atomic fragments, which move with the nuclei to approximate the density at a new geometry and the energy is evaluated with the Harris-Foulkes functional. Preliminary results for a biological quantum-mechanics/molecular-mechanics trajectory are promising: the errors of reference-geometry Harris-Foulkes (compared to full self-consistent Kohn-Sham) for the PBE exchange-correlation functional have the same magnitude as the difference between the energies of PBE and BLYP.