Examining the impact of harmonic correlation on vibrational frequencies calculated in localized coordinates

Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.