Embedded fragmentation of vibrational energies

Abstract

Can the zero-point vibrational energies (ZPVE) of molecular clusters and crystals be evaluated as sums of ZPVE of constituent molecular fragments embedded in the cluster or crystal electrostatic environment? What is the appropriate unit of fragmentation: monomers or overlapping dimers? Can the contributions of acoustic phonons, which are fundamentally delocalized, be recuperated at satisfactory accuracy? These questions are answered by this study applying embedded monomer- and dimer-fragmentation methods to the harmonic ZPVE of hydrogen fluoride clusters, hydrogen fluoride crystal, and water clusters. Our findings are as follows: (1) ZPVE are reproduced accurately by both fragmentation schemes within a few percents of exact values or a few tenths of 1 kcal mol(-1) per molecule even for crystalline hydrogen fluoride, which has acoustic phonons. (2) Both the monomer- and dimer-based fragmentation are nearly equally accurate and useful for the absolute values of ZPVE, but the latter is more reliable than the former in reproducing the relative ZPVE of cluster isomers of the same size. (3) The embedding field is essential as it renders nonzero frequencies to the translational and rotational motions of monomers and dimers, accounting for the pseudo-translational and librational motions of the entire clusters or crystals. (4) Some of these low-frequency modes of fragments are calculated to have imaginary frequencies because the fragments are not at their equilibrium geometries, causing ZPVE to be complex. The imaginary part of ZPVE, which is nonphysical and is guaranteed to vanish in the exact limit of the many-body expansion, is nonetheless a useful estimate of errors in the real part.