The Insignificance of Long-Distance Interactions for Molecular Frequencies. Analyses of Sparse Forceconstant Matrices

The experimentally observed group additivity of temperature dependent molecular properties of organic molecules i.e. the heat capacity, suggests that molecular vibrational frequencies primarily are determined by short-distance atomic interactions. Based on the molecular graph a consistent hierarchy of molecular force constant (FC) matrices has be constructed. These sparse and low-density matrices systematically include the force constants for the uncoupled atomic displacement, neighbour (1-2), next-neighbour (1-3) and longer-range atomic interactions. Such FC matrices were constructed for a number of hydrocarbons and hetero atomic molecules, and the error on the vibrational frequencies decrease rapidly with the inclusion of more interactions in the matrices. With inclusion of 1-4 interactions average relative errors between 1.3 % and 3.8 % are obtained based on B3LYP/6-311(d,p) calculations. The largest relative errors are found for low frequency vibrations below 50 cm-1 . The results were largely independent of the calculational level. The insignificance of the long-distance interactions was confirmed by the improvement in the calculated frequencies of hetero atomic molecules when FC matrices with only short-distance interactions is complemented with matric elements from a FC matrix of a hydrocarbon with similar geometry. Further confirmation is provided by calculations of molecular frequencies from the FC matrices constructed from fragments and supplemented with matrix elements for the interactions between atoms belonging to different fragments taken from appropriate compounds. The difference between the vibrational frequencies obtained in this way without the molecular FC matrix an those obtained from the full FC matrix are within a few cm-1 .