On the mean accuracy of the separable vscf approximation for large molecules

The separable VSCF approximation and the VSCF-PT2 method are extensively used for anharmonic vibrational spectroscopy calculations of large molecules. VSCF-PT2 uses second-order perturbation theory to correct the VSCF level, and is thus more accurate. It is shown by test calculations for a series of amino acids and peptides that the mean deviation of VSCF from VSCF-PT2 frequencies decreases for an increasing number of modes N, the decrease scaling roughly with log N. It is conjectured that the result is a manifestation of improved mean accuracy of VSCF as a mean-field approximation, a consequence of increased averaging with increasing numbers of modes. There is no systematic increase in VSCF accuracy with N for individual vibrational transitions. Increased accuracy of VSCF with N is found for certain groups of transitions, e.g., N - H stretches. The results are expected to be useful in choosing methods for spectroscopy calculations of extended systems such as large peptides, proteins, and nucleic acids.