On the fallibility of variational calculations: A b i n i t i o versus empirical potential energy functions for HCN

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Abstract
HCN is one of the most advantageous candidates among the polyatomics for an empirical determination of the anharmonic potential energy function because of the extensive list of precise spectroscopic data available for a number of isotopomers. We have determined an empirical stretching potential energy surface for HCN with a rms error of less than 3 cm−1 for vibrational energy levels of up to 18 400 cm−1. The best ab initio stretching potential has a rms error of 10.5 cm−1 for the same levels. However, using the ab initio dipole moment surface and vibrational wave functions from the empirical vs ab initio potentials, we find that the predicted intensities are remarkably different, a factor of 4 for the (0,0,6) band at 18 377 cm−1. Furthermore, the predicted intensities from the theoretical potential agree significantly better with the experimental values. The most natural explanation of these results is that the ab initio potential is closer to reality than an empirical surface obtained from exhaustive spectroscopic data.

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