Estimation of Anharmonic Potential Constants. I. Linear XY2 Molecules

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Abstract
On the basis of a normal-coordinate analysis of a series expansion of the anharmonic potential field, a set of general expressions has been derived for a linear XY2 molecule for relating the cubic and quartic potential constants (k) to the coefficients (f) of the potential function expanded in terms of the internal coordinates. The constants k and f for CO2 and CS2 have been calculated by using the observed values of α and x taken from the literature, and the physical significance of the dependence of k on f has been studied. The anharmonic constants related to the C-O(C-S) bond-stretching vibrations are represented as functions of the parameters of anharmonicity, a3 and a4, which are shown to be transferable from the CO(CS) diatomic molecule. Most of the k, α, and x values for CO2 and CS2 can be predicted quantitatively by assuming a simple potential function, comprised of ordinary quadratic terms and the anharmonic terms for the bond-stretching vibrations mentioned above, with all other higher-order potential terms ignored. A number of methods for estimating the parameters a3 and a4, and a general rule regarding their relative magnitudes, have been discussed. The k, α, and x values of the linear radicals, NH2, ND2, and BO2, may be predicted in the present scheme by making simple assumptions about their potential constants.