Anharmonic potential functions of polyatomic molecules: Part VII. Iterational calculation of anharmonic corrections to fundamental frequencies

Abstract

An iterational method based on the application of empirical anharmonic potential functions to polyatomic molecules is used for the calculation of approximate anharmonicity corrections to observed fundamental frequencies of vibrations in polyatomic molecules. Each iterational step involves a least squares adjustment of the quadratic force constants and a calculation of the cubic and quartic potential constants from the empirical anharmonic potential function followed by a nonlinear transformation from the valence-force to normal coordinate representation. The transformed potential constants are then used to calculate anharmonic constants χss′ from Nielsen's formulas thus yielding approximate anharmonicity corrections. Three different anharmonic functions of the valence-force type and one Urey-Bradley-type function have been employed to explore the influence of the type of potential used on the results. Sample calculations have been performed for the molecules H2O and D20, H2S and D2S, H2Se and D2Se, and for 14NO2 and 15NO2 and a remarkable convergence stability of the process has been observed. The converged sets of corrected frequencies are in good agreement with the experimental zero-order frequencies, in particular with the use of a modified valence-type potential involving a Lippincott function for each stretching motion, a double minimum function for the bending potential, and two additional terms accounting for cubic and quartic stretch-bend interactions.