A New Approach to Vibrational Analysis of Large Molecules by Density Functional Theory: Wavenumber-Linear Scaling Method

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Abstract

Normal vibration calculations were performed on 164 basic organic and inorganic compounds by the density functional method of B3LYP/6-311+G** using the wavenumber-linear scaling (WLS) method, in which essentially only one parameter is involved for the whole wavenumber region. The average deviation of the WLS-scaled calculated wavenumbers from the observed wavenumbers for a total of 1223 normal modes was 3.4%. The present results and the previous results on 205 compounds have shown the high performance of the WLS method in vibrational analysis of a variety of compounds. The effect of anharmonicity on the observed wavenumbers was examined on the basis of the calculated wavenumbers for 224 diatomic molecules and ions in comparison with their experimental harmonic wavenumbers. The results indicate that the larger positive deviations of the unscaled calculated wavenumbers from the observed values at higher wavenumbers are attributed almost exclusively to the neglect of anharmonicity in the calculated wavenumbers. To generalize and simplify the WLS method for more convenient use, the wavenumber-linear scale factors were derived from 17 well-defined wavenumbers of liquid indene at different calculation levels. The application of the derived scale factors to vibrational analysis of all-trans-1,3,5,7,9-decapentaene yielded results in close agreement with the experimental data. This WLS indene calibration method is a convenient technique to obtain vibrational wavenumbers of large molecules with high accuracy.

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