Density functional vibrational analysis using wavenumber-linear scale factors

Normal coordinate calculations were performed by the density functional method of B3LYP/6-311+G∗∗ on 205 basic organic and inorganic compounds taken from the `Tables of Molecular Vibrational Frequenciesʹ (T. Shimanouchi, 1972). The calculated wavenumbers, νcalc, of 1729 vibrational modes were correlated with the observed wavenumbers, νobs, by a single least-squares fitting. The relationship obtained, after omitting the vibrational modes that give deviations of more than 10%, is νobs/νcalc=1.0087−0.0000163 (νcalc/cm−1). The wavenumber-linear scaling method with this relationship predicts vibrational wavenumbers with high accuracy and is applicable to any compounds, except for the compounds for which the effect of dispersion forces is significant.