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Calculation of molecular vibrations: Selective scaling factors for semiempirical force constants

The complete force constant matrices of a set of 50 aliphatic and aromatic hydrocarbons are calculated at the density functional theory B3LYP/6–31+G(d, p) and semiempirical PM3 levels of theory. After transformation from Cartesian to nonredundant internal coordinates, the errors in the semiempirical force constants are systematically analyzed. The force constants of the C(SINGLE BOND)C stretching coordinates can be easily corrected by a second‐order fit. Thus, only two parameters are needed to reduce the mean error from 21.2 to 1.23%. The errors of other internal coordinates, particulary those including torsional modes, exhibit a larger diversity. The performance of the correction scheme in predicting vibrational spectra is shown for several examples including buckminsterfullerene (C60). © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 2050–2059, 1997