An effective scaling frequency factor method for scaling of harmonic vibrational frequencies: The use of redundant primitive coordinates

A modified effective scaling frequency factor (ESFF) method that takes advantage of the potential energy distribution (PED) coefficients calculated in the basis of redundant primitive internal coordinates is presented. This approach is simpler and more flexible than that based on the natural internal coordinates. The sets of optimal scaling factors for routine 9- and 11-parameter ESFF calculations based on B3LYP/6-311G∗∗ force fields are derived from Baker's training set of 30 molecules (660 frequencies). The calculated root-mean-square (RMS) deviations for all frequencies are 11.42 and 11.44 cm−1 for 9- and 11-parameter scaling, respectively. They are somewhat lower than in the case of ordinary ESFF calculations. The new sets of factors seem to be particularly well suited for scaling of frequencies in the middle region of the vibrational spectra (1000-2500 cm−1) - the RMS values in this range are 8.37 for 9-, and 9.56 cm−1 for 11-parameter scaling. These values are to be compared with 9.20 and 10.29 cm−1, respectively, calculated within the natural coordinates based ESFF formalism.