An Evaluation of Scaling Factors for Multiparameter Scaling Procedures Based on DFT Force Fields

An extended database of scaling factors for calculating
fundamental
frequencies within multiparameter scaled quantum mechanical (SQM)
force field, and effective scaling frequency factor (ESFF) methods,
based on various DFT force fields is reported. Twenty-six density
functionals have been examined in conjunction with various Pople’s
and Dunning’s basis sets of VDZ and VTZ quality. The calculations
were based on a standard training set of 30 molecules proposed by
Baker et al., for which 660 vibrational modes were assigned. Six functionals
turned out to be particularly well-suited to the calculations oriented
toward determination of scaled frequencies. They are B3LYP, B3PW91,
B97, B97-1, B97-2, and O3LYP; they are all capable of providing reasonable
scaled frequencies even for the small, 6-31G* basis set (rms <15
cm–1). Correlations between the quality of the scaled
frequencies and the basis set quality as well as the accuracy of the
predicted molecular geometry were investigated. The 6-311+G** basis
set turned out to be preferable. In addition, correlation between
the rms values in the scaled frequencies and the errors in the predicted
geometric parameters was found. Both 11- and 9-parameter scaling frames
are compared. It is shown that 9-parameter scaling is preferable in
the middle range of the vibrational spectrum (500–2500 cm–1), provided it was based on high-quality force fields.
Finally, statistical uncertainties of the calculated scaling factors
are reported.