Single vibrational scaling factors for the calculation of enthalpies of formation at a given level of theory are widely used and statistically correct. However, it can be shown that for several molecules the error is substantial, and it is possible to determine selective molecular scaling factors that minimize or eliminate the deviation between theoretical enthalpies of formation with respect to accurate experimental data. Selective scaling factors for 248 enthalpies of formation relative to the experimental data using the G3(MP2)//B3-CEP composite method reduced the mean absolute error from 1.55 to 0.64 kcal mol . This error is smaller than the mean absolute error of some of the most sophisticated methods from the Gn family and other composite methods. The similarity among scaling parameters for molecules with comparable characteristics indicates that the optimum parameters are not a random empirical adjustment but must be related to the nature of the chemical bonds, the atomic species, and possibly the level of theory used. Molecules with the same functional groups and similar types of bonds presented similar vibrational scaling factors.
da Rocha, N.L., Custodio, R. On the role of vibrational selective scaling for the calculation of enthalpies of formation using a composite method. Theor Chem Acc 139, 38 (2020). https://doi.org/10.1007/s00214-020-2552-9