vibrational frequencies

vibrational frequencies: "Scaling Vibrational Frequencies


A final point concerns the accuracy obtained in vibrational frequency calculations as a function of
the theoretical method used. In many cases, the experimentally measured values will differ significantly
from those calculated theoretically. One source of discrepancy is that experimental values are often
measured in solution while calculated values refer to the
gas phase. A second source of error is the
assumption of the harmonic approximation. There is, however, also a
method-dependent difference between
calculated and experimentally measured harmonic vibrational frequencies in the gas phase. For more
economical methods such as HF or AM1, the deviations typically range around 10%. In order to account
for this systematic deviation, all vibrational frequencies can be scaled
(=multiplied with the
same value) down to fit the experimental harmonic frequencies. Radom et al. have published a list
of recommended scale factors for frequently used theoretical methods in J. Phys. Chem. 1996,
100, 16502. A small selection is:

method	scale factor	rms deviation (cm-1)
AM1	0.9532	126
PM3	0.9761	159
HF/6-31G(d)	0.8953	50
MP2(FC)/6-31G(d)	0.9427	61
QCISD(FC)/6-31G(d)	0.9537	37
BLYP/6-31G(d)	0.9945	45
B3LYP/6-31G(d)	0.9614	34

It is clear from these results that semiempirical methods such as AM1 and PM3 will, even after
scaling, not be particularly reliable in predicting vibrational spectra. Rather good results can
be obtained either from highly correlated, expensive methods such as QCISD, or from hybrid
density functional calculations such as B3LYP.

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