Here are some correction factors that have been calculated for various func-
tionals, as well as for some ab initio and semiempirical methods (slightly different
correction factors were recommended for the ZPE) [ 77 ]; except for HF/3-21G the
basis set for the ab initio and DFT methods is 6-31G*:
HF/3-21G HF/6-31G* MP2(FC) AM1 BLYP BP86 B3LYP B3PW91
0.909 0.895 0.943 0.953 0.995 0.991 0.961 0.957The BLYP/6-31G and BP/86 correction factors are very close to unity. For the
frequencies of polycyclic aromatic hydrocarbons calculated by the B3LYP/6-
31G method, Bauschlicher multiplied frequencies below 1,300 cm"^1 by 0.980
and frequencies above this by 0.967 [ 76 ]. In their paper introducing the modifica-
tion of Becke’s hybrid functional to give the B3LYP functional, Stephens et al.
studied the IR and CD spectra of 4-methyl-2-oxetanone and recommended the
B3LYP/6-31G* as an excellent and cost-effective way to calculate these spectra
[ 58 ]. With six different functionals, Brown et al. obtained an agreement with
experimental fundamentals of ca. 4–6%, except for BHLYP [ 103 ]. The 2007
review by Riley et al. [ 46 ]showsthatawideassortmentoffunctionals/basis
sets gives errors of ca. 50–120 cm"^1 .Forcharacterizingnewmoleculessuch
errors are probably not important, because each functional/basis (indeed, each
method) has a fairly constant multiplicative correction factor [ 77 ]whichbringsits
IR spectrum into reasonable positionalagreement with experiment. More impor-
tant than accurate wavenumber matching is reasonable agreement of relative
intensities with reality. Intensities are calculated from the variation of dipole
moments with vibrational distortions (Chapter 5,discussioninconnectionwith
Eq 5.204). If calculated dipole moments do not vary much from one method to
another and are similar to experimental values, as is suggested by Table7.8,
Table 7.8 Some calculated dipole moments (Debyes) compared to experiment. For each method
is given the number of positive, negative, and formal (to one decimal place) zero deviations from
experiment, and the unsigned arithmetic mean of the absolute values of the deviations. The basis
set for the B3LYP, M06 and MP2 calculations is 6-31G*. Experimental values are taken from
[ 67 , 69 ]; calculations are by the author
Computational method
B3LYP M06 AM1 MP2(fc) Exp
CH 3 NH 2 1.47 1.47 1.31 1.57 1.3
H 2 O 2.1 2.15 2.1 2.24 1.9
HCN 2.91 2.98 2.9 3.26 3
CH 3 OH 1.69 1.72 1.68 1.95 1.7
Me 2 O 1.28 1.27 1.25 1.44 1.3
H 2 CO 2.19 2.25 2.23 2.84 2.3
CH 3 F 1.72 1.72 1.65 2.11 1.9
CH 3 Cl 2.09 2.05 1.91 2.21 1.9
Me 2 SO 3.93 3.89 3.98 4.63 4
CH 3 CCH 0.69 0.69 0.66 0.66 0.8
Deviation 3 þ, 5–, two 0 3 þ, 4–, three 0 2 þ, 4–, four 0 9 þ, 1–, none 0
mean 0.11 mean 0.11 mean 0.22 mean 0.31
7.3 Applications of Density Functional Theory 485