a frequency calculation are usually not needed, since the semiempirical energy is
normally not adjusted by adding the ZPE (Section6.2.5.2). As with ab initio cal-
culations, semiempirical frequencies are used to characterize a species as a mini-
mum or a transition state (or a higher-order saddle point), and to get an idea of what
the IR spectrum looks like. As with ab initio frequencies too, in semiempirical
methods the wavenumbers (“frequencies”) of vibrations are calculated from a
mass-weighted second-derivative matrix (a Hessian) and intensities are calculated
from the changes in dipole moment accompanying the vibrations. Like their ab
initio counterparts, semiempirical frequencies are higher than the experimental
ones; presumably this is at least partly due to the harmonic approximation, as was
discussed in Section5.5.3.
Correction factors improve the fit between semiempirically calculated and
experimentally measured spectra, but the agreement does not become as good as
does the fit of corrected ab initio to experimental spectra. This is because deviations
from experiment are less systematic for semiempirical than for ab initio methods (a
characteristic that has been noted for errors in semiempirical energies [ 98 ]). For
AM1 calculations, correction factors of 0.9235 [ 99 ] and 0.9532 [ 100 ], and for PM3,
factors of 0.9451 [ 99 ] and 0.9761 [ 100 ], have been recommended. A factor of 0.86
has been recommended for SAM1 for non-H stretches [ 101 ]. However, the varia-
tion of the correction factor with thekindof frequency is bigger for semiempirical
than for ab initio calculations; for example, for correcting carbonyl stretching
frequencies, examination of a few molecules indicated (author’s work) that (at
least for C, H, O compounds) correction factors of 0.83 (AM1) and 0.86 (PM3) give
a much better fit to experiment.
The calculated intensities of semiempirical vibrations seem likely to be in
general more approximate than those for ab initio vibrations [ 102 ], which latter
are typically within 30% of the experimental intensity at the MP2 level [ 103 ]. This
is somewhat surprising, since semiempirical (AM1 and PM3 and later derivatives)
dipole moments, from the vibrational changes of which intensities are calculated,
are fairly accurate (Section6.3.4). Note however that unlike the case with UV
spectra, IR intensities are rarely actually measured; rather, one usually simply
visually classifies a band as strong, medium, etc., by visual comparison with the
strongest band in the spectrum. There do not seem to have been any published
surveys comparing, for a variety of compounds, the intensities of IR bands calcu-
lated by modern NDDO methods with those from experiment, but an idea of the
reliability of semiempirical frequencies and intensities is given by the IR spectra in
Figs.6.5–6.8, which compare experimental spectra with AM1 and ab initio (MP2/6-
31G*) spectra, for the same four compounds (acetone, benzene, dichloromethane,
methanol) shown in Figs.5.33–5.36. The experimental and MP2 spectra are the
ones used in Figs.5.33–5.36. For acetone and methanol (Figs.6.5and6.8) the MP2
spectra match the experimental distinctly better than do the AM1; and other work
[ 102 ] indicates that MP2 IR spectra resemble the experimental spectra more closely
than do AM1 spectra.
424 6 Semiempirical Calculations