molecules gave mean absolute errors of: AM1, 0.35 D and PM3, 0.38 D [ 70 ]. So
with these larger samples the AM1 errors were somewhat bigger. Nevertheless, all
these results taken together do indicate that unless one is prepared to use a slower
approach, e.g. large basis sets with density functional (Chapter 7) methods (errors
of ca. 0.1 D [ 108 ]; this paper also gives some results for ab initio calculations),
AM1 dipole moments using AM1 geometries may be as good a way as any to
calculate this quantity. This applies, of course, only to conventional molecules;
molecules of exotic structure and “hypervalent” molecules (Sections6.3.1 and
6.3.2.1) often defy accurate semiempirical predictions.
6.3.4.2 Charges and Bond Orders
The conceptual and mathematical bases of these concepts were outlined in
Section5.5.4.Wesawthatunlike,say,frequenciesanddipolemoments,there
are problems with regarding charges and bond orders as experimental observables
(carefully defined atom charges can, it is said be measured 109 ), and with settling
on a single, right way to calculate them.Somewouldarguethattheatoms-in-
molecules theory does provide such a unique ansatz. Nevertheless, we saw that
there are several prescriptions for calculating charges and bond orders, and
as with ab initio calculations, semiempirical charges and bond orders can be
defined in various ways. The concepts are nevertheless useful, and electrostatic
potential charges and L€owdin bond orders are preferred nowadays to the Mulliken
parameters.
Figure6.9shows charges and bond orders calculated for an enolate (the conju-
gate base of ethenol or vinyl alcohol) and for a protonated enone system (protonated
Table 6.4 Some calculated dipole moments compared to experimental ones. Dipole moments are
in Debyes. Calculations are by the author; experimental values are taken from [ 88 ] and [ 107 ]. For
each method is given the number of positive and negative deviations from experiment and the
arithmetic mean of the absolute values of the deviations
Computational method
AM1 HF/6–31G* //
AM1
PM3 HF/6–31G* //
PM3MP2/6–31G* ExpCH 3 NH 2 1.5 1.42 1.4 1.54 1.6 1.3
H 2 O 1.86 2.25 1.74 2.16 2.24 1.9
HCN 2.36 3.24 2.7 3.24 3.26 3
CH 3 OH 1.62 1.9 1.49 1.88 1.95 1.7
Me 2 O 1.43 1.54 1.25 1.51 1.6 1.3
H 2 CO 2.32 2.87 2.16 2.76 2.84 2.3
CH 3 F 1.62 2 1.44 1.91 2.11 1.9
CH 3 Cl 1.51 2.07 1.38 2.14 2.21 1.9
Me 2 SO 3.95 4.56 4.49 4.83 4.63 4
CH 3 CCH 0.4 0.58 0.36 0.6 0.66 0.8
Deviations 4 +, 6" 9+, 1" 2+, 8" 9+, 1" 9+, 1"
mean 0.21 mean 0.29 mean 0.27 mean 0.29 mean 0.34
6.3 Applications of Semiempirical Methods 429