values [ 115 , 116 ], for the molecules of Table5.17. This admittedly very small
sample suggests that semiempirical IEs calculated as energy differences might be
comparable to ab initio values. Koopmans’ theorem (the IE for an electron is
approximately the negative of the energy of its molecular orbital; applying this to
the HOMO gives the IE of the molecule) values are consistently bigger than those
from energy differences using the same method (by 0.1–0.8 eV). No consistent
advantage for any of the six methods is evident here, but a large sample would
likely show the most accurate of these methods to be the energy difference using
MP2(fc)/6-31G (see Table 5.17 and accompanying discussion).
Calculations by Stewart on 256 molecules (of which 201 were organic), using
Koopmans’ theorem, gave mean absolute IE errors of 0.61 eV for AM1 and 0.57 eV
for PM3; 60 of the AM1 errors (23%) and 88 of the PM3 (34%) were negative
(smaller than the experimental values) [ 70 ]. Particularly large errors (2.0–2.9 eV)
were reported for nine molecules: 1-pentene, 2-methyl-1-butene, acetylacetone,
alanine (AM1), SO 3 (AM1), CF 3 Cl (AM1), 1,2-dibromotetrafluoroethane, H 2 SiF 2
(PM3), and PF 3 (AM1). For some of these it may be theexperimentalresults that
are at fault; for example, there seems to be no reason why 2-methyl-1-butene and
2-methyl-2-butene should have such different IEs, and in the opposite order to those
calculated: experimental, 7.4 and 8.7 eV; calculated, 9.7 and 9.3 (AM1), 9.85 and
9.4 (PM3) eV, respectively. Ab initio HF/3-21G()energy-difference calculations
by the author give IEs in line with the AM1, rather than the claimed experimental,
results: 2-methyl-1-butene, 9.4 eV; 2-methyl-2-butene, 9.1 eV. Calculations by the
author on the first 50 of these 256 molecules (of these 50 all but H 2 and H 2 O are
organic) gave these mean absolute IE errors: AM1, 0.46 (12 negative); PM3, 0.58
(five negative); ab initio HF/3-21G(), 0.71 (11 negative). So for the set of 256
mostly organic molecules AM1 and PM3 gave essentially the same accuracy, and
for the set of 50 molecules AM1 was slightly better than PM3 and the ab initio
method was slightly worse than the semiempirical ones. The HF/3-21G()level is
the lowest ab initio one routinely used (or at least reported) nowadays, and is less
popular now than HF/6-31G*. Ionization energies and electron affinities compara-
ble in accuracy to those from experiment can be obtained by high-accuracy ab initio
calculations (Sections5.5.2.2b and5.5.5) and by DFT (Chapter 7), using the energy
difference of the two species involved.
Dewar and Rzepa found that the MNDO (Section6.2.5.3) electron affinities of
26 molecules with delocalized HOMOs (mostly radicals and conjugated organic
molecules) had an absolute mean error of 0.43 eV; for ten molecules with the
Table 6.6 Some ionization energies (eV). TheDE values (cation energy minus neutral energy)
correspond to adiabatic, and the Koopmans’ theorem values to vertical IEs. The ab initio energies
are MP2(fc)/6–31G* (Table 5.17). Experimental values are adiabatic, from [ 115 ] (CH 3 OH and
CH 3 COCH 3 ) and [ 116 ] (CH 3 SH)
DE Koopmans’
AM1 PM3 ab in. AM1 PM3 ab in. Exp
CH 3 OH 10.5 10.7 10.6 11.1 11.1 12.1 10.9
CH 3 SH 8.7 9 9 8.9 9.2 9.7 9.4
CH 3 COCH 3 9.9 10.1 9.6 10.7 10.8 11.2 9.7
6.3 Applications of Semiempirical Methods 433