geometries of the reactants and products (energy minima) are quite good, taking the
MP2/6-31G results as our standard. The semiempirical transition state geometries,
however, are also surprisingly good: with only small differences between the AM1
and PM3 results, in all four cases the semiempirical transition states resemble the ab
initio ones so closely that qualitative conclusions based on geometry would be the
same whether drawn from the AM1 or PM3, or from the MP2/6-31G calculations.
The largest bond length error (if we accept the MP2 geometries as accurate) is
about 0.09 A ̊(for the CH 3 NC transition state, 1.897–1.803), and the largest angle
error is 9(for the HNC transition state, 72.8–63.9; most of the angle errors are
less than 3).
These results, together with those of Schr€oder and Thiel [ 47 ], indicate that semi-
empirical geometries are usually quite good, even for transition states. Exceptions
might be expected for hypervalent compounds, and for unusual structures like the
C 2 H 5 cation; for the latter AM1 and PM3 predict the classical CH 3 CH 2 structure, but
MP2/6-31G* calculations predict this species to have a hydrogen-bridged structure
(Fig.5.17). Semiempirical energies are considered in Section6.3.2.
6.3.2 Energies..........................................................
6.3.2.1 Energies: Preliminaries
As with ab initio (Chapter 5) and molecular mechanics (Chapter 4) calculations, the
molecular parameters usually sought from semiempirical calculations are geome-
tries (preceding section) and energies. As explained (Section6.2.5.2), the most
widely-used semiempirical methods, AM1 and PM3, give standard (room tempera-
ture, 298 K) heats of formation. This is in distinct contrast to ab initio calculations,
which give (the negative of) the energy for total dissociation of the molecule
into nuclei and electrons, starting from a hypothetical zero-vibrational energy
state or from the 0 K state with ZPE included (Section5.5.2.1). Ab initio methods
can be made to provide heats of formation, by slightly roundabout methods
(Section5.5.2.2c). The errors in semiempirical heats of formation might at first
strike one as being very large; thus for the common diatomic molecules, which by
definition have standard heats of formation of zero, AM1/PM3 give these heats
of formation (kJ mol"^1 ): H 2 ,"21.7/"56.0; N 2 ,þ46.7/þ73.5; O 2 (triplet),"116/"17.5;
F 2 ,"94.0/"90.8/ Cl 2 ,"59.2/"48.5; Br 2 ,"22.0/þ20.6. An extensive compilation
of AM1 and PM3 heats of formation (which corrects errors in earlier values) [ 70 ]
gave for 657 normal-valent compounds these average errors for the absolute
deviations (AM1/PM3, kJ mol"^1 ): 53/33; for 106 hypervalent compounds 348
(sic)/57. These results are not as bad as they may at first seem if we note that (1)
the heats of formation of organic compounds are commonly in the region of
,400–800 kJ mol"^1 , (2) often we are interested in trends, which are more likely
to be qualitatively right than actual numbers are to be quantitatively accurate, and
(3) usually chemists are concerned with energydifferences, i.e.relativeenergies
6.3 Applications of Semiempirical Methods 419