however, this is likely to be due to an atypical cancellation of errors. The transition
state relative energies are best-approximated in one case (H 2 C¼CHOH reaction) by
AM1 and PM3, and in the other three cases by MP2; for these three latter reactions
the semiempirical relative energies are considerably higher than the experimental
and MP2 values, which accords with other work mentioned above [ 47 , 95 ]. The
newer semiempirical methods, RM1 and PM6, have evidently not been systemati-
cally tested for their accuracy in calculating transition state energies. Since they were
parameterized with ground state molecules, it is unlikely that they represent much
improvement over AM1 and PM3 in this regard. A check of RM1 on the reactions of
Fig.6.3suggests this is the case: comparing the barriers and reaction energies for the
four reactions we find (experiment or MP2/6-31G*/RM1, kJ mol"^1 ):
H 2 C¼CHOH barrier 282/243 reaction energy"42/" 35
HNC barrier 129/337 reaction energy"59/" 50
CH 3 NC barrier 161/320 reaction energy"98/" 101
Cyclopropylidene barrier 13–20/97 reaction energy"293/" 284These RM1 barriers do not represent any improvement over those from AM1
and PM3, but the reaction energies are all within 10 kJ mol"^1 of the experimental,
while some of the AM1/PM3 errors are as much as"41 (HNC, PM3). Despite the
lack of quantitative accuracy, semiempirical methods have been used fairly fre-
quently in recent years to study transition states in biochemical reactions, because
of the large molecules involved [ 97 ].
From this information then, we can conclude that semiempirical heats of formation
and reaction energies (reactant cf. product) are semiquantitatively reliable for AM1 and
PM3, and tend to approach modest quantitative accuracy for RM1 and PM6. Activa-
tion energies (reactant cf. transition state) are usually considerably overestimated by
AM1 and PM3, but are handled better by MNDOC, which actually gives results
somewhat better than those from RHF calculations, at least in many cases. It remains
to be seen what improvement, if any, RM1 and PM6 offer over for activation energies.
An extensive comparison of AM1 with ab initio and density functional methods for
calculating geometries and relative energies is given in Hehre’s book [ 88 ]. Consis-
tently good calculated reaction energies and especially activation energies require
correlated ab initio methods (Section 5.4) or DFT methods (Chapter 7). However,
semiempirical methods are well suited for a preliminary exploration of a potential
energy surface, and are usually good for creating input structures for refinement by
ab initio or DFT. It is interesting that AM1 and PM3, which were parameterized mainly
to give good energies (heats of formation) actually provide quite good geometries but
on the whole energies of no more than modest quality.
6.3.3 Frequencies and Vibrational Spectra.............................
The general remarks and the theory concerning frequencies in Section5.5.3, apply
to semiempirical frequencies too, but the zero-point energies associated with
6.3 Applications of Semiempirical Methods 423