considerably exaggerate the barriers (assuming high-level ab initio calculations are
correct here!). High-level calculations are available for oxirene and dimethyloxir-
ene. For oxirene, these gave a barrier of merely 1–4 kJ mol"^1 [ 49 ] and 3 kJ mol"^1
[ 50 ]; in this later case the carbene is not a stationary point and the barrier is for
direct rearrangement of oxirene to ketene (H 2 C¼C¼O) with hydrogen migration.
For dimethyloxirene there do not appear to be high-level results for the actual
barrier, but based on a not-fully-optimized transition state a barrier of about 11 kJ
mol"^1 was estimated [ 50 ], and a “periodic scan” (R¼H, BH 2 , CH 3 , NH 2 , OH, F) by
Fowler et al. showed only dimethyloxirene to be clearly stabilized by the substi-
tuents [ 51 ]. The oxirene problem has been reviewed [ 52 ]; it is one that does not
yield readily to even high-level probing (see particularly [ 53 ]), and thus constitutes
a quite rigorous test for a semiempirical method. Curiously, more than 2 decades
after its development, it could be said that MNDOC “has not yet been compared to
other NDDO methods to the degree necessary to evaluate whether the formalism
lives up to [its] potential” [ 54 ]. This may be because MNDOC (and MNDO/d) are
not widely available, unlike MNDO, AM1 and PM3, which have been included in
popular “multimethod” (molecular mechanics, semiempirical, ab initio and DFT)
program suites like Gaussian [ 55 ] and Spartan [ 56 ]. MNDOC and MNDO/d are
included in the AMPAC [ 57 ], but apparently not in the MOPAC [ 58 ] suites, which
are specifically semiempirical.
6.2.5.5 AM1
AM1 (Austin method 1, developed at the University of Texas at Austin [ 59 ]) was
introduced by Dewar, Zoebisch, Healy and Stewart in 1985 [ 60 ]. AM1 is an
improved version of MNDO in which the main change is that the core–core repul-
sions (Eq.6.18) were modified to overcome the tendency of MNDO to overestimate
repulsions between atoms separated by about their van der Waals distances (the
other change is that the parameterzin the exponent of the Slater function – see
parameter three in the listing of the six parameters above – need not be the same for
sandpAOs on the same atom). The core–core repulsions were modified by
introducing attractive and repulsive Gaussian functions centered at internuclear
points [ 61 ], and the method was then re-parameterized. The great difficulties
experienced in the parameterization of AM1 and its predecessors are emphasized
by Dewar and coworkers in many places, e.g.: “All our work has therefore been
based on a very laborious purely empirical technique...” for the MINDO methods
[ 33 ]; parameterization is a “purely empirical affair” and “needs infinite patience
and enormous amounts of computer time” for AM1 [ 60 ]. In his autobiography
Dewar says [ 62 ] “This success [of these methods] is no accident and it has not been
obtained easily” and summarizes the problems with parameterizing these methods:
(1) the parametric functions are of unknown form, (2) the choice of molecules for
the training set affects the parameters to some extent, (3) the parameters are not
unique, there is no way to tell if the set of values found is the best one, and there is
no systematic way to find alternative sets, (4) deciding if a set of parameters is
408 6 Semiempirical Calculations