(below). AM1 heats of formation for hypervalent compounds (above and reference
[ 47 ]) appear to be distinctly inferior to those from PM3. Thiel has compared
MNDO, AM1, PM3, and MNDO/d heats of formation with those from some ab
initio and DFT methods [ 92 ]. The results (ca. 1998) are somewhat dated, as more
accurate ab initio (e.g. G3- and G4-type; Section5.5.2.2b) and semiempirical
(RM1, PM6) methods (above) are now available. However, it remains true that
multistep high-accuracy ab initio methods are the most accurate ways to calculate
heats of formation (Section5.5.2.2c). These give an error of about 3–5 kJ mol"^1
([ 93 ] and Section5.5.2.2c), compared with about 20 kJ mol"^1 for RM1 and PM6.
Nevertheless, the fact that semiempirical calculations are faster than ab initio by
factor of the order of about 1,000 can be decisive when dealing with big molecules
or with a large collection of molecules. As mentioned, such a survey uncovered
several errors in reported experimental heats of formation [ 84 ].
The discussion of enthalpy, free energy, and reaction and activation energies
in Section5.5.2.1applies to semiempirical calculations too. Now let’s retrace
some of the calculations ofChapter 5, using AM1 and PM3 rather than ab initio
methods.
6.3.2.2 Energies: Calculating Quantities Relevant to Thermodynamics
and Kinetics
We are usually interested inrelativeenergies. An ab initio energy difference (for
isomers, or isomeric systems like reactants cf. products), corrected only with ZPE,
represents a 0 K energy difference, i.e. a 0 K enthalpy difference, whereas a
semiempirical (e.g. AM1 or PMx) energy difference represents a room temperature
enthalpy difference; thus even if the ab initio and semiempirical calculations both
had negligible errors, they would not be expected to give exactly the same relative
energy, unless the 0–298 K enthalpy change on both sides of the equation cancelled.
A typical change in heat of formation is shown by methanol; the (ab initio
calculated) heats of formation of methanol at 0 and 298 K are"195.9 and
"207.0 kJ mol"^1 , respectively (Section5.5.2.2c). This change of 11 kJ mol"^1 is
fairly small compared to the errors in semiempirical and many ab initio calcula-
tions, so discrepancies between energy changes calculated by the two approaches
must be due to factors other than the 0–298 K enthalpy change. The errors in heats
of formation cannot be counted on to consistently cancel when we subtract to obtain
relative energies, and because of average errors in individual heats of formation of
ca. 20 kJ mol"^1 (above) for the best current methods, RM1 and PM6, errors of about
40 kJ mol"^1 should not be surprising, although much smaller errors are often
obtained. Consider the relative energies of (Z)- and (E)-2-butene (Fig. 5.24). The
HF/3-21G(*)energy difference, corrected for ZPE (although in this case the ZPE is
practically the same for both isomers) is (Z)"(E)¼"155.12709"("155.13033)
h¼0.00324 h¼8.5 kJ mol"^1. AM1 calculations (ZPE is not considered here, since
as explained in Section6.2.5.2,thisistakenintoaccountintheparameterization)
give (Z)"(E)¼"9.24"("14.01) kJ mol"^1 ¼4.8 kJ mol"^1 .Theexperimental
420 6 Semiempirical Calculations