heats of formation (298 K, gas phase) are (Z)¼"29.7 kJ mol"^1 ,(E)¼"47.7 kJ
mol"^1 , i.e. (Z)"(E)¼18.0 kJ mol"^1 [ 94 ].
The comparison by Schr€oder and Thiel [ 47 ] (Sections6.3.1and6.3.2) of semi-
empirical (MNDO and MNDOC) and ab initio geometries and energies concluded
that the semiempirical methods usually overestimate activation energies. Of 21
activation energies (Table IV in ref. [ 47 ], entries I, K, W omitted), MNDO over-
estimated (compared with “best” correlated ab initio calculations) 19 and under-
estimated two; the overestimates ranged from 8 to 201 kJ mol"^1 and the
underestimates were 46 and 13 kJ mol"^1. MNDOC overestimated 16 and under-
estimated five; the overestimates ranged from 2 to 109 kJ mol"^1 and the under-
estimates from 4 to 63 kJ mol"^1. Thus for calculating activation energies MNDOC
is significantly better than MNDO, and it is probably better than AM1 for this
purpose, since, like MNDO but unlike MNDOC, AM1 does not explicitly take into
account electron correlation, which can be important for activation energies. For
these 21 reactions, restricted Hartree-Fock calculations overestimated 18 activation
energies and underestimated three; the overestimates of energies ranged from 3 to
105 kJ mol"^1 and the underestimates from 13 to 28 kJ mol"^1. The mean absolute
deviations from the “best” correlated ab initio calculations for the 21 reactions
were: MNDO, 92 kJ mol"^1 ; MNDOC, 38 kJ mol"^1 ; RHF, 50 kJ mol"^1. Evidently
MNDOC is somewhat better than RHF (uncorrelated) calculations for activation
energies. Correlated-level ab initio calculations, however, appear to be superior
to MNDOC; in particular, MNDOC predicts substantial barriers for isomerization
of carbenes by hydrogen migration. Other work showed that AM1 greatly over-
estimates the barrier for decomposition or rearrangement of some highly reactive
species [ 95 ].
Some semiempirical reaction energies and relative energies of isomers are given
in Table6.3; these are analogous to the ab initio results in Table5.9. These
calculations suggest that, like the Hartree-Fock-level calculations of Table 5.9,
AM1 and PM3 can give useful, although sometimes only rough, indications of the
Table 6.3Reaction energies (kJ mol"^1 ) of isomers (AM1 andPM3). The calculations on O 2 are
UHF, on triplet O 2. Calculations are by the author, experimental energies are from [ 88 ]
Reactants Products Reaction energy, or relative
energy of isomers, calculated
Exp kJ
mol"^1
H 2 þCl 2 2HCl "206.0"("81.0)¼" 125 " 192
"21.7þ("59.3)¼"81.0 2("103.0)¼"206.0 "171.2"("104.4)¼" 67
"56.0þ("48.4)¼"104.4 2("85.6)¼"171.2
2H 2 þO 2 2H 2 O " 523
2("21.7)þ("116.0)¼"159.4 2("247.9)¼"495.8 "495.8"("159.4)¼" 336
2("56.0)þ("17.5)¼"129.5 2("223.5)¼"447.0 "447.0"("129.5)¼" 318
(E)-2-butene (Z)-2-butene 4.6
"14.0 "9.2 "9.2"("14.9)¼5.7
"15.8 "14.9 "14.9"("15.8)¼0.9
HCN HNC 204.3"129.7¼74.6 60.7
129.7 204.3 236.8"137.9¼98.9
137.9 236.8
6.3 Applications of Semiempirical Methods 421