error in dihedrals (Table6.2), omitting the PM3 result for HOOH, is 16(PM3 for
FCH 2 CH 2 F).
From Fig.6.2and Table6.1, the mean error in 39 (13þ 8 þ 9 þ9) bond lengths
is ca. 0.01–0.03 A ̊for the AM1 and PM3 methods, with PM3 being somewhat better
except for O–H and O–S. The mean error in 18 bond angles is ca. 2for both AM1
and PM3. From Table6.2, the mean dihedral angle error for nine dihedrals for AM1
and PM3 (omitting the case of HOOH, where PM3 simply fails) is ca. 5; if we
include HOOH, the mean errors for AM1 and PM3 are 6and 10, respectively.
Schr€oder and Thiel have compared MNDO (Section6.2.5.3) and MNDOC
(Section6.2.5.7) with ab initio calculations for the study of the geometries and
energies of 47 transition states [ 47 ]. AM1 and PM3 calculations should give
somewhat better results than MNDO for these systems, since these two methods
Table 6.2 AM1, PM3, MP2(fc)/6–31G and experimental dihedral angles (degrees). Errors are
given in theErrorscolumn as AM1/PM3/MP2/6–31G. A minus sign means that the calculated
value is less than the experimental. The numbers of positive and negative deviations from
experiment and the average errors (arithmetic means of the absolute values of the errors) are
summarized at the bottom of theErrorscolumn. Calculations are by the author; references to
experimental measurements are given for each measurement. The AM1 and PM3 dihedrals vary
by a fraction of a degree depending on the input dihedral. Some molecules have calculated minima
at other dihedrals in addition to those given here, e.g. FCH 2 CH 2 F at FCCF 180
Errors Dihedral angles
Molecule AM1 PM3 MP2/6–31G* Exp.
HOOH 128 180 121.3 119.1a 9/61(sic)/2.2
FOOF 89 90 85.8 87.5b 1.5/2.5/"1.7
FCH 2 CH 2 F 81 57 69 73 b 8/"16/" 4
(FCCF)
FCH 2 CH 2 OH 65
(FCCO) 58 66 60.1 64.0c 1/2/"3.9
(HOCC) 62 54.1 54.6c 3/7/"0.5
ClCH 2 CH 2 OH
(ClCCO) 74 65 65.0 63.2b 11/2/1.8
(HOCC) 62 59 64.3 58.4b 4/1/5.9
ClCH 2 CH 2 F
(ClCCF) 79 61 65.9 68 b 11/"7/"2.1
HSSH 99 93 90.4 90.6a 8/2/"0.2
FSSF 89 87 88.9 87.9b 1/"1/1.0
Deviations:
10 þ,0"/7þ,3"/4þ,6"
mean of 10:
6/10/2.3;
mean of 9,
omitting 9/61/2.2
errors: 5/4.5/1.9
aHehre et al. [ 107 ], pp.151, 152.
bM. D. Harmony, V. W. Laurie, R. L. Kuczkowski, R. H. Schwenderman, D. A. Ramsay, F. J. Lovas,
W. H. Lafferty, A. G. Makai, “Molecular Structures of Gas-Phase Polyatomic Molecules Deter-
mined by Spectroscopic Methods”, J. Physical and Chemical Reference Data, 1979, 8 , 619–721.
cJ. Huang and K. Hedberg, J. Am. Chem. Soc., 1989, 111 , 6909.
6.3 Applications of Semiempirical Methods 417