although the latter is much faster and often of comparable accuracy (of course with
correlated methods like MP2 a smaller basis than 6–31G should not be used, as
pointed out inSection 5.4). The errors in calculated dihedral angles are ca. 2–3for
HF/6–31G, and ca. 2 for MP2/6–31G: omitting the ClCH 2 CH 2 OH HOCC
dihedral errors of 8.6and 5.9from the sample lowers the HF error from 2.9to
2.3and the MP2 error from 2.3 to 1.9.
The accuracy of ab initio geometries is astonishing, in view of the approxima-
tions present: the 3–21G()basis set is small and the 6–31G* is only moderately
large, and so these probably cannot approximate closely the true wavefunction; the
HF method does not account properly for electron correlation, and the MP2 method
is only the simplest approach to handling electron correlation; the Hamiltonian in
both the HF and the MP2 methods used here neglects relativity and spin-orbit
coupling. Yet with all these approximations the largest error (Table5.7) in bond
Table 5.8 HF/3–21G(), HF/6–31G and MP2(fc)/6–31G dihedral angles (degrees)
Molecule Dihedral angles
HF/3–21G() HF/6–31G MP2/6–31G Experiment Errors
HOOH 180.0 116.0 121.3 119.1a 61(sic)/#3.1/2.2
FOOF 84.1 84.1 85.8 87.5b #3.4/#3.4/#1.7
FCH 2 CH 2 F(FCCF) 74.9 69.4 69.0 73 b 1.9/#4/# 4
FCH 2 CH 2 OH
(FCCO) 58.4 61.3 60.1 64.0c #5.6/#2.7/#3.9
(HOCC) 52.7 57.8 54.1 54.6c #1.9/2.5/#0.5
ClCH 2 CH 2 OH
(ClCCO) 65.8 65.7 65.0 63.2b 2.6/2.5/1.8
(HOCC) 66.0 67.0 64.3 58.4b 7.6/8.6/5.9
ClCH 2 CH 2 F 65.9 67.0 65.9 68 b #2.1/#1/#2.1
(ClCCF)
HSSH 89.8 89.8 90.4 90.6a #0.8/#0.8/#0.2
FSSF 89.4 88.7 88.9 87.9b 1.5/0.8/1.0
Deviations:
5 þ,5#/4þ,
6 #/4þ,6#
mean of 10:
8.8/2.9/ 2.3.
Omitting the largest error for each of the three methods (61/8.6/8.9/ for HF/3–21G()/
HF/6–31G/MP2(fc)/6–31G, respectively, the mean of nine errors for each method is 3.0/2.3/1.9.
Errors are given in theErrorscolumn as HF/3–21G()/HF/6–31G/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 the Errors column. Calculations are by the author;
references to experimental measurements are given for each measurement. Some molecules
have calculated minima at other dihedrals in addition to those given here, e.g. FCH 2 CH 2 F at
180 . Errors are presented: HF/3–21G()/HF/6–31G/MP2/6–31G*.
a[ 1 g], 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 (1979) Molecular Structures of Gas-Phase Polyatomic Molecules
Determined by Spectroscopic Methods. J. Phys. Chem. Ref. Data, 8 , 619–721.
cJ. Huang and K. Hedberg (1989) J. Am. Chem. Soc., 111 , 6909.
5.5 Applications of the Ab initio Method 287