Clearly, the X-ray-inferred H–X distance will be less than the actual internuclear
distance measured by electron diffraction, neutron diffraction, or microwave spec-
troscopy, methods which see nuclei rather than electrons. These and other sources
of error that can arise in experimental bond length measurements (like bond length,
bond angles and dihedral angles will obviously also depend on nuclear positions)
are detailed by Burkert and Allinger [ 111 ], who mention nine (!) kinds of internu-
clear distancer, and a comprehensive reference to the techniques of structure
determination may be found in the book edited by Domenicano and Hargittai
[ 112 ]. Despite all these problems with defining and measuring molecular geometry
(see e.g. [ 112 b], we will adopt the position that it is meaningful to speak of
experimental geometries to within 0.01 A ̊or better for bond lengths, and to within
0.5for bond angles and dihedrals [ 113 ].
Let’s briefly compare HF/3–21G(), HF/6–31G and MP2/6–31G* geometries.
Figure5.23gives bond lengths and angles calculated at these three levels and
experimental bond lengths and angles, for 20 molecules. The geometries shown
in Fig.5.23are analyzed in Table5.7, and Table5.8provides information on
dihedral angles in eight molecules. There should be little difference between MP2
(full) geometries and the MP2(fc) geometries used here. This (admittedly limited)
survey suggests that:
HF/3–21G()geometries are almost as good as HF/6–31G geometries.
MP2/6–31G geometries are on the whole slightly but significantly better than
HF/6–31G geometries, although individual MP2 parameters aresometimesa
bit worse.
HF/3–21G()and HF/6–31G C–H bond lengths are consistently slightly (ca.
0.01–0.03 and ca. 0.01 A ̊, respectively) shorter than experimental, while
MP2/6–31G C–H bond lengths are not systematically over- or underestimated.
HF/6–31G O–H bonds are consistently slightly (ca. 0.01 A ̊) shorter than
experimental, while MP2/6–31G O–H bond lengths are consistently slightly
(ca. 0.01 A ̊) longer. HF/3–21G()O–H bond lengths are not consistently over- or
underestimated.
None of the three levels consistently over- or underestimates C–C bond lengths.
HF/6–31G C–X (X¼O, N, Cl, S) bond lengths tend to be underestimated slightly
(ca. 0.015 A ̊) while MP2/6–31G C–X bond lengths may tend to be slightly
(ca. 0.01 A ̊) overestimated. HF/3–21G()C–X bond lengths are not consistently
over- or underestimated.
HF/6–31G bond angles may tend to be slightly larger (ca. 1) than experimental,
while MP2/6–31G angles may tend to be slightly (0.7) smaller.
HF/3–21G()bond angles are not consistently over- or underestimated. Dihe-
drals do not seem to be consistently over-or underestimated by any of the three
levels. The HF/3–21G()level breaks down completely for HOOH, where a dihe-
dral angle of 180, far from the experimental 119.1, is calculated; omitting
this error of 61 and the ClCH 2 CH 2 OH HOCC dihedral error of 7.6 lowers
the HF/3–21G()error from 8.8 to 2.5. The experimental value of 58.4 for
the ClCH 2 CH 2 OH HOCC dihedral is suspect because of its anomalously large
5.5 Applications of the Ab initio Method 283