usually not much better. Some calculated and experimental dipole moments are
compared in Table5.14. These results, which are quite typical, indicate that
calculated values tend to be about 0.0–0.5 D higher than experimental, with a
mean deviation of about 0.3 D; negative deviations are rare. HF/3–21G()//HF/
3–21G()(the lowest ab initio level likely to be used) calculations may show the
largest deviations. Single-point HF/3–21G()calculations on HF/6–31G geome-
tries appear to give results about as good as (or better than? Note CH 3 NH 2 , and
ref. [ 39 ], pp. 76, 77) those from MP2(fc)/6–31G//MP2(fc)/6–31G calculations.
As is the case for other properties, 3–21G()calculations of dipole moments on
molecules with atoms beyond neon require polarization functions for reasonable
results (the 3–21G()basis; ref. [ 39 ], pp. 23–30). The 3–21G()calculations in
Table5.14show a mean deviation 0.33; the HF/6–31G calculations are only
slightly better (mean deviation 0.26) and the MP2/6–31G* calculations appear to
be, if anything, slightly worse (mean error 0.34). If high-accuracy calculated dipole
moments (0.1 D or better) are needed, high-level correlation and large basis sets
must be used; such calculations may be needed to reproduce the magnitude and
even the direction of small dipole moments [ 252 ], such as in carbon monoxide, a
notorious case [ 253 ].
5.5.4.2 Charges and Bond Orders
Chemists make extensive use of the idea that the atoms in a molecule can be
assigned electricalcharges. Thus in a water molecule each hydrogen atom is
considered to have an equal, positive, charge, and the oxygen atom to have a
negative charge (equal in magnitude to the sum of the hydrogen charges). This
Table 5.14 Some calculated dipole moments compared to experimental ones
Computational level
HF/3–21G()// HF/6–31G// HF/6–31G// MP2(fc)/6–31G// Exp.
HF/3–21G() HF/3–21G() HF/6–31G MP2(fc)/6–31G
CH 3 NH 2 1.44 1.3 1.53 1.6 1.3
H 2 O 2.39 2.18 2.2 2.24 1.9
HCN 3.04 3.2 3.21 3.26 3
CH 3 OH 2.12 1.95 1.87 1.95 1.7
Me 2 O 1.85 1.64 1.48 1.6 1.3
H 2 CO 2.66 2.79 2.67 2.84 2.3
CH 3 F 2.34 2.18 1.99 2.11 1.9
CH 3 Cl 2.31 2.32 2.25 2.21 1.9
Me 2 SO 4.27 4.55 4.5 4.63 4
CH 3 CCH 0.71 0.64 0.64 0.66 0.8
Deviations 9þ,1# 8 þ,2# 9 þ,1# 9 þ,1#
Mean 0.33 0.31 0.26 0.34
Dipole moments are in Debyes; the computational levels are arranged, from left to right, in what is
conventionally considered lowest to highest. Calculations are by the author; experimental values
are taken from reference [ 1 g], pp 326, 329, 332, 335. For each level is given the number of positive
and negative deviations and the arithmetic mean of the absolute values of the deviations.
5.5 Applications of the Ab initio Method 343