2.4 Electronic Properties
45
Table 2.11 Dipole, quadrupole, and octapole moments and dipole polarizability of formaldehyde
obtained by calculation with the available experimental data
Moment
DFT/B3LYP/6-31G** DFT/B3LYP/6-31+G* Experimental a
Dipole moment μ (in
D)
xx
0.0000
0.0000
–
yy
0.0000
0.0000
–
zz
2.1836
2.5151
–
Tot
2.1836
2.5151
2.332
Quadrupole moment Q
(traceless) (in D Å)
xx
0.2170
0.1933
−0.270
yy
0.1161
0.2353
0.330
zz
−0.3331
−0.4286
−0.060
Octapole moment O
(in D Å 2 )
xxx
0.0000
0.0000
n/a
yyy
0.0000
0.0000
zzz
1.2798
0.2945
xyy
0.0000
0.0000
xxy
0.0000
0.0000
xxz
0.9192
0.6098
xzz
0.0000
0.0000
yzz
0.0000
0.0000
yyz
0.0460
−0.5382
xyz
0.0000
0.0000
Dipole polarizability α
(in Å 3 )
iso
1.9632
2.2542
2.770 b
aniso
1.4966
1.5916
xx
1.0337
1.3182
yy
2.1141
2.2895
zz
2.7419
3.1550
a Dipole moment from Hellwege and Hellwege (1982), quadrupole moment from Hellwege and
Hellwege (1974), and dipole polarizability from Olney et al. (1997)
b Corresponding to the iso component (α iso )
2.4.4 Polarizability
The induced dipole moment μ ind under the external static electric field F can be
expanded as
μ ind = αF +
1
2
βF
2
+
1
6
γ F
3
+ · · · · · ·
(2.33)
where α is called dipole polarizability or simply polarizability, and β, γ , and so
on hyperpolarizabilities (Buckingham and Orr 1967). For weak field μ ind is well
represented by