46
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
Table 2.12 Dipole, quadrupole, and octapole moments and dipole polarizability of water 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
2.0428
2.2491
–
Tot
2.0428
2.2491
1.855
Quadrupole moment Q
(traceless) (in D Å)
xx
−1.3341
−1.6678
−2.500
yy
1.5065
1.9240
2.630
zz
−0.1724
−0.2562
−0.130
Octapole moment O
(in D Å 2 )
xxx
0.0000
0.0000
n/a
yyy
0.0000
0.0000
zzz
−1.1613
−1.6502
xyy
0.0000
0.0000
xxy
0.0000
0.0000
xxz
−0.2979
−0.4919
xzz
0.0000
0.0000
yzz
0.0000
0.0000
yyz
−1.1939
−1.4313
xyz
0.0000
0.0000
Dipole polarizability α
(in Å 3 )
iso
0.7933
1.0234
1.501 b
aniso
0.5811
1.8742
xx
0.4436
0.9655
yy
1.1126
1.1483
zz
0.8236
0.9565
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 )
μ ind = αF
(2.34)
as a matter of course. The polarizability α has the form of tensor
α =
⎛
⎝
α xx α xy α xz
α yx α yy α yz
α zx α zy α zz
⎞
⎠
(2.35)
with symmetric components under arbitrary coordinate system.The isotropic α
signifying the mean of the diagonal components is given as
α iso =
1
3
α xx + α yy + α zz
(2.36)