The ion-ion interactions which vary as 1/r will be considered in the lectures on the solid state. In the present section, we will consider the ion-dipole, dipole-dipole, ion-induced dipole and the dipole- induced dipole interactions. The induced-dipole induced-dipole case, which is the same as the dispersion or van der Waals force has already been discussed in the previous section.
If qi are the charges (inclusive of sign) in a molecule (or any other general object), the dipole moment vector
is defined by
= qi
(10.7)
Here is the vector from the center of mass to the location of charge. If the charge density is not discrete, but continuous and defined by a spatial charge density
(x,y,z) where
(x,y,z) is charge per unit volume at the location (x,y,z), the dipole moment is defined by
=
(x,y,z)
(x,y,z) dxdydz
(10.8)
Dipole moment is a moment of first order in r (first power in r). Higher moments such as the quadrupole moment is defined by
Qxy =
xy
(x,y,z) dxdydz
(10.9)
This is the xy component of the quadrupole moment. In a diatomic, out of the six components xx, xy, xz, yy, yz and zx only one is independent. With z axis as the molecular axis, the value of the quadrupole moment is given by
Q = qi (3zi2 -ri2) / e
(10.10)
The unit of M is Debye (D) or 10-18 esu.cm., the MKS unit is Cm. If e and -e are separated by 1, then the dipole moment is 4.8 x 10 -10 esu x 10 -8 cm = 4.8x10-18 esu.cm = 4.8 D. The unit of quadrupole moment is area (cm2). This is the rationale for dividing by e (the electronic charge) in eq. (10.10)
is defined by 
qi 
(x,y,z) where
(x,y,z)
xy
, then the dipole moment is 4.8 x 10 -10 esu x 10 -8 cm = 4.8x10-18 esu.cm = 4.8 D. The unit of quadrupole moment is area (cm2). This is the rationale for dividing by e (the electronic charge) in eq. (10.10) 
