Computational Chemistry

moments. It is often convenient to think of the molecular dipole moment in a more
pictorial form than that presented by Eq. (5.205), namely as the vector sum of bond
moments (Fig.5.37c). Two points should be noted: we are discussing anaverage
dipole moment, because electron and nuclear motions will cause the dipole moment

m 1 m 2

O

H H

a

z

x

y

Q 1

Q 2

Q 3

.

.

.

b

+Q –Q

r

r 1

r 2

r 3

(vector sum of products of charges and distance vectors)

c

m = vector sum of m 1 and m 2

m=∑Qiri

m=Qr

Fig. 5.37(a) Chemists usually consider the dipole moment of a diatomic molecule, the vectorQr,
to be directed from the positive to the negative atom. (b) The dipole moment of a collection of
charges, such as a molecule, arises from the magnitudes of the charges, and their locations (i.e.
distances and directions from the origin. (c) The dipole moment of a molecule can be thought of as
the vector sum of bond moments

5.5 Applications of the Ab initio Method 341