Dipole moments of molecules

29.1 DIPOLE MOMENTS OF MOLECULES
B
A
(a) HCl
A
(b) CO2
B
(c) O3
Figure 29.1 Three molecules, (a) hydrogen chloride, (b) carbon dioxide and
(c) ozone, for which symmetry considerations impose varying degrees of
constraint on their possible electric dipole moments.
29.1 Dipole moments of molecules
Some simple consequences of symmetry can be demonstrated by considering
whether a permanent electric dipole moment can exist in any particular molecule;
three simple molecules, hydrogen chloride, carbon dioxide and ozone, are illustrated in figure 29.1. Even if a molecule is electrically neutral, an electric dipole
moment will exist in it if the centres of gravity of the positive charges (due to
protons in the atomic nuclei) and of the negative charges (due to the electrons)
do not coincide.
For hydrogen chloride there is no reason why they should coincide; indeed, the
normal picture of the binding mechanism in this molecule is that the electron from
the hydrogen atom moves its average position from that of its proton nucleus to
somewhere between the hydrogen and chlorine nuclei. There is no compensating
movement of positive charge, and a net dipole moment is to be expected – and
is found experimentally.
For the linear molecule carbon dioxide it seems obvious that it cannot have
a dipole moment, because of its symmetry. Putting this rather more rigorously,
we note that any rotation about the long axis of the molecule leaves it totally
unchanged; consequently, any component of a permanent electric dipole perpendicular to that axis must be zero (a non-zero component would rotate although
no physical change had taken place in the molecule). That only leaves the possibility of a component parallel to the axis. However, a rotation of π radians
about the axis AA shown in figure 29.1(b) carries the molecule into itself, as
does a reflection in a plane through the carbon atom and perpendicular to the
molecular axis (i.e. one with its normal parallel to the axis). In both cases the two
oxygen atoms change places but, as they are identical, the molecule is indistinguishable from the original. Either ‘symmetry operation’ would reverse the sign
of any dipole component directed parallel to the molecular axis; this can only be
compatible with the indistinguishability of the original and final systems if the
parallel component is zero. Thus on symmetry grounds carbon dioxide cannot
have a permanent electric dipole moment.
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