23.5 Spectra of Polyatomic Molecules 975
PROBLEMS
Section 23.4: Electronic Spectra of Diatomic Molecules
23.33H^35 Cl has an important excited electronic state that lies
above the ground state by 77575 cm−^1. Describe the
bands in the ultraviolet spectrum arising from the
transition from the ground state to this excited electronic
state, including only the values 0 and 1 for the vibrational
quantum numbers andJ0, 1, and 2 for the rotational
quantum numbers. Give numerical values for the band
origin (corresponding to the forbidden transitionJ0to
J0) and the splittings between lines. The selection
rules allow∆vto have any value, but∆Jfollows the
same selection rules as for the microwave and infrared
spectra. Assume the harmonic oscillator–rigid rotor
energy levels. For the excited state^14̃ve 2684 .0cm−^1 and ̃Be 9 .33 cm−^123.34Look up the necessary data and repeat the calculation of
Problem 23.33 for HBr. The data can be found in the
book by Huber and Herzberg.^1523.5 Spectra of Polyatomic Molecules
The spectra of polyatomic molecules are more complicated than those of atoms or
diatomic molecules. As with diatomic molecules, rotational transitions can occur with-
out vibrational or electronic transitions, vibrational transitions can occur without elec-
tronic transitions but are generally accompanied by rotational transitions, and electronic
transitions are accompanied by both vibrational and rotational transitions.Microwave Spectra of Polyatomic Molecules
Transitions between the rotational states of a polyatomic molecules can produce a
microwave spectrum. We will not discuss the details of the microwave spectra of
polyatomic molecules, but make some elementary comments.^16 As with diatomic
molecules, we apply the rigid-rotor approximation, assuming that a rotating poly-
atomic molecule is locked in its equilibrium conformation. Any molecule in its equi-
librium conformation must belong to one of four classes: linear molecules, spherical
top molecules, symmetric top molecules, and asymmetric top molecules.
As with diatomic molecules, the principal selection rule is that a permanent dipole
moment is required for a molecule to produce a microwave spectrum. Linear polyatomic
molecules have rotational wave functions exactly like those of diatomic molecules, so
their rotational selection rules and spectra are the same as those of diatomic molecules.
A symmetric linear molecule such as acetylene (ethyne) has no permanent dipole
moment, and does not have a microwave spectrum. The fact that N 2 O has a microwave
spectrum establishes the fact that it is NNO, not NON. Spherical top molecules such
as CCl 4 and SF 6 are so symmetrical that they cannot have a nonzero permanent dipole
moment, and they have no microwave spectrum. A symmetric top molecule with a
permanent dipole moment will have a microwave spectrum. A microwave spectrum
is always observed for an asymmetric top molecule, because it has so little symmetry
that it must have a nonzero permanent dipole moment.(^14) K. P. Huber and G. Herzberg,Molecular Spectra and Molecular Structure, Vol. IV, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York,
1979, p. 284ff.
(^15) K. P. Huber and G. Herzberg,op. cit., p. 280ff (note 14).
(^16) J. C. Davis,op. cit., p. 322ff (note 2).