to visualize all three of the principal axes. (Can you do it?) One axis is the
molecular threefold rotational symmetry axis. The other two axes aren’t so ob-
vious. Calculation of the moments of inertia shows that ammonia is an oblate
symmetric top.Example 14.3
Classify the following molecules as linear or as spherical, prolate symmetric,
oblate symmetric, or asymmetric tops. Drawing the structure of the mole-
cules will help you visualize them.
a.Wa t e r, H 2 O
b.The all-transconformation of butane, C 4 H 10
c.Chlorobenzene, C 6 H 5 Cl
d.Uranium hexafluoride, UF 6
e.Hydrogen cyanide, HCN
f.Carbonyl sulfide, OCS
g.The sulfate ion, SO 42 Solution
a.Water has a single C 2 axis and so is an asymmetric top.
b.With its long carbon backbone, butane is a prolate top.
c.Chlorobenzene has C2vsymmetry and, like water, is an asymmetric top.
Note how the substitution of one H in benzene with Cl changed the symme-
try and, therefore, the rotational behavior of the molecule.
d.Uranium hexafluoride has several noncoincident C 4 axes, so it is a spheri-
cal top.
e.HCN is a linear molecule.
f.OCS is also a linear molecule.
g.SO 42 is a tetrahedral ion, having several noncoincident C 3 rotational axes.
Therefore it is a spherical top.Example 14.4
From the general shape of the following molecules, define them as either pro-
late or oblate symmetric tops, or neither.
a.Tetrafluoroethylene, CF 2 CF 2
b.Boron trifluoride, BF 3
c.Trimethylamine, N(CH 3 ) 3
d.Dimethyldiacetylene, CH 3 –CC–CC–CH 3Solution
a.Though roughly a cigar-shaped molecule, tetrafluoroethylene does not
have a threefold axis of symmetry. Therefore it is not a symmetric top.
b.The planar triangular boron trifluoride is an oblate symmetric top.
c.Borrowing from the statement above that ammonia, NH 3 , is an oblate sym-
metric top, we might correctly assume that the trimethyl-substituted amine
is also an oblate symmetric top.
d.The roughly linear molecule dimethyldiacetylene is a prolate symmetric top.In considering the energy of rotation for symmetric tops, it is convenient to
label the moments of inertia in order of magnitude,lowest to highest,using Ia,468 CHAPTER 14 Rotational and Vibrational Spectroscopy