Triatomic molecules, angular linear

Triatomic molecules may be linear or bent (i.e. V-shaped or angular). The shape adopted by any particular molecule is that which is consistent with the minimization of its total energy. 

There are several important effects associated with degenerate vibrational levels. We begin by considering the doubly degenerate v2a and v2b vibrational modes of a linear triatomic molecule. In these modes, the three atoms each vibrate in a plane perpendicular to the molecular axis, the vibrations being either in the xz or the yz plane, where the z axis is the molecular axis (Fig. 6.2). Classically, if both these modes are excited, the vibrations may give rise to vibrational angular momentum about the internuclear axis for example, if v2a and v2b are of equal amplitude and differ in phase by 90°, then the resultant motion of each nucleus is a circle about the molecular axis, as shown in Fig. 6.8 (see Problem 6.18). 

A triatomic molecule is never called triangular or planar, even though it always is both it always should be called either linear or angular. In either case, the three atoms will lie in the same plane, because any three noncollinear points always determine a plane. 

Morse, M.D. and Freed, K.F. (1981). Rotational and angular distributions from photodissociations. III. Effects of dynamic axis switching in linear triatomic molecules, J. Chem. Phys. 74, 4395-4417. 

In Table 20.1 we compare the valence angles of some representative triatomic molecules or ions formed from elements in Groups 14 to 18. It is seen that the shapes of the molecules are determined by the numbCT of valence electrons carbon dioxide and aU other 16 valence electron species are linear, and species with 17 to 20 valence electrons are angular. When the number of valence electrons is increased to 22, the shape reverts to linearity. The author is not aware of any exception to this trend. 

More generally, further complications arise for angular momentum couplings when the fragments show electronic angular momentum, but the fundamental symmetry rules are not affected by this. Early examples for detailed correlations include triatomic systems, and another more recent example is the correlation for atom + linear molecule. While for such simple cases, and planar molecules in general, parity is... 

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