Acetylene vibrational motion

Other linear molecules (acetylene, CjHj, for example) have similarly described vibrational spectra either stretching vibrations or bending vibrations. It is only when a molecule becomes nonlinear that additional complexities arise. Unfortunately, most molecules are nonlinear. Fortunately, similar rough descriptions of the vibrations can be applied. Also fortunately, symmetry considerations combine with the change-in-dipole-moment selection rule to limit the number of IR-active vibrational motions of large, symmetric molecules. The next few sections will illustrate some of the procedures used to simplify our understanding of molecular vibrations. 

For larger polyatomic molecules the vibrational motions can become very complicated, with dozens of normal modes contributing to the observed spectra. However, the basic principles outlined here apply, at least as a first order approximation, to the motion of molecules as large as methyl acetylene (C3H4), shown in Fig. 3.4.4, and propane (C3H8), shown in Fig. 3.4.5. For some large molecules with simple structures, such as ring-shaped benzene (CeHe), the observed spectra are often quite simple (see, for example, Sadtler, 1972). 

The polyad model for acetylene is an example of a hybrid scheme, combining ball-and-spring motion in a two-dimensional configuration space [the two Franck-Condon active modes, the C-C stretch (Q2) and the tram-bend (Q4)] with abstract motion in a state space defined by the three approximate constants of motion (the polyad quantum numbers). This state space is four dimensional the three polyad quantum numbers reduce the accessible dimensionality of state space from the seven internal vibrational degrees of freedom of a linear four-atom molecule to 7 - 3 = 4. 

Hydrocarbon sorbate vibrations. IINS spectra have been recorded for a number of simple sorbate molecules within aluminosilicate zeolites, including hydrogen in A (40, 41). acetylene in X (4, ethylene in A (42) and X (44-46). and p-xylene (42) in X type materials. In addition to intramolecular modes, where interaction between the sorbate and the non-framework cations is strong (for example in the ethylene - silver zeolite A system (42)), vibrational transitions associated with sorbate motion with respect to the zeolite s internal surface can be observed. The latter modes, and the dependence of their frequencies on loading, structure and composition are of particular interest as they convey detailed information about the character of the zeolite - sorbate... 

Figure 10.6 A 2-D potential energy surface and the corresponding contour plot of the "T" shaped conformation of Ar-HCCH in the acetylene ground vibrational energy level. This X-Y coordinate plot shows the wide amplitude motion of the Ar atom around the acetylene unit. Taken with permission from Bemish et al. (1993).

For the tetraatomic system HXXH, representing both the linear acetylene and the non-linear hydrogen peroxide, we expect to be able to construct twelve symmetry coordinates. Three of them are translational, whereas two of the remaining nine in the linear conformation and three in the non-linear one are reserved for rotations. Linear tetraatomics thus have seven vibrational coordinates, motion along which changes the potential energy, whereas their nonlinear counterparts have six. Those of the linear HXXH molecule are shown in Fig. 4.4 with the subgroup into which each is taken, if only momentarily, by the displacement. 

For example, let us consider the vibrational spectrum of methylacetylene, CH3C=CH. The 15 normal vibrations reduce to five Aj-labeled motions and five -labeled motions. Table 14.6 lists the 10 unique vibrational frequencies of methyl-acetylene. Also listed are other absorptions that are attributed to various overtones and combination bands. The nonideality of the molecule permits some of these combinations to appear with detectable intensity. 

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