Trapped motion

From the overall shape of the spectrum and possible structures one can draw general conclusions about the dissociation dynamics. The A band of H2O is (almost) structureless indicating a mainly direct dissociation mechanism. The B band exhibits some weak undulations which can be attributed to a special type of trapped motion with a lifetime of the order of one internal vibration (see Section 8.2). However, the broad background indicates that the dissociation via the B state also proceeds primarily in a direct way. Finally, the C band consists of rather pronounced structures which immediately tell us that the excited H20(C1Hi) complex lives on the order of at least several internal vibrations. Although the absorption spectrum is a highly averaged quantity it contains a wealth of dynamical information more of this in Chapters 6-8. 

Figure 7. (a) A typical time evolution of gyration radii, a and a2 (01 > a2), which shows a trapped motion in the vicinity of the collinear saddle structure from t ss 150 to t ss 700 recrossing the so-called dividing surface many times. Total internal energy of the trajectory is E = — 1.6e. (b) The corresponding trajectory on the gyration space from t = 110 to t = 770 in (a). 

The resultant topography of Veff is shown in Fig. 8, where tp is set to 0 or 7i/3 or 2ji/3 and cp = 0.05 for (a) and cp = 0.15 for (b), both of which are proper values for cp during the locking of tp. It clearly demonstrates that a new basin does appear around the saddle region of the potential energy surface. The new basin becomes broader and wider as cp becomes larger. Thus the trapped motion is rationalized from the viewpoints of energetics. 

These plots are shown in Figure 5, with trapped motion indicated by a T and reactive motion indicated by an R. Note that the curve labeled T corresponds to an ellipse that does not span both isomers (there is another trapped curve that corresponds to being trapped in isomer B with the same torsional energy),... 

First, consider the case of trapped motion within a single isomer. The phase space of 2 is (always) an ellipse, which has the same topology as a onedimensional sphere (which a mathematician would name S ). However, the phase space of is also elliptical and has the same topology (S ). The topology of the two-dimensional phase-space surface on which the dynamics lies is the Cartesian product of these two, which is a two-dimensional torus, or a phase-space doughnut (T = SI X The toroidal geometry is shown in... 

Time-delay induced by the trapping motion above the transition state... 

Fig. 4.60. Ion motion for co+ = 4c0z and cOz = 8co in an ICR cell. Pure magnetron motion dashed), magnetron plus trapping motion dotted), and the resulting overall motion solid). Reproduced from Ref. [198] by permission. Elsevier Science Publishers, 1995.

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