Dissociation coordinate

The coupling between the angle y and the dissociation coordinate R is always large if Jacobi coordinates are used. At low energies deep inside the well, this coupling is linear and normal coordinates are usually better suited for interpretation and assignment than are Jacobi coordinates. However, if the molecular dynamics above the dissociation threshold is studied, the normal-mode picture breaks down and scattering coordinates have to be employed. 

Resonances with pure excitation of the CO stretching mode (0, U2, 0) (an example with Vi - 8 is shown in Fig. 5) have the smallest rate and therefore the longest lifetime energy transfer from r to R is rather inefficient, and therefore the system needs a long time before enough eneigy is accumulated in the dissociation coordinate to permit dissociation. On the other extreme, direct excitation in R allows a rather rapid bond rupture, and therefore the resonances (t>i, 0, 0) have the shortest lifetimes. Excitation of the bending mode (0,0, U3) leads to lifetimes that are between C-O excitation as the lower limit and H-C excitation as the upper extreme. This mode specificity is further elucidated in Fig. 8, where we show the widths for several... 

The OH radical is produced in a particular vibrational and rotational quantum state specified by the quantum numbers n and j. The corresponding energies are denoted by tnj. The probabilities with which the individual quantum states are populated are determined by the forces between the translational mode (the dissociation coordinate) and the internal degrees of freedom of the product molecule along the reaction path. Final vibrational and rotational state distributions essentially reflect the dynamics in the fragment channel. They are one major source of information about the dissociation process. 

The width of the absorption spectrum is determined not only by the steepness of the upper-state potential along the dissociation coordinate R but also by its steepness along the internal vibrational coordinate r. 

If the partial spectra cr(E, n) are broader than the spacing between them, the total spectrum atot(E) is structureless the upper part of Figure 6.4 provides a typical example. However, if the widths of the cr(E, n) are smaller than the separations, atot(E) exhibits broad, so-called diffuse vibrational structures. The necessary condition for this to happen is that, according to (6.7), the upper-state PES in the FC region is relatively flat along the dissociation coordinate R. The lower part of Figure 6.4 illustrates this case. 

The free BC oscillator is assumed to be harmonic with force constant k and equilibrium separation r the parameter e controls the coupling between the dissociation coordinate R and the vibrational coordinate r. For e = 0 (elastic limit) the equations of motion for (R, P) and (r, p) decouple and energy cannot flow from one degree of freedom to the other. As a consequence, the vibrational energy of the oscillator remains constant throughout the dissociation and the corresponding vibrational excitation function, which for zero initial momentum po is given by... 

The photodissociation of trifluoromethyl iodide, CF3I —> CF3 + I/I, which was briefly discussed in Section 6.4, seems to illustrate case (a) of Figure 9.4 while the photo dissociation of methyl iodide, CH3I —> CH3 + I/I, appears more to represent case (b). In both examples, the 1/2 umbrella mode, in which the C atom oscillates relative to the Irrespectively F3-plane, is predominantly excited. Following Shapiro and Bersohn (1980) the dissociation of CH3I and CF3I may be approximately treated in a two-dimensional, pseudo-linear model in which the vibrational coordinate r describes the displacement of the C atom from the H3-/F3-plane and the dissociation coordinate R is the distance from iodine to the center-of-mass of CH3/CF3 (see Figure 9.6).t... 

Let us consider, as a simple prototype, the photodissociation of the nitrites X-NO with X=CHsO, HO, Cl, or F, for example. The dissociation of CH3ONO has been discussed in detail in Sections 7.3 and 7.4. The excited-state PES has a barrier along the X-NO dissociation coordinate R, as sketched in Figure 10.12(a), which traps the excited complex for an appreciable time before it breaks apart. Figure 10.12(b) shows schematically a two-dimensional representation featuring the three essential re-... 

Along this OH dissociation coordinate, we also find a conical intersection between the ttct state,. S , and the ground state, S0, which could act as an efficient route for internal conversion. Such a scenario has been advocated by Domcke and Sobolewski [23, 84, 86] to be responsible for the photostability of nucleobases. However, in the present case, the free energy activation barrier for OH dissociation was computed to be 52 kJ/mol [47], Hence this de-excitation pathway is unlikely to explain the ultrafast nonradiative decay observed experimentally [5, 11, 37], Shukla and Leszczynski [80] find an activation barrier of 154 kJ/mol for the keto-enol tautomerisation of 7H G. However, this result is for tautomerisation in the tttt state, whereas the ROKS study involves two different excited states [47],... 

Figure 3 Potential energy curve along the Cr-CO dissociation coordinate for singlet states (in C4V symmetry) arising from the lowest excited configuration. (Reprinted with permission from Ref. 52b. 1997 American Chemical Society)...

The dissociation of weakly bound van der Waals complexes is a special case of unimolecular dissociation [20]. Because of the exceedingly weak coupling between the dissociation coordinate and the mode (or modes) initially excited, and the very low density of states of the energized complex, narrow resonances are the dominant features of van der Waals spectra. There are, of course, many similarities between the dynamics of physically bound and chemically bound molecules. The dissociation dynamics of these special molecules (or clusters) has been studied in great detail, both experimentally and theoretically. Exhaustive review articles are available [85-89] and therefore van der Waals molecules will not be particularly considered in this chapter. However, one must keep in mind that, as the density of states of van der Waals molecules increases, their dynamics becomes more and more comparable with the dynamics of strongly bound molecules [90,91]. 

---