Vibrationally adiabatic curves

The dynamics of a reaction that proceeds directly over the transition state is expected to be qualitatively different from that of a resonance-mediated reaction. In particular, one expects that the branching ratios into the product rovibrational states will be very different between the direct and the resonant mechanisms. For example, if a given Feshbach resonance corresponds to trapping on the v = 1 vibrationally adiabatic curve, then one might expect that the population of the v = l vibrational state of the product molecule may be greatly enhanced by the resonant mechanism. Similarly, the rotational product distribution resulting from the fragmentation of a resonance molecule may show a quite distinct pattern from that of a direct reaction. Indeed, Liu and coworkers [94], and Nesbitt and coworkers [95] have noted distinct rotational patterns in the F+HD resonant reaction. 

The maxima in the quantal density of reactive states and in the vibrationally adiabatic curves occur at almost the same energies. Thus, as for the H + H2 reaction, the... 

Quantal spectroscopic constants, as defined in Eq. (25), were calculated for the three reactions from fits to assigned peak energies in the finite-resolution density. Vibrationally adiabatic thresholds (the maxima in vibrationally adiabatic curves calculated using the procedure described for H 4- H2) were also least-squares fit with Eq. (25). Results are... 

The ability to measure reactive scattering data for reaction products in their different quanmm states leads to a very interesting possibility of smdying quantal effects in reactive scattering. Indeed, by building PESs, vibrationally adiabatic curves, which are effective potentials for the translational motion from reactants or products, can be described by a single quantum number for the vibrational action. An example of such potentials is shown in Figure 21.15. 

It is also important to note how, even in the case that a well on the PES is not present, the (vibrationally) adiabatic curves can show wells and barriers, as the PES perpendicular to the translational coordinate widens and narrows respectively. These wells can support quasi-bound states similar to shape resonances. Therefore, reactive scattering through this temporarily bound state can give rise to reactive resonances. 

As an example we can take the excited states of NO. It has been shown that there are two excited states of the same symmetry ( 11) whose vibrational levels are best interpreted on the basis of diabatic curves which cross as in Fig. 1 (75-7 7). One of these states (B) arises from the electron excitation to an antibonding valence molecular orbital and the other (C) from excitation to a Rydberg orbital. The Born-Oppenheimer adiabatic curves cannot cross (by virtue of the non-crossing rule which is to be discussed in a later section) and must fullow the dashed curves shown in the figure. 

Figure 3.1 A schematic diagram showing the relationship of reactive resonances to the vibrationally adiabatic potential curve. The upper panel illustrates a Feshbach resonance trapped in a well the lower panel shows a barrier resonance or QBS.

Fig. 6.4. Schematic illustration of the multi-dimensional reflection principle in the adiabatic limit. The left-hand side shows the vibrationally adiabatic potential curves en(R). The independent part of the bound-state wavefunction in the ground electronic state is denoted by

Fig. 7.10. (a) Adiabatically corrected vibrational energy curves en(R), defined... 

Figure 6 (a) Vibrationally adiabatic potential energy curves with v-, = 0 for the... 

The choice of an adiabatic picture leads to difficulties when one of the potentials has a double minimum (see Fig. 3.5). The vibrational level separations of such a curve do not vary smoothly with vibrational quantum number, as do the levels of a single minimum potential. In the separate potential wells (below the barrier), the levels approximately follow two different smooth curves. However, above the potential barrier the separation between consecutive energy levels oscillates. The same pattern of behavior is found for the rotational constants below and above the potential barrier. In addition, the rotational levels above the barrier do not vary as BVJ(J + 1). An adiabatic deperturbation of the (E,F+G,K) states of H2 has been possible (Dressier et al., 1979) only because the adiabatic curves were known from very precise ab initio calculations. 

The energies of the nine features in Table 4 all correspond closely to the energies of maxima in the vibrationally adiabatic potential curves (8). Table 5 illustrates the agreement between the energies predicted by the spectroscopic constants and maxima, max, in the quantal density of reactive states. 

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