Vibrational states nonadiabatic collisions

In the presence of coupling between the two excited manifolds, represented by the operator W, the bound states n) generated, for example, either by absorption of a photon (as illustrated in Figure 7.5), by electron impact, or in an atom-molecule collision will decay because they undergo transitions to the continuum states. W is assumed to be time-independent and for the discussion in this section its origin and particular form is not pertinent. It may represent nonadiabatic coupling between two electronic or two vibrational states, for example. We explicitly assume that W couples only the bound and the continuum states and that there is no coupling between the bound or between the continuum states,... 

Certain features of the results are quite interesting. The cross sections show a strong dependence on the vibrational quantum number for both reactant electronic states. If the Franck-Condon principle were valid for the nonadiabatic transitions which occur in this system, then the charge transfer cross section would be independent of the reactant vibrational level [19]. It is well known that the Franck-Condon principle breaks down badly at low collision energies for most charge transfer systems. The most remarkable result seen in Fig. 4 is the very small cross section for N2+ (X v = 0) + Ar at all three collision energies its maximum value is 1.6 A2 at 20 eV. (By comparison the cross sections for other N2+ (X v) -I- Ar states are at least 14 A2.) This occurs even though there is a product state, Ar+(2P3/2) + N2(v = 0), which is only 0.18 eV away thus, this. In addition, the Franck-Condon factor for the transition N2 (X v = 0) - N2 (v = 0) is 0.92 ... 

We explore two physical events in this system One is a vibrational decay through the nonadiabatic coupling, the initial wavepacket of which is prepared at the left chff of the lower curve (i = 2, with the initial momentum hk = 25). The other one is a collision event, with an initial packet coming in from the dissociation channel (from R = 7, with hk = —45). For these events, we construct the total wavepacket states with PSANB-ADF-NVG according to Eq. (6.147). These total wavefunctions are projected onto the nuclear configuration space and thereby compared with the full quantmn nuclear wavepacket attained through the standard method, Eq. (6.5). 

Fig. 6.22 Four miscellaneous quantities that are calculated in terms of the quantum nuclear wavepackets given in the present nonadiabatic dynamics. Panels (al,bl) A time for a wavepacket to stay in the upper electronic surface. (a2,b2) Flux to the dissociation channel on the ground state (the values are multiplied by 10). (a3,b3) Acumulated population to the dissociation channel, which is given by the time integration of the above flux. (a4,b4) The dispersion of the wavepacket around its center, which is monitored on the upper surface. The left and right panels are for the vibrational decay ((a o, ko) = (2, 35)) and collision ((xo, fco) = (7, —45)), respectively. (Reprinted with permission from T. Yonehara et al, J. Chem. Phys. 130, 214113 (2009)).

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