Trapping above the potential barrier Time-delay in reaction dynamics

4 Trapping above the potential barrier Time-delay in reaction dynamics 

The precise mechanism is as follows. The paths come about the strong interaction area, where the electronic-state mixing is induced. The forces originated from the excited state trap some paths as though they undergo vibrational motion on the excited state adiabatic potential curve. However, again due to the nonadiabatic interactions, the trapped paths gradually 

We now proceed to confirm the physical picture drawn by the pathbranching representation is indeed consistent with the full-quantmn results. The nuclear quantum wavepackets can be readily calculated, provided that both and X12 are available globally, in terms of the Born Huang 

The initial conditions for the quantum dynamics corresponding to those in the preceding section are as follows. Suppose that a total wavefunction totai(r, i , t) is expanded as in Eq. (6.104) and we are interested only in the nuclear wavepackets xi R,t) and x2 R,t). We propagate them with the extended split operator method. [77] The initial nuclear wavepackets xi R,t) are chosen to be a coherent-type Gaussian function only on the adiabatic ground state as 

Rq and Pq are the same quantities as those defined in Sec. 6.6.1 for the path-branching representation. The wavepacket width in coordinate space is set to AR = 1. The number of grid points for FFT is 512 on the space 

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