Nonadiabatic events

Figure 8. Li + H2 Ground-state population as a function of time for a representative initial basis function (solid line) and the average over 25 (different) initial basis functions sampled (using a quasi-classical Monte Carlo procedure) from the Lit2/j) + H2(v — 0, j — 0) initial state at an impact parameter of 2 bohr. Individual nonadiabatic events for each basis function are completed in less than a femtosecond (solid line) and due to the sloped nature of the conical intersection (see Fig. 7), there is considerable up-funneling (i.e., back-transfer) of population from the ground to the excited electronic state. (Figure adapted from Ref. 140.)...

One expects the timescale of the nonadiabatic transition to broaden for a stationary initial state, where the nuclear wavepacket will be less localized. To mimic the case of a stationary initial state, we have averaged the results of 25 nonstationary initial conditions and the resulting ground-state population is shown as the dashed line in Fig. 8. The expected broadening is seen, but the nonadiabatic events are still close to the impulsive limit. Additional averaging of the results would further smooth the dashed line. 

Nonadiabatic events (transition from the excited state to the ground state at the conical intersection) pose a serious challenge because the nonadiabatic transition is rigorously quantum mechanical without a well-defined classical analog. At a simple level of theory13 (we return to a better treatment subsequently), the probability of a surface hop is given as follows ... 

We now briefly describe the way in which the nonadiabatic event (surface hop) can be described in on the fly dynamics methods. We can represent the time-dependent wavefunction in the Cl space as a vector ... 

A fundamental theoretical issue for computational photochemistry is the treatment of the hop (nonadiabatic) event. One needs to add the time propagation of the solutions of the time-dependent Schrodinger equation for electronic motion to the classical propagation of the nuclei, thus obtaining the populations of each adiabatic state. The time-dependent wave function for electronic motion is just a time-dependent configuration interaction vector ... 

The mixed-state Ehrenfest dynamics has problems after leaving the region of the nonadiabatic event. When the surfaces are sufficiently close in energy, the semi-classical Ehrenfest dynamics is switched on. Away from the degeneracy, the population on a single surface is recovered by reverting to the single-state quasi-classical dynamics. 

Figure 4.9 The pyramidalization angle of one of the methylene groups plotted against the p5namidalization of the other for each Si/So nonadiabatic event of the four isotopomers studied. As in Figure 4.8, the size of each circle represents the weight of the ground state basis function at the end of the simulation. Notice that in 1,1-CgHgDg pyramidalization of the CHg pyramidalization leads to greater population quenching than does CDg pyramidalization.

Matsika S, Krause P (2011) Nonadiabatic Events and Conical Intersections. Annu. Rev. Phys. Chem. 62 621-643... 

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