Predissociation, metastable tunneling state

Fig. 6.4. Ground- and excited-state potential energy curves illustrating possible dissociation pathways. For a diatomic molecule r is the internuclear distance in a polyatomic molecule r is a normal mode displacement. Vibrational separations are greatly exaggerated. The vertical arrows correspond to Franck-Condon allowed transitions. Where possible, molecular examples are indicated, (a) Repulsive excited state—immediate dissociation, (b) Crossing of bound and repulsive excited states—intersystem crossing leads to predissociation. (c) Metastable excited state—tunneling leads to dissociation, (d) Bound state— excitation energy greater than dissociation limit.

If excitation is to a repulsive state (Fig. 6.4a), dissociation is immediate, occurring within one vibrational period, t < 10 sec. Another rapid process involves predissociation (Fig. 6.4b). Here the molecule is excited to a bound state which, because there is a resonant continuum level of the repulsive electronic state, undergoes radiationless conversion followed by immediate dissociation. Excitation could also be to a metastable vibronic state (Fig. 6.4c) which dissociates via tunneling. The dissociation probability would be very sensitive to the height and the width of the barrier to be overcome, and the decomposition rate greatly enhanced by vibrational excitation in the excited state. Finally, as in Fig. 6.4d, excitation may be to a bonding state but into a continuum level above the dissociation limit decomposition is again immediate. 

B. Decay of Metastable State through Tunneling (Predissociation)... 

Needless to say, tunneling is one of the most famous quantum mechanical effects. Theory of multidimensional tunneling, however, has not yet been completed. As is well known, in chemical dynamics there are the following three kinds of problems (1) energy splitting due to tunneling in symmetric double-well potential, (2) predissociation of metastable state through... 

The theory developed for tunneling splitting can be easily extended to the decay of the metastable state through multidimensional tunneling, namely, tunneling predissociation of polyatomic molecules. In the case of predissociation, however, the instanton trajectory cannot be fixed at both ends, but one end should be free (see Fig. 17). The boundary conditions are... 

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