Time-independent view Resonances

The main characteristics of indirect dissociation are resonances in the time-independent picture and recurrences in the time-dependent approach. Resonances and recurrences are the two sides of one coin they reveal the same dynamical information but provide different explanations and points of view. To begin this chapter we discuss in Section 7.1, on a qualitative level, indirect photodissociation of a one-dimensional system. A more quantitative analysis follows in Section 7.2. The time-dependent and the time-independent views of indirect photodissociation are outlined and illustrated in Sections 7.3 and 7.4, respectively, with emphasis on vibrational excitation of the NO moiety in the photodissociation of CH30N0(S i). Section 7.5 accentuates the relation between... 

The form (2) describes resonance states in the continuous spectrum of the total time-independent Hamiltonian. It is evident that if this form is adopted as a property of the resonance state, then, when considering the physics from a time-dependent point of view, i.e., as being caused by a decaying state, it yields exponential decay for all t > 0. 

In the case of electron transfers in solution there appears to be a greater cohesiveness of views, and the need for vibrational assistance is well established for reactions accompanied by vibrational changes (e.g., changes in bond lengths). A detailed analysis of the experiments could be made because of the existence of independent data, which include X-ray crystallography, EXAFS, resonance Raman spectra, time-dependent fluorescence Stokes shifts, among others. 

---