Franck-Condon stationary phase

The situation is much more complicated for a vibrational wavepacket launched from a r" 0 initial eigenstate (see Fig. 9.7). However, a simple picture based on the classical Franck-Condon (stationary phase) principle (see Section 5.1.1) captures the essential details of the wavepacket produced at to on the electronically excited potential surface. First, there is the limiting case of an excitation pulse sufficiently short that an exact replica of the electronic ground state vibrational eigenstate, (R v" / 0), is created at to on the excited potential surface,... 

If the photodissociation starts from a / 0 level, the a E) will be an oscillatory curve with v" + 1 lobes (v" nodes) (see Fig. 7.5). The possibility of destructive interference arising from multiple stationary phase points (e.g. i i,i 2) (Tellinghuisen, 1984) is negligible for direct dissociation because the difference potential V R) — V" R) = AV(R) will be single valued (i.e. AV(-Ri) AV(R2)) over the Franck-Condon region, R in < R < R max-... 

Because the initial vibrational state for absorption spectra often is v = 0, the vibrational nonstationary state typically produced initially is an only slightly distorted Gaussian wavepacket centered at R"g. Conservation of momentum requires that this approximately minimum-uncertainty wavepacket be launched at the turning point on the upper surface, R e = R"g, which lies vertically above R"g. [This is a consequence of the stationary phase condition, see Sections 5.1.1 and 7.6 and Tellinghuisen s (1984) discussion of the classical Franck-Condon... 

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