Franck-Condon bright state

Long progressions of feature states in the two Franck-Condon active vibrational modes (CC stretch and /rani-bend) contain information about wavepacket dynamics in a two dimensional configuration space. Each feature state actually corresponds to a polyad, which is specified by three approximately conserved vibrational quantum numbers (the polyad quantum numbers nslretch, "resonance, and /total, [ r, res,fl)> and every symmetry accessible polyad is initially illuminated by exactly one a priori known Franck-Condon bright state. 

The finer structure within each feature state corresponds to the dynamics of the Franck-Condon bright state within a four-dimensional state space. This dynamics in state space is controlled by the set of all known anharmonic resonances. The state space is four dimensional because, of the seven vibrational degrees of freedom of a linear four-atom molecule, three are described by approximately conserved constants of motion (the polyad quantum numbers) thus 7-3 = 4. 

An example of an application to actual spectroscopy is shown in Figure 6.9. This shows the states computed in the range of the 0 —> 3 CH spectral transition. The intensities were computed as a Franck-Condon overlap of the optically bright CH overtone state (Holme and Levine, 1989 Levine and Berry, 1989) with the relevant eigenstate. 

Fig. 2. Pump and probe scheme within a tiers picture (schematic). The zeroth order bright state which is not Franck-Condon (FC) active in the electronic transition is excited via the near IR- laser pulse. FC-active modes m later tiers having no population at t=0 are probed and their time dependent population is a measure for IVR (Vj being matrix elements connecting zeroth order states) in the molecule giving rise to an enhancement of the electronic absorption.

Franck-Condon dissociative continuum. At long times (Af = 3500 fs), a sharp photoelectron spectrum of the free NO(A, 3,v) product is seen. The 10.08 eV band shows the decay of the (NO)2 excited state. The 9.66 eV band shows both the decay of (NO)2 and the growth of free NO(A, 3,v) product. It is not possible to fit these via single exponential kinetics. However, these 2D data are fit very accurately at all photoelectron energies and all time delays simultaneously by a two-step sequential model, implying that an initial bright state (NO)2 evolves to an intermediate configuration (NO)2f, which itself subsequently decays to yield free NO(A, 3s) products [138]... 

As is ISC, IC is very slow for electronic states with similarly shaped potential energy surfaces. When the potential surfaces have very different shapes, there will be a small number of vibrational doorway states that are especially effective in coupling to the bright state. Conical intersections are a special class of potential surfaces of very different shapes. But even when potential surfaces have very different shapes, many normal coordinate displacements and the associated vibrational normal modes will have nearly identical forms on both surfaces. These normal modes are Franck-Condon inactive and do not contribute to IC. The normal coordinate displacements that express the differences in shapes of the potential surfaces are embodied in vibrational normal modes that are Franck-Condon active. These modes are called promoting modes because, when such a mode on one potential surface is plucked from an eigenstate on the other surface, intramolecular dynamics is promoted or initiated. 

Oppenheimer / Franck-Condon approximation 43), In particular, states that would otherwise be forbidden can borrow intensity from nearby bright states. The broad feature at 14.05 eV might thus be explained by the interaction of the nominally dark state with the nearby, allowed E state. 

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