Vibrational spectroscopy Franck-Condon principle

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

The calculation of UV/vis spectra, or any other form of electronic spectra, requires the robust calculation of electronic excited states. The absorption process is a vertical transition, i.e. the electronic transition happens on a much faster timescale than that of nuclear motion (i.e. Bom-Oppenheimer dynamics, more correctly referred to as the Franck-Condon principle in the context of electronic spectroscopy). The excited state, therefore, maintains the initial ground-state geometry, with a modified electron density corresponding to the excited state. To model the corresponding emission processes, i.e. fluorescence or phosphorescence, it is necessary to re-optimize the excited-state nuclear geometry, as emission in condensed phases generally happens from the lowest vibrational level of the emitting excited state. This is Kasha s Rule. 

The lines within each set correspond to different vibrational states of the ion produced by the ionization. The absorption of a photon with removal of an electron is sufficiently rapid that the nuclei do not have time to move appreciably, as in the Franck-Condon principle. The ionization potential that is determined through photoelectron spectroscopy is referred to as the vertical ionization energy, as represented by a vertical line in a diagram such as that of Figure 23.11. In the nitrogen spectrum it appears that the ionization to the n = 1 vibrational state of the ion is the most probable process for the center set of lines, while in the other two sets the transition to the v = 0 vibrational state is the most probable transition. 

To see how we should be able to study the evolution of a collision let us consider first how intermolecular potentials between atoms bound together are studied. This is done, of course, via spectroscopy. One starts with the Born-Oppenheimer approximation for the total molecular wave function this enables one to describe the motion of the nuclei in a potential that depends on the separation between them. This result, the existence of a specific adiabatic potential, rests on there being no appreciable mixing between electronic states. One of its corollaries, the Franck-Condon Principle, enables one to interpret and invert (e.g. using the R.K.R. method) the vibrational spectra in terms of the interatomic potentials in different electronic states. To what extent can we extend such a technique to free-free spectra, in other words, to absorption in the middle of a transient molecule — a collision complex — and deduce information about the potentials between atoms as they collide ... 

Fig. 1. The principle of pumjvprobe spectroscopy by means of transient two-photon ionization A first fs-laser pulse electronically excites the particle into an ensemble of vibrational states creating a wave packet. Its temporal evolution is probed by a second probe pulse, which ionizes the excited particle as a function of the time-dependent Franck Condon-window (a) shows the principle for a bound-bound transition, where the oscillative behaviour of the wave packet will appear (b) shows it for a bound-free transition exhibiting the exponential decay of the fragmentizing particle, and (c) shows the process across a predissociated state, where the oscillating particle progressively leads into a fragmentation channel.

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