Electronic 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... 

Spectroscopy provides a window to explain solvent effects. The solvent effects on spectroscopic properties, that is, electronic excitation, leading to absorption spectra in the nltraviolet and/or visible range, of solutes in solution are due to differences in the solvation of the gronnd and excited states of the solute. Such differences take place when there is an appreciable difference in the charge distribution in the two states, often accompanied by a profonnd change in the dipole moments. The excited state, in contrast with the transition state discussed above, is not in equilibrium with the surrounding solvent, since the time-scale for electronic excitation is too short for the readjustment of the positions of the atoms of the solute (the Franck-Condon principle) or of the orientation and position of the solvent shell around it. 

On the other hand, it is pleasing to see that the organic chemist s standard evidence for structural identification such as NMR and IR spectral data can be computed quite accurately UV/vis spectra can also be computed with time-dependent methods, which, however, cannot yet be used to optimise the excited states as the Franck-Condon principle is a common assumption in electron spectroscopy, this is no serious drawbackfor computing... 

With reference to absorption spectroscopy, we deal here with photon absorption by electrons distributed within specific orbitals in a population of molecules. Upon absorption, one electron reaches an upper vacant orbital of higher energy. Thus, light absorption would induce the molecule excitation. Transition from ground to excited state is accompanied by a redistribution of an electronic cloud within the molecular orbitals. This condition is implicit for transitions to occur. According to the Franck-Condon principle, electronic transitions are so fast that they occur without any change in nuclei position, that is, nuclei have no time to move during electronic transition. For this reason, electronic transitions are always drawn as vertical lines. 

Franck-Condon principle - An important principle in molecular spectroscopy which states that the nuclei in a molecule remain essentially stationary while an electronic transition is taking place. The physical interpretation rests on the fact that the electrons move much more rapidly than the nuclei because of their much smaller mass. 

Of considerable significance to any discussion of electronic spectroscopy is the Franck-Condon principle the time taken for an electronic transition is short compared with the times taken for nuclear movements. This means that the Franck-Condon excited state of a molecule, i.e. that existing momentarily after excitation, has the same nuclear geometry as the ground state from which the transition occurred. Further, the solvent molecules around the excited molecules also remain in the same position during the transition. Only after the transition is completed will the excited molecule in the Franck-Condon excited state and its solvation sphere (if any) rearrange into their new equilibrium (excited state) positions. This has an important bearing on the interpretation of solvent effects. 

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.

---