Franck-Condon transition spectroscopy

Although theoretical techniques for the characterization of resonance states advanced, the experimental search for reactive resonances has proven to be a much more difficult task [32-34], The extremely short lifetime of reactive resonances makes the direct observation of these species very challenging. In some reactions, transition state spectroscopy can be employed to study resonances through "half-collision experiments," where even very short-lived resonances may be detected as peaks in a Franck-Condon spectrum [35-38]. Neumark and coworkers [39] were able to assign peaks in the [IHI] photodetachment spectrum to resonance states for the neutral I+HI reaction. Unfortunately, transition state spectroscopy is not always feasible due to the absence of an appropriate Franck-Condon transition or due to practical limitations in the required level of energetic resolution. The direct study of reactive resonances in a full collision experiment, such as with a molecular beam apparatus, is the traditional and more usual environment to work. Unfortunately, observing resonance behavior in such experiments has proven to be exceedingly difficult. The heart of the problem is not a... 

The observation of a bend progression is particularly significant. In photoelectron spectroscopy, just as in electronic absorption or emission spectroscopy, the extent of vibrational progressions is governed by Franck-Condon factors between the initial and final states, i.e. the transition between the anion vibrational level u" and neutral level u is given by... 

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. 

Resonance Raman Spectroscopy. If the excitation wavelength is chosen to correspond to an absorption maximum of the species being studied, a 10 —10 enhancement of the Raman scatter of the chromophore is observed. This effect is called resonance enhancement or resonance Raman (RR) spectroscopy. There are several mechanisms to explain this phenomenon, the most common of which is Franck-Condon enhancement. In this case, a band intensity is enhanced if some component of the vibrational motion is along one of the directions in which the molecule expands in the electronic excited state. The intensity is roughly proportional to the distortion of the molecule along this axis. RR spectroscopy has been an important biochemical tool, and it may have industrial uses in some areas of pigment chemistry. Two biological appHcations include the deterrnination of helix transitions of deoxyribonucleic acid (DNA) (18), and the elucidation of several peptide stmctures (19). A review of topics in this area has been pubHshed (20). 

Vibrationally mediated photodissociation (VMP) can be used to measure the vibrational spectra of small ions, such as V (OCO). Vibrationally mediated photodissociation is a double resonance technique in which a molecule first absorbs an IR photon. Vibrationally excited molecules are then selectively photodissociated following absorption of a second photon in the UV or visible [114—120]. With neutral molecules, VMP experiments are usually used to measure the spectroscopy of regions of the excited-state potential energy surface that are not Franck-Condon accessible from the ground state and to see how different vibrations affect the photodissociation dynamics. In order for VMP to work, there must be some wavelength at which vibrationally excited molecules have an electronic transition and photodissociate, while vibrationally unexcited molecules do not. In practice, this means that the ion has to have a... 

The emission spectrum observed by high resolution spectroscopy for the A - X vibrational bands [4] has been very well reproduced theoretically for several low-lying vibrational quantum numbers and the spectrum for the A - A n vibrational bands has been theoretically derived for low vibrational quantum numbers to be subjected to further experimental analysis [8]. Related Franck-Condon factors for the latter and former transition bands [8] have also been derived and compared favourably with semi-empirical calculations [25] performed for the former transition bands. Pure rotational, vibrationm and rovibrational transitions appear to be the largest for the X ground state followed by those... 

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... 

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. 

The probability of a particular vertical transition from the neutral to a certain vibrational level of the ion is expressed by its Franck-Condon factor. The distribution of Franck-Condon factors, /pc, describes the distribution of vibrational states for an excited ion. [33] The larger ri compared to ro, the more probable will be the generation of ions excited even well above dissociation energy. Photoelectron spectroscopy allows for both the determination of adiabatic ionization energies and of Franck-Condon factors (Chap. 2.10.1). 

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. 

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. 

The lower triplet state corresponds to the 3a (3a ) transition of the tt,x type. This band could underlie the 385-to 200-nm band since the Franck-Condon accessible region may be quite high in energy. Excited electronic states of ketene have been recently studied by electron impact spectroscopy (87). 

In the case of MCD spectroscopy, for a fully allowed electronic transition based on the rigid shift, Bom-Oppenheimer, and Franck Condon approximations, the intensity equation, according to the modified conventions recommended by Stephens, Piepho and Schatz, is... 

The vibrational sateHite structures of the two fast decaying substates II and III could not be separated from each other by the applied method of time-re-solved emission spectroscopy, because the decay times are too similar (130 ps, 235 ps). Further, both transitions between the substates II and III, respectively, and the ground state 0 are very likely connected with the same Franck-Condon active vibrations. This can directly be shown for Pt(2-thpy)2, for which the corresponding two emissions are spectrally well resolvable. (Sect. 4.2.4 and Refs. [ 59,60].) In this situation, one would not observe any obvious difference between the spectra stemming from the two substates II and III of Pd(2-thpy)2. 

The improved numerical stability of the new deMon2K version also opened the possibility for accurate harmonic Franck-Condon factor calculations. Based on the combination of such calculations with experimental data from pulsed-field ionization zero-electron-kinetic energy (PFl-ZEKE) photoelectron spectroscopy, the ground state stmcture of V3 could be determined [272]. Very recently, this work has been extended to the simulation of vibrationaUy resolved negative ion photoelectron spectra [273]. In both works the use of newly developed basis sets for gradient corrected functionals was the key to success for the ground state stmcture determination. These basis sets have now been developed for aU 3d transition metal elements. With the simulation of vibrationaUy resolved photoelectron spectra of small transition metal clusters reliable stmcture and... 

Although Dispersed Fluorescence (DF) spectroscopy is probably better classified as a form of double resonance spectroscopy, DF is discussed here because it is a form of emission spectroscopy where all of the emission originates from a single, laser-populated, upper electronic-vibrational-rotational level, (e, v, J ). A DF spectrum typically contains two [R J" = J — 1), P(J" = J + 1)] or three [i ( J — 1), Q(J ), P J +1)] rotational transitions per electronic-vibrational e",v" level. Often there is a progression of vibrational bands, [ v, v" = n), (v, v" = n + 1),. .. (v, v" = n + to)] where v" = n is the lowest vibrational level (band farthest to the blue) and v" = n + m is the highest vibrational level observable (limited either by the detector response or Franck-Condon factors) in the DF spectrum (see Fig. 1.8 and Fig. 1.15). 

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