Electronic transition frequency correlation

Figure 18. The normalized electronic transition frequency correlation function M(t) 1= S(i)] obtained from the experimental three-pulse photon echo peak shifts and transient grating data for IR144 in ethanol (—) total W(t) ( ) ultrafast Gaussian component in M(t) ( ) oscillatory component that arises from intramolecular vibrational motion.

Here, I(co) is the Fourier transform of the above C(t) and AEq f is the adiabatic electronic energy difference (i.e., the energy difference between the v = 0 level in the final electronic state and the v = 0 level in the initial electronic state) for the electronic transition of interest. The above C(t) clearly contains Franck-Condon factors as well as time dependence exp(icOfvjvt + iAEi ft/h) that produces 5-function spikes at each electronic-vibrational transition frequency and rotational time dependence contained in the time correlation function quantity <5ir Eg ii,f(Re) Eg ii,f(Re,t)... 

All of these time correlation functions contain time dependences that arise from rotational motion of a dipole-related vector (i.e., the vibrationally averaged dipole P-avejv (t), the vibrational transition dipole itrans (t) or the electronic transition dipole ii f(Re,t)) and the latter two also contain oscillatory time dependences (i.e., exp(icofv,ivt) or exp(icOfvjvt + iAEi ft/h)) that arise from vibrational or electronic-vibrational energy level differences. In the treatments of the following sections, consideration is given to the rotational contributions under circumstances that characterize, for example, dilute gaseous samples where the collision frequency is low and liquid-phase samples where rotational motion is better described in terms of diffusional motion. 

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... 

Redox potential data frequently correlate with parameters obtained by other spectroscopic measurements. The correlation of E° potentials with gas-phase ionization potentials has already been briefly discussed. Electronic transitions observed by UV-visible spectroscopy involve the promotion of an electron from one orbital to another and this can be viewed as an intramolecular redox reaction. If the promotion involves the displacement of an electron from the HOMO to the LUMO, then the redox potentials for the reduction of the compound, °REd, and for its oxidation, °ox, are of importance. For a closely related series of compounds, trends in oxidation and reduction potentials can be related to shifts in the absorption frequency, v. If the structural perturbation causes the HOMO and the LUMO to rise or fall in energy in tandem, then (E°RED — E°ox) will remain constant in such cases the HOMO—LUMO frequency (energy) will be essentially independent of the structural perturbation. Where there is a differential influence of the perturbation on the HOMO and the LUMO, then ( °red E°ox) will vary as will the energy of the electronic transition. In such cases a linear correlation of °red or E°0x may result. In the limit the energy of the HOMO, or more usually the LUMO, will be unaffected by structural perturbation where the acceptor orbital is pinned, direct linear correlation of E°Gx with v should be apparent. With E°ox and v in a common energy unit, the plot E°0x versus v should have a slope close to one.33-36... 

Because of the small size of the utilized test molecules and the fact that the molecules remain in their electronic ground states, accurate calculations of the transition frequency fluctuation correlation function of these systems fluctuations would seem to be achievable with state-of-the-art quantum dynamics calculations. 

It is evident from these data that the transition frequency fluctuation correlation function of samples that have the same probe molecule (azide) embedded into two different proteins (hemoglobin and carbonic anhydrase), or of the sample with different probe molecules (azide, carbon monoxide) embedded to one protein (hemoglobin), all differ considerably. This, we believe, is a consequence of sensitivity of this spectroscopic technique to the local structure, which is different in each case. This result must be contrasted with electronic dephasing, where it was found that the energy gap fluctuation correlation function reflects the response of the bulk solvent and is essentially independent of the chromophore used as a probe (81). 

Polarographic studies show, in addition to oxidation waves for [Os(bipy)3]2+, several reduction waves 130,158 this is also the case for [Os(4,4 -Me2bipy)3]2+, [Os(5,5 -Me2bipy)3]2+121 and [Os-(phen)3]2+. Recent cyclic voltammetry and coulombetry studies on [Os(bipy)3]2+ and [Os(phen)3]2+ in liquid S02 show successive one-electron oxidations to [Os(LL)3]3+ and [Os(LL)3]4+.lls There is a small but real difference in the Os111/u redox potential for [Os(phen)3]2+ in aqueous and in non-aqueous sodium lauryl sulfate micellar solutions.138 Correlations have been made between the oxidation potentials and charge-transfer transition frequencies in complexes [M(LL)3]2+ (Me = Fe, Ru, Os LL = bipy, 4,4 -Me2bipy, 5,5 -Me2bipy).159... 

One can argue that correlations such as equations (4.9.2) and (5.10.2) are not physically reasonable in that they are based on the wavelength of the electronic transition related to the solvatochromic effect, not its frequency. The frequency is... 

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