Time- and frequency-resolved

Melinger J S and Albrecht A C 1986 Theory of time- and frequency-resolved resonance secondary radiation from a three-level system J. Chem. Phys. 84 1247-58... 

A. Mokhtari, J. Chesnoy and A. Laubereau, Femtosecond time-and frequency-resolved fluorescence spectroscopy of a dye molecule, Chem. Phys. Letts, 155, 593-598 (1989). 

Describing complex wave-packet motion on the two coupled potential energy surfaces, this quantity is also of interest since it can be monitored in femtosecond pump-probe experiments [163]. In fact, it has been shown in Ref. 126 employing again the quasi-classical approximation (104) that the time-and frequency-resolved stimulated emission spectrum is nicely reproduced by the PO calculation. Hence vibronic POs may provide a clear and physically appealing interpretation of femtosecond experiments reflecting coherent electron transfer. We note that POs have also been used in semiclassical trace formulas to calculate spectral response functions [3]. 

The solvated electron in methanol. Novel time- and frequency-resolved pump-probe spectroscopy of short-lived precursors. 

Wt-GFP was expressed in E. coli and purified as described in Ref. [4]. Time- and frequency resolved pump-probe transients were recorded with 40-fs, 400-nm excitation pulses and probe pulses with durations of approximately 40 fs throughout the visible spectral range. Since photo-conversion strongly alters the GFP response, rapid scan data acquisition was performed... 

Since exact formulas for time and frequency resolved emission spectra are less standard we shortly comment on the derivation of the full quantum expressions [43-45]. To characterize the emission we introduce the rate R k(t) which follows as the number of photons emitted per time into the state with polarization A and wave vector k. Since emission appears into the photon vacuum we may set R k = dN k/dt, where... 

Consequently, F(u> t) will contain the transition dipole matrix elements in forming a common scalar product. The full quantum expression for the emission rate (rate of ideal time and frequency resolved emission) takes the form... 

As already indicated Eq. (39) (Eq. (40)) gives the rate of ideal time and frequency resolved emission. If compared with experimental data gained by single photon counting, F(iv t) has to undergo a time averaging with the respective apparatus function which determines the possible time resolution of the measurement (for up conversion techniques see [44]). 

Fig. 11 Normalized time and frequency resolved emission spectrum of the CC P4. A 6 ps time averaging has been carried out to mimic the apparatus function of the single photon detector. Radiative and non-radiative decay has been accounted for by a common chromophore excited-state life time of 5 ns.

Mixed Description of Time and Frequency Resolved Emission... 

The survey in this section, which describes progress in a rapidly developing field, demonstrates that many problems remain to be solved. It is clear, however, that time and frequency resolved photocurrent measurements hold the key to understanding the behaviour of these novel electrode/elec-trolyte systems. 

Peter L.M. and Vanmaekelbergh D. (1999), Time- and frequency-resolved techniques in photoelectrochemistry , in Advances in Electrochemical Science and Engineering, Vol. 6, Alkire D. M and Kolb D., eds., Wiley VCH, Weinheim, pp. 77-163. 

The role of vibrational relaxation and solvation dynamics can be probed most effectively by fluorescence experiments, which are both time- and frequency-resolved,66-68 as indicated at the end of Sec. V. We have recently developed a theory for fluorescence of polar molecules in polar solvents.68 The solvaion dynamics is related to the solvent dielectric function e(co) by introducing a solvation coordinate. When (ai) has a Lorentzian dependence on frequency (the Debye model), the broadening is described by the stochastic model [Eqs. (113)], where the parameters A and A may be related to molecular... 

The second major section (Section III), comprising the bulk of the chapter, pertains to the studies of IVR from this laboratory, studies utilizing either time- and frequency-resolved fluorescence or picosecond pump-probe methods. Specifically, the interest is to review (1) the theoretical picture of IVR as a quantum coherence effect that can be manifest in time-resolved fluorescence as quantum beat modulated decays, (2) the principal picosecond-beam experimental results on IVR and how they fit (or do not fit) the theoretical picture, (3) conclusions that emerge from the experimental results pertaining to the characteristics of IVR (e.g., time scales, coupling matrix elements, coupling selectivity), in a number of systems, and (4) experimental and theoretical work on the influence of molecular rotations in time-resolved studies of IVR. Finally, in Section IV we provide some concluding remarks. 

Suppose, now, that the molecule, initially in the ground-state vibrational level gt), is excited by a delta-function pulse of light to the excited state manifold, whereupon time- and frequency-resolved fluorescence to the ground-state vibrational level /> is detected. The signal38 in such an experiment is... 

Other excitation energies Other than the ones at S, + 1380 and S, + 1420 cm-, there are three prominent bands in the intermediate region of jet-cooled anthracene s excitation spectrum. Time- and frequency-resolved measurements subsequent to excitation of these bands have also been made. Without going into any detail concerning the results of these measurements, we do note that all three excitations give rise to quantum beat-modulated decays whose beat patterns (phases and modulation depths) depend on the fluorescence band detected.42 Figure 16 shows an example of this behavior for excitation to S, + 1514 cm-1. The two decays in the figure correspond to the detection of two different fluorescence bands in the S, + 1514 cm-1 fluorescence spectrum. 

Figure 22. Time- and frequency-resolved fluorescence of jet-cooled d, -anthracene (top) and d10-anthracene (bottom). The d, decay corresponds to excitation toS, + 1411cm-1 and detection of the 388 cm-1 band in the fluorescence spectrum. The dl0 decay corresponds to excitation to St + 1452 cm-1 and detection of the 372 cm-1 band in the spectrum. Quantum beats are clearly present in both decays.

Mukamel s group74 in trying to understand the time- and frequency-resolved spectra of anthracene in terms of a vibrational force field for the molecule. Such studies have great potential for developing deeper insight into the coupling associated with IVR. 

Figure 54. Time- and frequency-resolved spectra of stilbene and stilbene-He (1 1) complex. Excitation energies relative to the respective complex or bare molecule Og transition energies are given at left. Excitation frequencies are marked by an asterisk in the upper spectra. Spectral resolutions for (A), (B), and (C) are 4, 1, and 5 cm"1, respectively. The difference in resolution accounts totally for the broadening of (A) relative to (B). The time-resolved data are presented in the form of polarization anisotropies. B is % B + C) of the complex or bare stilbene.

Time and Frequency Resolved Studies of Photoelectrochemical Kinetics... 

It can be seen from this discussion that a more broadly based approach to the characterisation of the dynamic properties of electrochemical systems is desirable. One of the objectives of this review is to provide a cohesive and unifying approach to the application of time and frequency resolved methods in photoelectrochemistry. The input functions are generally either light or voltage, and the output functions may be current, charge, voltage, optical absorbance/reflectance or microwave reflectivity. 

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