Fluorescence Stokes’ shifts

Transition from an excited potential energy surface (PES) back to the ground state is referred to as fluorescence. The majority of the photoactive molecules have a spin-singlet ground state. The latter is referred to as the Sq state in photophysics. There are several excited singlet states, of course (S , n 0). The transition Sn Sq is spin allowed, but it was early discovered (1950) that only the lowest excited state. Si, makes any significant contribution to the fluorescence (Kasha s rule, after an American spectroscopist and theoretical chemist). 

The name fluorescence is related to Cap2 (fluorspar latin mineralis), which 

FIGURE 12.5 Potential energy surfaces for the ground state and the excited state. 

In polyenes, single bonds go to double bonds and vice versa at excitation. This means that a di-trans-isomerization takes place around double bonds (that is, double bonds in the ground state). A polyene called retinal is involved in the vision 

FIGURE 12.6 Absorption spectrum of an organic jt-system and the corresponding fluorescence spectrum beside each other. 

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FIG. 4 Time-resolved fluorescence Stokes shift of coumarin 343 in Aerosol OT reverse micelles, (a) normalized time-correlation functions, C i) = v(t) — v(oo)/v(0) — v(oo), and (b) unnormalized time-correlation functions, S i) = v i) — v(oo), showing the magnitude of the overall Stokes shift in addition to the dynamic response, wq = 1.1 ( ), 5 ( ), 7.5 ( ), 15 ( ), and 40 (O) and for bulk aqueous Na solution (A)- Points are data and lines that are multiexponential fits to the data. (Reprinted from Ref 38 with permission from the American Chemical Society.)... 

The goal of theory and computer simulation is to predict S i) and relate it to solvent and solute properties. In order to accomplish this, it is necessary to determine how the presence of the solvent affects the So —> Si electronic transition energy. The usual assmnption is that the chromophore undergoes a Franck-Condon transition, i.e., that the transition occurs essentially instantaneously on the time scale of nuclear motions. The time-evolution of the fluorescence Stokes shift is then due the solvent effects on the vertical energy gap between the So and Si solute states. In most models for SD, the time-evolution of the solute electronic stracture in response to the changes in solvent environment is not taken into accoimt and one focuses on the portion AE of the energy gap due to nuclear coordinates. 

Fig. 1 represents schematically the usual physical interpretation of polar SD The solute undergoes vertical electroitic excitation and the dynamic fluorescence Stokes shift arises Ifom the reorganization of the solvent molecules. In the case... 

The wavelengths of the steady state absorption (Aabs) and fluorescence (A,) spectral peaks and magnitudes of the fluorescence Stokes shift (Av) of these PYP analogues in comparison with those of w.-t. PYP, denatured PYP and several site-directed mutants are given in Table 1. The observed fluorescence decay curves at various wavelengths of these PYP analogues are... 

Both experiments and theory show that solvation may proceed exceedingly rapidly. Figure 2 shows the fluorescence Stokes shift function S(f) for a coumarin dye in water obtained by experiment and simulation [4]. Here, S(t) is a normalized function describing the progress toward equilibrium ... 

Figure 2. Experimental and simulated fluorescence Stokes shift function 5(f) for coumarin 343 in water. The curve marked Aq is a classical molecular dynamics simulation result using a charge distribution difference, calculated by semiempirical quantum chemical methods, between ground and excited states. Also shown is a simulation for a neutral atomic solute with the Lennard-Jones parameters of the water oxygen atom (S°). (From Ref. 4.)...

To establish the connection between M(f) and the fluorescence Stokes shift function 5(f) defined in Eq. (1), we first rewrite 5(f) as... 

The definition of the spectral density [Eq. (15)] allows to connect the various correlation functions relevant to spectral broadening and spectral diffusion. For example, the fluorescence Stokes shift function S(t) can be written as... 

Thus we see that the first moment of the spectral density multiplied by h is the reorganization energy (i.e., one half of the Stokes shift magnitude), whereas the time dependence of the first moment of p(w) corresponds to the fluorescence Stokes shift. Thus the time dependence of S t) is determined entirely by the spectral density. At high temperature [i.e., when p(w) contains frequencies less than 2kBT], S(t) becomes the classical correlation function [36] used by many previous authors [7-10], This follows from... 

Thus Eqs. (17) and (22) establish the explicit correlation between the fluorescence Stokes shift function and the line-broadening function that gives linear absorption and emission spectra via... 

We have done a study by time-resolved hole-burning spectroscopy for dye molecules in polar solvents and found that the time correlation function of the hole width decays much slower than that of the peak shift of the hole, which occurs very rapidly, as you observed in the case of the fluorescence Stokes shift [K. Nishiyama, Y. Asano, N. Hashimoto, and T. Okada, J. Mol. Liquids 65/66, 41 (1995)]. 

In the case of electron transfers in solution there appears to be a greater cohesiveness of views, and the need for vibrational assistance is well established for reactions accompanied by vibrational changes (e.g., changes in bond lengths). A detailed analysis of the experiments could be made because of the existence of independent data, which include X-ray crystallography, EXAFS, resonance Raman spectra, time-dependent fluorescence Stokes shifts, among others. 

One may inquire as to what this experience with solutions suggests for the study of reactions in clusters. In the case of electron transfers supplementary information, such as time-dependent fluorescence Stokes shift in clusters, would again be helpful. Equation (2.3) can be modified to include a D(t), as in the isothermal case, if needed from the results of such data. For isomerizations, also, it would be useful to have, for solutions or clusters, detailed analogous data such as the above Stokes shift. However, because of the low intensity of such a fluorescence in this case, such data appear to be absent or scarce. 

There are a number of empirical tests for the near ideality of potential probes. Ideal probes should exhibit a solvent dependence of the fluorescence Stokes-shift (hvabs - hvn) that is in account with the Lippert-Mataga equation [9,10]. 

The Practical Determination of C(0- The time-dependent fluorescence Stokes shift of the spectrum should manifest itself as (i) a rapid decay in the fluorescence intensity on the blue edge of the fluorescence spectrum, (ii) a... 

TABLE 2 Low Temperature Solvation Dynamics Determined from Time-Dependent Fluorescence Stokes Shift Measurements... 

S. C. Tucker, Solvent density inhomogeneities in supercritical fluids, Chem. Rev., 99 (1999) 391—418 O. Kajimoto, Solvation in supercritical fluids Its effects on energy transfer and chemical reactions, Chem. Rev., 99 (1999) 355-89 S. Nugent and B. M. Ladanyi, The effects of solute-solvent electrostatic interactions on solvatochromic shifts in supercritical C02, J. Chem. Phys., 120 (2004) 874-84 F. Ingrosso and B. M. Ladanyi, Solvation dynamics of C153 in supercritical fluoroform a simulation study based on two-site and five-site models of the solvent, J. Phys. Chem. B, 110 (2006) 10120-29 F. Ingrosso, B. M. Ladanyi, B. Mennucci and G. Scalmani, Solvation of coumarin 153 in supercritical fluoroform, J. Phys. Chem. B, 110 (2006) 4953-62 Y. Kimura and N. Hirota, Effect of solvent density and species on static and dynamic fluorescence Stokes shifts of coumarin 153, J. Chem. Phys., Ill (1999) 5474 ... 

We recently developed a systematic method that uses the intrinsic tryptophan residue (Trp or W) as a local optical probe [49, 50]. Using site-directed mutagenesis, tryptophan can be mutated into different positions one at a time to scan protein surfaces. With femtosecond temporal and single-residue spatial resolution, the fluorescence Stokes shift of the local excited Trp can be followed in real time, and thus, the location, dynamics, and functional roles of protein-water interactions can be studied directly. With MD simulations, the solvation by water and protein (residues) is differentiated carefully to determine the hydration dynamics. Here, we focus our own work and review our recent systematic studies on hydration dynamics and protein-water fluctuations in a series of biological systems using the powerful intrinsic tryptophan as a local optical probe, and thus reveal the dynamic role of hydrating water molecules around proteins, which is a longstanding unresolved problem and a topic central to protein science. 

Fluorescence from singlet excited states of [Re(X)(CO)3(bpy)] (X = Cl, Br, I) and [Re(Etpy)(CO)3(bpy)]+ appears concomitantly with 400 mn, 80 fs pulse excitation as a very broad band peaking at -530 nm (in Chap. 1 of this book). The large instantaneous fluorescence Stokes shift and broadness indicate a femtosecond energy dissipation and ultrafast population of many vibrational modes. TD-DFT calculations [10]... 

Volmer F, Rettig W, Birckner E (1994) Photochemical mechanisms producing large fluorescence Stokes shifts. J Fluorescence 4 65-69... 

In view of the great importance of chemical reactions in solution, it is not surprising that basic aspects (structure, energetics, and dynamics) of elementary solvation processes continue to motivate both experimental and theoretical investigations. Thus, there is growing interest in the dynamical participation of the solvent in the events following a sudden redistribution of the charges of a solute molecule. These phenomena control photoionization in both pure liquids and solutions, the solvation of electrons in polar liquids, the time-dependent fluorescence Stokes shift, and the contribution of the solvent polarization fluctuations to the rates of electron transfer in oxidation-reduction reactions in solution. 

Unie resolved ground state hole spectra of cresyl violet in acetonitrile, methanol, and ethanol at room temperature have been measured in subpicosecond to picosecond time region. The time correlation function of the solvent relaxation expressed by the hole width was obtained. The main part of the correlation function decayed much slower compared with that of the reported correlation function observed in time dependent fluorescence Stokes shift. Some possible mechanisms are proposed for understanding of the time depencences of the spectral broadening under the condition with the distribution of the relaxation times in fluid solution based on the entropy term in the solvent orientation as well as the site dependent response of the solvent. 

The plot shows a distribution closely around a slope of unity indicated by the solid line in Figure 2 except for the alcohols and nitrobenzene. Such anomaly in alcohols is also reported for other chemical processes and time-dependent fluorescence stokes shifts and is attributed to their non-Debye multiple relaxation behavior " the shorter relaxation components, which are assigned to local motions such as the OH group reorientation, contribute the friction for the barrier crossing rather than the slower main relaxation component, which corresponds to the longitudinal dielectric relaxation time, tl, when one regards the solvent as a Debye dielectric medium. If one takes account of the multiple relaxation of the alcohols, the theoretical ket (or v,i) values inaease and approach to the trend of the other solvents. (See open circles in Figure 2.)... 

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