Solvation dynamics function

Time-resolved fluorescence spectroscopy of polar fluorescent probes that have a dipole moment that depends upon electronic state has recently been used extensively to study microscopic solvation dynamics of a broad range of solvents. Section II of this paper deals with the subject in detail. The basic concept is outlined in Figure 1, which shows the dependence of the nonequilibrium free energies (Fg and Fe) of solvated ground state and electronically excited probes, respecitvely, as a function of a generalized solvent coordinate. Optical excitation (vertical) of an equilibrated ground state probe produces a nonequilibrium configuration of the solvent about the excited state of the probe. Subsequent relaxation is accompanied by a time-dependent fluorescence spectral shift toward lower frequencies, which can be monitored and analyzed to quantify the dynamics of solvation via the empirical solvation dynamics function C(t), which is defined by Eq. (1). 

Investigation of water motion in AOT reverse micelles determining the solvent correlation function, C i), was first reported by Sarkar et al. [29]. They obtained time-resolved fluorescence measurements of C480 in an AOT reverse micellar solution with time resolution of > 50 ps and observed solvent relaxation rates with time constants ranging from 1.7 to 12 ns. They also attributed these dynamical changes to relaxation processes of water molecules in various environments of the water pool. In a similar study investigating the deuterium isotope effect on solvent motion in AOT reverse micelles. Das et al. [37] reported that the solvation dynamics of D2O is 1.5 times slower than H2O motion. 

Chandra and his coworkers have developed analytical theories to predict and explain the interfacial solvation dynamics. For example, Chandra et al. [61] have developed a time-dependent density functional theory to predict polarization relaxation at the solid-liquid interface. They find that the interfacial molecules relax more slowly than does the bulk and that the rate of relaxation changes nonmonotonically with distance from the interface They attribute the changing relaxation rate to the presence of distinct solvent layers at the interface. Senapati and Chandra have applied theories of solvents at interfaces to a range of model systems [62-64]. 

From the above equation it appears convenient to characterize solvation dynamics by means of the solvation time correlation function C(t), defined asa)... 

Fig. 2 shows the effect of creating hydrogen-bonding complexes between HPTA and oxygen-bases on the solvation correlation function of HPTA, C(t) [10]. Utilizing a pump-probe set-up described elsewhere [11], with 400 nm excitation, the dynamic stokes shift of HPTA was analyzed with about 50fs time-resolution. The hydrogen-bonded HPTA exhibited much faster dynamics than the solvation dynamics of the uncomplexed HPTA in pure DCM. 

In the Brownian oscillator overdamped model as an attempt to simulate the solvation dynamics, the explicit forms of the line-shape functions gr(t) are... 

An additional piece of information can be obtained by studying a synthetic compound derived from the GFP chromophore (1-28) fluorescing at room temperature. In Fig. 3a we show the chemical structure of the compound that we studied in dioxan solution by pump-probe spectroscopy. If we look at the differential transmission spectra displayed in Fig. 3b, we observed two important features a stimulated emission centered at 508 nm and a huge and broad induced absorption band (580-700 nm). Both contributions appear within our temporal resolution and display a linear behavior as a function of the pump intensity in the low fluences limit (<1 mJ/cm2). We note that the stimulated emission red shifts with two characteristic time-scales (500 fs and 10 ps) as expected in the case of solvation dynamics. We conclude that in the absence of ESPT this chromophore has the same qualitative dynamical behavior that we attribute to the relaxed anionic form. 

To measure solvation dynamics in a liquid we follow the rearrangement of surrounding solvent molecules after photo-excitation of a dissolved dye by recording its fluorescence as a function of time. The Stokes shift response function S(t) = (v(t), v(0), and v(oo) re-... 

Contemporary theories go beyond and treat solvation dynamics in detail. In Section III we review many recent papers in this field [62-73,136-142], A key result is that the rate of a charge transfer reactions should be a function of the microscopic dynamics of the specific solvent. In fact, in the case of very small intrinsic charge transfer activation barrier, the rate is predicted to be roughly equal to the rate of solvation (i.e., rf1 for a solvent with a single relaxation (td) time). This result was first derived over 20 years ago by... 

TABLE 1 Experimentally Observed Solvation Dynamics at 298K Determined by the Correlation Function C(t) tj, 2 Relaxation Times, Average Relaxation Time (First Moment of C(t))... 

A number of analogous compounds to BA have been reported, including 5,5 -dibenzo-[a]-pyrenyl (BBPY) [116]. These compounds exhibit emission spectra similar to BA. It would be interesting to explore the ultrafast dynamics of BBPY in order to test the generality of the GLE model. It would also be interesting to study the femtosecond dynamics of BA as a function of applied pressure. Static experiments on the emission of BA, reported by Hara et al. [123], demonstrate that in low viscosity solvents an increase of pressure affects the emission similarly to an increase of solvent polarity. As the pressure is increased, however, the LE/CT interconversion is slowed down. It would be interesting to measure C(r) in these environments and compare the solvation dynamics with LE/CT dynamics, in order to test the generality of the GLE dielectric friction model. 

The solvation dynamics response is reported usually in terms of the frequency v(t) at the peak of the fluorescence band [1], The experimental solvation response function is given by... 

Figure 3.15 Results of simulation of solvation dynamics of chromophore C153 in room-temperature acetonitrile via nonequilibrium and equilibrium MD simulation methods. SRF stands for solvation response function. In the notation used here neq is the nonequilibrium response S(t), ground is the equilibrium TCF C0(t) and excited is the equilibrium TCF C, (f). (Reprinted from F. Ingrosso, B. M. Ladanyi, B. Mennucci, M. D. Elola, and J. Tomasi, I. Phys. Chem. B, 109, 3553-3564. Copyright (2005), with permission from American Chemical Society).

Solvation dynamics are measured using the more reliable energy relaxation method after a local perturbation [83-85], typically using a femtosecond-resolved fluorescence technique. Experimentally, the wavelength-resolved transients are obtained using the fluorescence upconversion method [85], The observed fluorescence dynamics, decay at the blue side and rise at the red side (Fig. 3a), reflecting typical solvation processes. The molecular mechanism is schematically shown in Fig. 5. Typically, by following the standard procedures [35], we can construct the femtosecond-resolved emission spectra (FRES, Stokes shifts with time) and then the correlation function (solvent response curve) ... 

The solvation dynamics of bulk water have been well studied. Jarzeba et al. [33] obtained a correlation function with 160 fs (33%) and 1.2 ps (67%), and Jimemez et al. [34] reported an initial Gaussian-type component (frequency 38.5 ps-1 25 fs in time width, 48%) and two exponential decays of 126 fs (20%) and 880 fs (35%). Using Eq. (6), the correlation function we obtained for bulk water, as shown in Fig. 4, is best fitted by double exponential decays integrated with an initial Gaussian-type contribution through a stretched mode c t) = + c2e tlZl, where for a pure Gaussian-type decay, / = 2. The... 

In this section, we review our first examinations of tryptophan probing sensitivity and water dynamics in a series of important model systems from simple to complex, which range from a tripeptide [70], to a prototype membrane protein melittin [70], to a common drug transporter human serum albumin [71], and to lipid interface of a nanochannel [86]. At the end, we also give a special case that using indole moiety of tryptophan probes supramolecule crown ether solvation, and we observed solvent-induced supramolecule folding [87]. The obtained solvation dynamics in these systems are linked to properties or functions of these biological-relevant macromolecules. 

Figure 19 shows the typical fluorescence transients of TBE from more than 10 gated emission wavelengths from the blue to the red side. At the blue side of the emission maximum, all transients obtained from four Trp-probes in the cubic phase aqueous channels drastically slow down compared with that of tryptophan in bulk water. The transients show significant solvation dynamics that cover three orders of magnitude on time scales from sub-picosecond to a hundred picoseconds. These solvation dynamics can be represented by three distinct decay components The first component occurs in about one picosecond, the second decays in tens of picoseconds, and the third takes a hundred picoseconds. The constmcted hydration correlation functions are shown in Fig. 20a with anisotropy dynamics in Fig. 20b. Surprisingly, three similar time scales (0.56-1.431 ps, 9.2-15 ps, and 108-140 ps) are obtained for all four Trp-probes, but their relative amplitudes systematically change with the probe positions in the channel. Thus, for the four Trp-probes studied here, we observed a correlation between their local hydrophobicity and the relative contributions of the first and third components from Trp, melittin, TME to TBE, the first components have contributions of 40%, 35%, 26%, and 17%, and the third components vary from 32%, to 38%, 43%, and 53%, respectively. The...

Strikingly, the solvation dynamics for all mutants are nearly the same. All correlation functions can be best described by a double exponential decay with time constants of 0.67 ps with 68% of the total amplitude and 13.2 ps (32%) for D60, 0.47 ps (67%) and 12.7 (33%) for D60G, and 0.53 ps (69%) and 10.8 ps (31%) for D60N. Relative to SNase above, the solvation dynamics are fast, which reflects the neighboring hydrophobic environment. We also measured the anisotropy dynamics and, as shown in the inset of Fig. 33, the local structure is very rigid in the time window of 800 ps. This observation is consistent with the inflexible turn (-T30W31-) in the transition from the second /1-sheet and the second x-helix (Fig. 31). Thus, the three mutants, with a charged, polar, or hydrophobic reside around the probe (Fig. 34) but with the similar time scales of... 

A mode coupling theory is recently developed [135] which goes beyond the time-dependent density functional theory method. In this theory a projection operator formalism is used to derive an expression for the coupling vertex projecting the fluctuating transition frequency onto the subspace spanned by the product of the solvent self-density and solvent collective density modes. The theory has been applied to the case of nonpolar solvation dynamics of dense Lennard-Jones fluid. Also it has been extended to the case of solvation dynamics of the LJ fluid in the supercritical state [135],... 

There are also a number of theories taking into account dipolar solvation dynamics. These theories use the solvent s dielectric response function as the dynamical input and also include effects due to the molecular nature of the solvent. The most sophisticated of these theories, by Raineri et al. [136] and by Friedman [137], uses fully atomistic representations for both solute and solvent and recent comparisons have shown it to be capable of quantitatively reproducing both the static and dynamic aspects of solvation of C153 [110]. In these cases the theoretical nature of solvation dynamics is fully understood. However, it must be remembered that much of the success of these theories rests on using the dynamical content of the complicated function, dielectric response function, determined from experiment. Although there... 

A time-resolved fluorescence measurement collects the emission spectra at regular time intervals after the excitation, defined at t=0, from which one constructs the normalized solvation dynamics response function, S(t) = [hv(t)—hv(oo)]/[hv(0)— hv(oo)] [55], In our simulations, hundreds of uncorrelated equilibrium molecular configurations with the electron in its ground state were selected as initial configurations (t=0). From each of these initial configurations, the electronic state is adiabatically promoted to the first excited state, the system is then propagated in... 

The calculation of the lifetime is thus reduced to the problem of calculating (F(t)F(O)). This is a problem that has had a fairly long association with studies of solvation dynamics, where it usually appears in the context of efforts to model friction coefficients. A great deal of activity in this field has been directed at using the methods of density functional theory (83) to derive expressions for the correlation function that involve the thermodynamic parameters of the system (72,84), which themselves are often amenable to further analytical treatment or else may be determined experimentally or through simulations. In the treatment of vibrational relaxation... 

Wishart JF, LaU-Ramnarine SI, Raju R, Scumpia A, Bellevue S, Ragbir R, Engel R. (2005) Effects of functional group substitution on electron spectra and solvation dynamics in a family of ionic liquids. Radiat Phys Chem 72 99-104. 

While there is no unique criterion for choosing 4 E, the selection must lead to an accurate theory of solvation dynamics without invoking two-time many-point correlation functions. We have found that this goal can be achieved with a new theory for the nonequilibrium distribution function in which the renormalized solute-solvent interactions enter linearly. In this theory and are chosen such that the renormalized linear response theory accurately describes the essential solute-solvent static correlations that rule the equilibrium solvation both at t = 0 (when solvent is in equilibrium with the initial charge distribution of the solute) and at 1 = oc (when the solvent has reached equilibrium with the new solute charge distribution). ... 

A recent develtyiment in the theoty ftx- the dynamics structure factor of molecular liquids, which employs the interaction-site modd, is outlined. The theory is applied for a d cription of the solvation dynamics associated with a photo-excitation of a molecule in polar liquid. Preliminary results of the solvation time correlation functions for an atomic molecule in a variety of solvents are presented. 

Here, we ve a brief review of a method presented in the eailier pqier to descrihe the scdvatkm dynamics associated with the photo ocdtation of a imdecule in polar liquids, which can be probed by the time resolved Stokes shifts. The quantity which ndates the dynamics theory widi the experiment is the solvation timecorrdation function (STCF) defined by,... 

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