On the microscopic theory of polar solvation dynamics

A microscopic model of the time-resolved Stokes shift is developed. The model calculates the solvation dynamics by combining the atomic resolution of the solute structure with dipolar dynamics from the polarization structure factors of the homogeneous solvent. Calculations are made for coumarin 153 and quinoxaline optical dyes with atomic geometries and charge distributions taken from quantum calculations. Stokes shift dynamics is calculated and compared to experiment in high-temperature acetonitrile and methanol and in low-temperature 2-methyl-tetrahydrofurane using dielectric relaxation data from experiment.     

Solute rotation and solvation dynamics in an alcohol-functionalized room temperature ionic liquid

Steady-state and time-resolved fluorescence behaviors of two dipolar solutes, coumarin 153 and 4-aminophthalimide, have been studied in an alcohol-functionalized room-temperature ionic liquid, 1-(hydroxyethyl)-3-methylimidazolium bis(trifluoromethanesulfonyl)imide. The steady-state fluorescence parameters have been exploited for the estimation of the polarity of this ionic liquid and to obtain information on the hydrogen bonding interaction between the ionic liquid and the probe molecules. The time-resolved measurements have been focused on the dynamics of solvation by studying the dynamic Stokes shift in the ps-ns time scale and solute rotation by measuring the time dependence of the fluorescence anisotropy. The time-resolved anisotropy studies reveal a significant slow down of the rotational motion of one of the probe molecules. The time-dependent fluorescence Stokes shift measurements suggest that the time-resolvable part of the dynamics is biphasic in nature, highly dependent on the probe molecule and the ultrafast component is comparatively less than that in other ionic liquids. The influence of the hydrogen bonding interaction between the probe molecules and the ionic liquids on the solute rotation and the various components of the solvation dynamics is carefully analyzed in an attempt to obtain further insight into the mechanism of solvation in these novel media.     

Dynamics of a supercooled ionic liquid studied by optical and dielectric spectroscopy

We have measured the dynamics of solvation of a triplet state probe, quinoxaline, in the glass-forming ionic liquid dibutylammonium formate near its glass transition temperature Tg=153 K. The Stokes-shift correlation function displays a relaxation time dispersion of considerable magnitude and the optical line width changes systematically along the solvation coordinate. The solvent dynamics in the viscous regime is compared with the rotational behavior of the solute and with the dielectric relaxation of the ionic liquid. Among the different quantities derived from the dielectric experiments, the relaxation of the macroscopic electric field, i.e., the modulus Mt, matches best the solvent response Ct regarding time scale and stretching exponent. Many other properties are reminiscent of the behavior of polar molecular liquids which lack the ionic character.     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

Excited state proton transfer and solvent relaxation of a 3-hydroxyflavone probe in lipid bilayers

The photophysics of a ratiometric fluorescent probe, N-[[4'- N, N-diethylamino-3-hydroxy-6-flavonyl]methyl]- N-methyl- N-(3-sulfopropyl)-1-dodecanaminium, inner salt (F2N12S), incorporated into phospholipid unilamellar vesicles is presented. The reconstructed time-resolved emission spectra (TRES) unravels a unique feature in the photophysics of this probe. TRES exhibit signatures of both an excited-state intramolecular proton transfer (ESIPT) and a dynamic Stokes shift associated with solvent relaxation in the lipid bilayer. The ESIPT is fast, being characterized by a risetime of approximately 30-40 ps that provides an equilibrium to be established between the excited normal (N*) and the ESIPT tautomer (T*) on a time scale of 100 ps. On the other hand, the solvent relaxation displays a bimodal decay kinetics with an average relaxation time of approximately 1 ns. The observed slow solvent relaxation dynamics likely embodies a response of nonspecific dipolar solvation coupled with formation of probe-water H-bonds as well as the relocation of the fluorophore in the lipid bilayer. Taking into account that ESIPT and solvent relaxation are governed by different physicochemical properties of the probe microenvironment, the present study provides a physical background for the multiparametric sensing of lipid bilayers using ESIPT based probes.     

Solvation in supercritical water

Solvation in supercritical water under equilibrium and nonequilibrium conditions is studied via molecular dynamics simulations. The influence of solute charge distributions and solvent density on the solvation structures and dynamics is examined with a diatomic probe solute molecule. It is found that the solvation structure varies dramatically with the solute dipole moment, especially in low-density water, in accord with many previous studies on ion solvation. This electrostrictive effect has important consequences for solvation dynamics. In the case of a nonequilibrium solvent relaxation, if there are sufficiently many water molecules close to the solute at the outset of the relaxation, the solvent response measured as a dynamic Stokes shift is almost completely governed by inertial rotations of these water molecules. By contrast, in the opposite case of a low local solvent density near the solute, not only rotations but also translations of water molecules play an important role in solvent relaxation dynamics. The applicability of a linear response is found to be significantly restricted at low water densities.     

Solvation dynamics in protein environments: comparison of fluorescence upconversion measurements of coumarin 153 in monomeric hemeproteins with molecular dynamics simulations

The complexes of the fluorescence probe coumarin 153 with apomyoglobin and apoleghemoglobin are used as model systems to study solvation dynamics in proteins. Time-resolved Stokes shift experiments are compared with molecular dynamics simulations, and very good agreement is obtained. The solvation of the coumarin probe is very rapid with approximately 60% occurring within 300 fs and is attributed to interactions with water (or possibly to the protein itself). Differences in the solvation relaxation (or correlation) function C(t) for the two proteins are attributed to differences in their hemepockets.     

Sub-picosecond fluorescence evolution of amino-cyano-stilbenes in methanol: polar solvation obeys continuum theory without evidence of twisting

The spectral evolution of fluorescence from 4-(dimethylamino)-4'-cyanostilbene (DCS) in methanol, and of two derivatives bearing either the anilino (ACS) or the julolidino (JCS) moiety, was measured by optical Kerr-gating with a time resolution of 0.35 ps. A special thin Glan polariser in the Kerr shutter allows high contrast without unnecessarily increasing the group delay dispersion. The emission band may thus be gated and observed even with highly fluorescent samples. The spectral dynamics consists of a continuous red-shift and narrowing with similar relaxation behavior throughout, i.e. between these two observables and the three compounds. This suggests that polar solvation is the common cause for spectral relaxation after 0.2 ps. The continuum model describes the dynamic Stokes shift quantitatively. Contrary to previous reports we do not find a temporary isosbestic point in the fluorescence of JCS, nor is there evidence for a dependence on anilino substituents. The crystal structures of DCS and JCS are provided.     

Measurement of solvation responses at multiple sites in a globular protein

Proteins respond to electrostatic perturbations through complex reorganizations of their charged and polar groups, as well as those of the surrounding media. These solvation responses occur both in the protein interior and on its surface, though the exact mechanisms of solvation are not well understood, in part because of limited data on the solvation responses for any given protein. Here, we characterize the solvation kinetics at sites throughout the sequence of a small globular protein, the B1 domain of streptococcal protein G (GB1), using the synthetic fluorescent amino acid Aladan. Aladan was incorporated into seven different GB1 sites, and the time-dependent Stokes shift was measured over the femtosecond to nanosecond time scales by fluorescence upconversion and time-correlated single photon counting. The seven sites range from buried within the protein core to fully solvent-exposed on the protein surface, and are located on different protein secondary structures including beta-sheets, helices, and loops. The dynamics in the protein sites were compared against the free fluorophore in buffer. All protein sites exhibited an initial, ultrafast Stokes shift on the subpicosecond time scale similar to that observed for the free fluorophore, but smaller in magnitude. As the probe is moved from the surface to more buried sites, the dynamics of the solvation response become slower, while no clear correlation between dynamics and secondary structure is observed. We suggest that restricted movements of the surrounding protein residues give rise to the observed long time dynamics and that such movements comprise a large portion of the protein's solvation response. The proper treatment of dynamic Stokes shift data when the time scale for solvation is comparable to the fluorescence lifetime is discussed.     

Measurements of the complete solvation response in ionic liquids

Dynamic Stokes shift measurements of the solvatochromic probe trans-4-dimethylamino-4'-cyanostilbene were used to measure the solvation response of five imidazolium and one pyrrolidinium ionic liquid at 25 degrees C. The Kerr-gated emission and time-correlated single-photon-counting techniques were used to measure spectral dynamics occurring over the time ranges of 100 fs-200 ps and 50 ps-5 ns, respectively, and a combination of data sets from these two techniques enabled observation of the complete solvation response. Observed response functions were found to be biphasic, consisting of a sub-picosecond component of modest (10-20%) amplitude and a dominant slower component relaxing over times of a few picoseconds to several nanoseconds. The faster component could be correlated to inertial characteristics of the constituent ions, and the slower component to solvent viscosity. Dielectric continuum calculations of the sort previously used to predict solvation dynamics in dipolar liquids were shown to work poorly for predicting the response in these ionic liquids.     

Glassy protein dynamics and gigantic solvent reorganization energy of plastocyanin

We report the results of molecular dynamics simulations of electron-transfer activation parameters of plastocyanin metalloprotein involved as an electron carrier in natural photosynthesis. We have discovered that slow, non-ergodic conformational fluctuations of the protein, coupled to hydrating water, result in a very broad distribution of donor-acceptor energy gaps far exceeding those observed for commonly studied inorganic and organic donor-acceptor complexes. The Stokes shift is not affected by these fluctuations and can be calculated from solvation models in terms of the linear response of the solvent dipolar polarization. The non-ergodic character of large-amplitude protein/water mobility breaks the strong link between the Stokes shift and the reorganization energy characteristic of equilibrium (ergodic) theories of electron transfer. This mechanism might be responsible for fast electronic transitions in natural electron-transfer proteins characterized by low reaction free energy.     

Exponential probe rotation in glass-forming liquids

Using time resolved optical depolarization, we have studied the rotational behavior of molecular probes in supercooled liquids near the glass transition temperature T(g). Simultaneously, the dynamics of the liquid immediately surrounding these rigid probes is measured by triplet state solvation experiments. This direct comparison of solute and solvent dynamics is particularly suited for assessing the origin of exponential orientational correlation functions of probe molecules embedded in liquids which exhibit highly nonexponential structural relaxation. Polarization angle dependent Stokes shift correlation functions demonstrate that probe rotation time and solvent response time are locally correlated quantities in the case of smaller probe molecules. Varying the size of both guest and host molecules shows that the size ratio determines the rotational behavior of the probes. The results are indicative of time averaging being at the origin of exponential rotation of probes whose rotational time constant is slower than solvent relaxation by a factor of 20 or more.     

Dipolar solvation dynamics in room temperature ionic liquids: an effective medium calculation using dielectric relaxation data

Solvation dynamics in four imidazolium cation based room temperature ionic liquids (RTIL) have been calculated by using the recently measured dielectric relaxation data [ J. Phys. Chem. B 2008, 112, 4854 ] as an input in a molecular hydrodynamic theory developed earlier for studying solvation energy relaxation in polar solvents. Coumarin 153 (C153), 4-aminophthalimide (4-AP), and trans-4-dimethylamino-4'-cyanostilbene (DCS) have been used as probe molecules for this purpose. The medium response to a laser-excited probe molecule in an ionic liquid is approximated by that in an effective dipolar medium. The calculated decays of the solvent response function for these RTILs have been found to be biphasic and the decay time constants agree well with the available experimental and computer simulation results. Also, no probe dependence has been found for the average solvation times in these ionic liquids. In addition, dipolar solvation dynamics have been predicted for two other RTILs for which experimental results are not available yet. These predictions should be tested against experiments and/or simulation studies.     

Polar solvation dynamics in water and methanol: search for molecularity

Time-dependent Stokes shifts (TDSS) were measured for diverse polarity probes in water, heavy water, methanol, and benzonitrile, by broadband fluorescence up-conversion with 85 fs time resolution. In water the spectral dynamics is solute-independent and quantitatively described by simple dielectric continuum theory of solvation. In methanol the slower part of the TDSS is solute-dependent. A correlation with anisotropy decay suggests that methanol solvation dynamics is modulated by orientational solute diffusion. An empirical power law which links the solvation relaxation function of a mobile solute to that of an immobile solute is experimentally verified. Activation energies for the average relaxation rate are also given. Solvation dynamics in H(2)O and D(2)O are identical at and above 20 °C but diverge below.     

Characterization of the solvation dynamics of an ionic liquid via molecular dynamics simulation

The solvation dynamics of ionic liquids have been the subject of intense experimental study but remain poorly understood. We present the results of molecular dynamics simulations of the solvation dynamics of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate in response to photoexcitation of the fluorescent dye coumarin-153. We reproduce the time-resolved fluorescence Stokes shift using linear response theory, then use novel statistical techniques to analyze cation and anion contributions to the signal. We find that the solvation dynamics are dominated by collective ionic motion and characterize the time scale for various features of the collective response. Further, we use the Steele analysis [Mol. Phys. 61, 1031 (1987)] to characterize the contributions to the observed Stokes shift made by translational and rovibrational degrees of freedom. Our results indicate that in contrast to molecular liquids, the rovibrational response is trivial and the observed fluorescence response arises almost entirely from ionic translation. Our results resolve previously open questions in the literature about the nature of the rapid dynamics in room-temperature ionic liquids and offer insight into the physical principles governing ionic liquid behavior on longer time scales.     

Ionic and dipolar solvation dynamics in liquid water

The solvation time correlation function for solvation in liquid water was measured recently. The solvation was found to be very fast, with a time constant equal to 55 fs. In this article we present theoretical studies on solvation dynamics of ionic and dipolar solutes in liquid water, based on the molecular hydrodynamic approach developed earlier. The molecular hydrodynamic theory can successfully predict the ultrafast dynamics of solvation in liquid water as observed from recent experiments. The present study also reveals some interesting aspects of dipolar solvation dynamics, which differs significantly from that of ionic solvation. Dedicated to Prof. C N R Rao on his 60th birthday     

Multiple time scales in solvation dynamics of DNA in aqueous solution: the role of water, counterions, and cross-correlations

Recent time domain experiments have explored solvation dynamics of a probe located inside a DNA duplex, in an effort to gain information, e.g., on the dynamics of water molecules in the DNA major and minor grooves and their environment. Multiple time constants in the range of a few picoseconds to several nanoseconds were obtained. We have carried out 15 ns long atomistic molecular dynamics simulations to study the solvation dynamics of bases of a 38 base-pair long DNA duplex in an aqueous solution containing counterions. We have computed the energy-energy time correlation function (TCF) of the four individual bases (A, T, G, and C) to characterize the solvation dynamics. All the TCFs display highly nonexponential decay with time. When the trajectories are analyzed with 100 fs time resolution, the TCF of each base shows initial ultrafast decay (with tau1 approximately equal 60-80 fs) followed by two intermediate components (tau2 approximately equal 1 ps, tau3 approximately equal 20-30 ps), in near complete agreement with a recent time domain experiment on DNA solvation. Interestingly, the solvation dynamics of each of the four different nucleotide bases exhibit rather similar time scales. To explore the existence of slow relaxation at longer times reported recently in a series of experiments, we also analyzed the solvation TCFs calculated with longer time trajectories and with a larger time resolution of 1 ps. In this case, an additional slow component with a time constant of the order of 250 ps is observed. Through an analysis of partial solvation TCFs, we find that the slow decay originates mainly from the interaction of the nucleotides with the dipolar water molecules and the counterions. An interesting negative cross-correlation between water and counterions is observed, which makes an important contribution to relaxation at intermediate to longer times.     

Computer simulations of the solvation dynamics of Coumarin 153 in dimethylsulfoxide

We report molecular dynamics (MD) simulations of the solvation dynamics of Coumarin 153 in liquid dimethylsulfoxide using two distinct sets of partial charges for the coumarin probe. The excited state dipole moment of the coumarin and the dynamic Stokes shift in solution depend significantly on the type of charge distributions used. Nevertheless, the overall characteristics of the solvation responses obtained from both sets of charges are very similar and show good agreement with time-dependent Stokes shift experiments. Microscopic details of the solvent reorganization around the probe are discussed in light of the charge transfer upon photoexcitation.     

Femtosecond dynamics on excited-state proton/charge-transfer reaction in 4'-N,N-diethylamino-3-hydroxyflavone. The role of dipolar vectors in constructing a rational mechanism

The excitation behaviors for 4'-N,N-diethylamino-3-hydroxyflavone (Ia) have been investigated via femtosecond fluorescence upconversion approaches to gain detailed insights into the mechanism of the proton/charge-transfer coupling reaction. In polar solvents such as CH2Cl2 and CH3CN, in addition to a slow, solvent-polarity-dependent rate (a few tens of picoseconds(-1)) of excited-state intramolecular proton transfer (ESIPT) reported previously, early femtosecond relaxation dynamics clearly reveal that the proton-transfer tautomer emission consists of a rise component of a few hundred femtoseconds. The temporal spectral evolution at the time domain of zero to a few hundred femtoseconds further resolves two distinct emission bands consisting of a proton-transfer tautomer emission and a time-dependent Stokes shifted emission. The results, in combination with ab initio calculations on the dipolar vectors for normal and tautomer species, lead us to unveil the importance of the relationship of the dipolar vectors among various states, and hence the corresponding solvation energetics in the overall ESIPT reaction. We conclude a similar dipolar character between ground-state normal (N) and excited proton-transfer tautomer (T*) species, whereas due to the excited-state intramolecular charge transfer (ESICT), the normal excited state (N*) possesses a large dipolar change with respect to N and T*. ESIPT is thus energetically favorable at the Franck-Condon excited N*, and its rate is competitive with respect to the solvation relaxation process. After reaching the solvent equilibration, there exists an equilibrium between N* and T* states in, for example, CH3CN. Due to the greatly different equilibrium polarization between N* and T*, both forward and reversed ESIPT dynamics are associated with a solvent-induced barrier. The latter viewpoint of the equilibrium type of ESIPT in Ia is in agreement with the previous reports based on steady-state, picosecond, and femtosecond dynamic approaches.