Solute-structure dependence of solvation dynamics studied by reference interaction-site model theory

Solvation dynamics on the diffusion timescale elucidated using energy-represented dynamics theory

Photoexcitation of a solute alters the solute-solvent interaction, resulting in the nonequilibrium relaxation of the solvation structure, often called a dynamic Stokes shift or solvation dynamics. Thanks to the local nature of the solute-solvent interaction, the characteristics of the local solvent environment dissolving the solute can be captured by the observation of this process. Recently, we derived the energy-represented Smoluchowski-Vlasov (ERSV) equation, a diffusion equation for molecular liquids, which can be used to analyze the solvation dynamics on the diffusion timescale. This equation expresses the time development for the solvent distribution on the solute-solvent pair interaction energy (energy coordinate). Since the energy coordinate can effectively treat the solvent flexibility in addition to the position and orientation, the ERSV equation can be utilized in various solvent systems. Here, we apply the ERSV equation to the solvation dynamics of 6-propionyl-2-dimethylamino naphthalene (Prodan) in water and different alcohol solvents (methanol, ethanol, and 1-propanol) for clarifying the differences of the relaxation processes among these solvents. Prodan is a solvent-sensitive fluorescent probe and is thus widely utilized for investigating heterogeneous environments. On the long timescale, the ERSV equation satisfactorily reproduces the relaxation time correlation functions obtained from the molecular dynamics (MD) simulations for these solvents. We reveal that the relaxation time coefficient on the diffusion timescale linearly correlates with the inverse of the translational diffusion coefficients for the alcohol solvents because of the Prodan-solvent energy distributions among the alcohols. In the case of water, the time coefficient deviates from the linear relationship for the alcohols due to the difference in the extent of importance of the collective motion between the water and alcohol solvents.

Diffusion theory of molecular liquids in the energy representation and application to solvation dynamics

The generalized Langevin equation (GLE) formalism is a useful theoretical fundament for analyzing dynamical phenomena rigorously. Despite the systematic formulation of dynamics theories with practical approximations, however, the applicability of GLE-based methods is still limited to simple polyatomic liquids due to the approximate treatment of molecular orientations involved in the static molecular liquid theory. Here, we propose an exact framework of dynamics based on the GLE formalism incorporating the energy representation theory of solution, an alternative static molecular liquid theory. A fundamental idea is the projection of the relative positions and orientations of solvents around a solute onto the solute-solvent interaction, namely the energy coordinate, enabling us to describe the dynamics on a one-dimensional coordinate. Introducing systematic approximations, such as the overdamped limit, leads to the molecular diffusion equation in the energy representation that is described in terms of the distribution function of solvents on the energy coordinate and the diffusion coefficients. The present theory is applied to the solvation dynamics triggered by the photoexcitation of benzonitrile. The long-time behavior of the solvation time correlation function is in good agreement with that obtained by the molecular dynamics simulation.

Solvation dynamics in electronically polarizable solvents: Theoretical treatment using solvent-polarizable three-dimensional reference interaction-site model theory combined with time-dependent density functional theory

The theory of solvation structure in an electronically polarizable solvent recently proposed by us, referred to as the "solvent-polarizable three-dimensional reference interaction-site model theory," is extended to dynamics in this study through the combination with time-dependent density functional theory. Test calculations are performed on model charge-transfer systems in water, and the effects of electronic polarizability on solvation dynamics are examined. The electronic polarizability slightly retards the solvation dynamics. This is ascribed to the decrease in the curvature of the nonequilibrium free energy profile along the solvation coordinate. The solvent relaxation is bimodal, and the faster and the slower modes are assigned to the reorientational and the translational modes, respectively, as was already reported by the surrogate theory combined with the site-site Smoluchowski-Vlasov equation. The relaxation path along the solvation coordinate is a little higher than the minimum free energy path because the translational mode is fixed in the time scale of the reorientational relaxation.

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.

First observation of ultrafast intramolecular proton transfer rate between electronic ground states in solution

Despite the importance of ultrafast (time scale exceeding 10(-11) s) intramolecular proton transfer (PT) events between electronic ground states in solution, experimental determination of the rates of such reactions has not yet been accomplished because of the limitations of the utilized methods. The objective of this study was to evaluate the PT rates of intramolecular O···H···O hydrogen-bonded systems in solution through the (1)H spin-lattice relaxation times of the hydroxyl protons, induced by the (1)H-(17)O dipolar interactions (T(1dd)(OH)), taking into account the contribution of the OH reorientational motion to T(1dd)(OH). Solutions of the benzoic acid dimer (BA dimer), 1-benzoyl-6-hydroxy-6-phenylfulvene (Fulvene), and dibenzoylmethane (DBM) were chosen as test systems. For Fulvene in CCl(4), the PT time, τ(PT), was deduced to be 7 × 10(-11) s. In the case of the BA dimer in CCl(4), the τ(PT) value was considerably greater than the OH reorientational correlation time, τ(R(OH)) = 4.3 × 10(-11) s. In contrast, the experimental results for DBM in CCl(4) indicated that the proton is located about midway between the two oxygen atoms, that is, the PT potential energy surface is a single well or a double well with a PT barrier near or below the zero-point energy.

Site-site memory equation approach in study of density/pressure dependence of translational diffusion coefficient and rotational relaxation time of polar molecular solutions: acetonitrile in water, methanol in water, and methanol in acetonitrile

We present results of the theoretical study and numerical calculation of the dynamics of molecular liquids based on the combination of the memory equation formalism and the reference interaction site model (RISM). Memory equations for the site-site intermediate scattering functions are studied in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors are deduced from RISM. The results include the temperature-density (pressure) dependence of translational diffusion coefficients D and orientational relaxation times tau for acetonitrile in water, methanol in water, and methanol in acetonitrile--all in the limit of infinite dilution. Calculations are performed over the range of temperatures and densities employing the extended simple point charge model for water and optimized site-site potentials for acetonitrile and methanol. The theory is able to reproduce qualitatively all main features of temperature and density dependences of D and tau observed in real and computer experiments. In particular, anomalous behavior, i.e, the increase in mobility with density, is observed for D and tau of methanol in water, while acetonitrile in water and methanol in acetonitrile do not show deviations from the ordinary behavior. The variety exhibited by the different solute-solvent systems in the density dependence of the mobility is interpreted in terms of the two competing origins of friction, which interplay with each other as density increases: the collisional and dielectric frictions which, respectively, increase and decrease with increasing density.

Solvent Effect on Intramolecular Electron Transfer Rates of Mixed-Valence Biferrocene Monocation Derivatives

Intramolecular electron transfer (ET) rates in various solvents of mixed-valence biferrocene monocation (Fe(II), Fe(III)) and the 1',1' ''-diiodo and 1',1' ''-diethyl derivatives (respectively abbreviated as BFC(+), I(2)BFC(+), and Et(2)BFC(+)) were determined by means of the spin-lattice relaxation times of the protons, taking into account the local magnetic field fluctuation caused by the electron hopping between the two ferrocene units. We also determined the ET rates of a mixed-valence diferrocenylacetylene monocation (DFA(+)) in order to examine the effect of the insertion of an acetylene bridge between the two ferrocene units. The insertion of the bridge decreased the ET rate, while the effect of substitution on the cyclopentadienyl rings on the rate was minor. The observed rates for each mixed-valence monocation in various solvents did not correlate with the reorganization energies, but we did find a significant contribution of the solvent dynamics. The observed rates were considerably higher than those expected on the basis of the Sumi-Marcus-Nalder model in which the solvents were regarded as dielectric continua. The slope of the logarithm plot of the pre-exponential factors in various solvents for each mixed-valence monocation versus the inverse of the longitudinal dielectric relaxation times of the solvents was significantly smaller than unity, and the slope for DFA(+) was larger than those for BFC(+), I(2)BFC(+), and Et(2)BFC(+). These results were ascribed to a partial contribution of the dielectric friction to the dynamics along the solvent coordinate; the extent of the contribution decreased with a reduction in the ET distance. For the dynamics along the solvent coordinate of the ET reactions in methanol, the observed rates indicated an important contribution by the minor dielectric relaxation components with faster relaxation times, rather than the major component with an extraordinarily long relaxation time.

Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.

Molecular multivalent electrolytes: microstructure and screening lengths

We study small rod-like molecular electrolytes solutions with their corresponding atomic counterions. The asymptotic length scales (decay length and wavelength) of the structural correlations are analyzed using the formalism of the dressed interaction site theory (DIST). The correlation functions are determined using the reference interaction site model equation complemented with a mixed approach in which the hypernetted-chain closure is used for the repulsive interactions, and the mean spherical approximation is used for the attractive interactions. The results from this scheme are in good agreement with the Monte Carlo computer simulations reported here. The asymptotic properties of the correlation functions of this molecular system are compared against those corresponding to two related simple (atomic) electrolyte models. The main conclusion is that the molecular structure of the ions lowers by two orders of magnitude the concentration at which the transition from monotonic to oscillatory decay occurs.

Molecular dynamics simulation study on the transient response of solvation structure during the translational diffusion of solute

The transient response function of the density profile of the solvent around a solute during the translational diffusion of the solute is formulated based on the generalized Langevin formalism. The resultant theory is applied to both neat Lennard-Jones fluids and cations in liquid water, and the response functions are obtained from the analysis of the molecular dynamics simulations. In the case of the self-diffusion of Lennard-Jones fluids, the responses of the solvation structures are in harmony with conventional pictures based on the mode-coupling theory, that is, the binary collision in the low-density fluids, the backflow effect from medium to high density fluids, and the backscatter effect in the liquids near the triple point. In the case of cations in water, the qualitative behavior is strongly dependent on the size of cations. The pictures similar to simple dense liquids are obtained for the large ion and the neutral molecule, while the solvent waters within the first solvation shell of small ions show an oscillatory response in the short-time region. In particular, the oscillation is remarkably underdumped for lithium ion. The origin of the oscillation is discussed in relation to the theoretical treatment of the translational diffusion of ions in water.