Volume 110, Issue 6, 08 February 1999
 CONDENSED PHASE DYNAMICS, STRUCTURE, AND THERMODYNAMICS: SPECTROSCOPY, REACTIONS, AND RELAXATION


Size dependence of transfer free energies: A hardspherechain based formalism
View Description Hide DescriptionThe main purpose of this paper is to present a theoretical scheme which describes the solvation and transfer free energies of small molecules and relate them to solvent contributions in the biomolecular processes. Several proposals, based originally on Flory–Huggins theory, have been made recently that there is a nonnegligible solute’s volumeproportional term in solvation free energy and the term should be subtracted to obtain solute/solvent contact free energy for biochemical applications. These proposals have resulted in the revision of the magnitude of the hydrophobic effect in biomolecules. The validity has been controversial, since the existence, physical origin, and magnitude of the volumeproportional term have been model dependent. In this paper, we cleared up this problem by using an accurate fusedhard sphere model and a perturbation scheme in which the compensation between the repulsive and attractive interactions has been clarified. The solvation free energy is shown to be dependent on the solute’s surface area and curvature: the volumeproportional term is shown to be negligibly small. This disproves the basic assumption of the previous theories whose purpose is to “correct” the magnitude of the solvation free energy by subtracting volumeproportional terms. The relationship of our theory to previous theories is also discussed.

Twocolor threepulse photon echoes as a probe of electronic coupling in molecular complexes
View Description Hide DescriptionA twocolor photon echo peak shift measurement to probe the electronic coupling strength in molecular complexes is proposed. Exciton transfer between the electronic eigenstates is neglected and the baths associated with each monomer are assumed to be independent of each other. Within this simplified model, we derive a useful relation which can be used to estimate the electronic coupling strength via a combination of a normal onecolor and the present twocolor peak shift measurements. A simulation based on the cumulant expansion technique illustrates the validity of our suggestion.

Computer simulation study of liquid with a new effective pair potential model
View Description Hide DescriptionA new effective pair potential model is proposed for computer simulations of liquid methylene fluoride and used in Monte Carlo simulations on the isothermalisobaric ensemble at two different temperatures. The new model is able to reproduce the thermodynamic (internal energy, density, heat capacity, vaporliquid equilibrium) and structural (neutron diffraction data) properties of liquid methylene fluoride with good accuracy. The structure of liquid methylene fluoride is analyzed in detail on the basis of the present simulation at 153 K. It is found that, unlike in liquid water, the preferential location of the nearest neighbors is in the direction of the face centers of the tetrahedron of the central molecule. However, the four nearest neighbors do not surround the central molecule in a highly tetrahedral arrangement: the obtained distribution of the tetrahedral angular order parameter is rather similar to that in liquidargon. Preferential headtotail type orientation is found for nearest neighbors, accompanied by a slight preference for antiparallel dipole–dipole arrangement. The orientational correlation of the molecules is found to be rather long ranged, extending over the first coordination shell. The observed preferential nearest neighbor arrangement is resulted from the competition of steric and electrostatic interactions. No evidence for type hydrogen bonding is found in liquid methylene fluoride.

Effects of molecular association on mutual diffusion: A study of hydrogen bonding in dilute solutions
View Description Hide DescriptionDiffusivities of pseudoplanar molecules at trace concentration in methanol have been measured at 298.2 K using Taylor’s dispersion method. The data of the polar and nonpolar aromatic solutes are compared, and the effects due to solute–solvent interactions on diffusion, together with the solvation numbers, are determined. In this study, the effects are combined with the recently developed solute hydrogenbond scales to unravel hydrogen bonding between solute and solvent. It is found that the degrees of association of the solutes with methanol decrease in the sequence aromatic compounds. Except for onitrophenol, which is capable of intramolecular hydrogen bonding, all aromatic acids, phenols, and amines studied behave more as hydrogenbond donor than acceptor in methanol. The present work also indicates that motions of associated molecules can be understood in terms of the molecular behavior of nonassociated solutes and the hydrogenbond acidity/basicity of polar solutes.

A theory for selfdiffusion in liquids
View Description Hide DescriptionWe propose an alternative approach to selfdiffusion in an atomic liquid. Our starting point is an oscillatory motion of a tagged particle in its first solvation shell (cage). Only after cage relaxation is taken into account is the tagged particle able to diffuse. This approach is suitable for describing liquids where the concept of binary collisions breaks down and the selfdiffusion coefficient is small. Our predictions quantitatively agree with the results of MD simulations in a broad range of densities and temperatures up to the freezing transition.

Negative vibrational shift of nitrogen diluted in xenon at the fluid–solid transition
View Description Hide DescriptionIt is known from experimental evidence that the Raman shift of nitrogen and nitrogen in argon, measured as a function of the pressure at ambient temperature, reveals a positive jump at the transition from the liquid to the solid phase. Intuitively, this increase is sometimes attributed to the increase of density, but recently it has been shown that the change in order at the transition also plays a role. The present study deals with the behavior of nitrogen diluted in xenon. In this system, even a negative jump is found experimentally. Computer simulations on a model system for the mixture make clear that in this case the effect of the change in order is opposite.

Dielectric relaxation of water and heavy water in the whole fluid phase
View Description Hide DescriptionRecently we developed a new microwave spectroscopy technique in the frequency range up to 40 GHz, and measured the static dielectric constant and the dielectric relaxation time for supercritical water. In the present work we report the dielectric properties of heavy water at temperatures and pressures up to 770 K and 59 MPa, respectively. The static dielectric constant of as well as are well described by the Uematsu–Franck formula when the number density instead of the mass density is used as the input parameter. The dielectric relaxation time decreases rapidly with increasing temperature in liquid and and jumps to a large value at the liquid–gas transition. The relaxation time of is longer than that of in the liquid state, and the difference becomes smaller with decreasing density in the gaseous state. For both and the most relevant parameter determining the relaxation time is the temperature at high densities or at low temperatures, and it is the density at low densities or at high temperatures. Based upon the observation that the dielectric relaxation time becomes fairly long in the dilute limit, we have concluded that the dielectric relaxation in the gaseous state is governed by the binary collision of water molecules and explained the relaxation time quantitatively by the collision time. We have extended the interpretation of the dielectric relaxation to the liquid state by taking into account the contribution of bound water molecules that are incorporated in the hydrogenbond network. Anomalous relaxation at low temperatures is also discussed.

Selfdiffusion in and With notes on the dynamic isotope effect in liquids
View Description Hide DescriptionSelfdiffusion coefficients D of and were measured with the NMRPGSEtechnique over a wide range of temperature and pressure (10–200 MPa, 150–450 K for 10–200 MPa, 200–450 K for When compared to the protonated species, both substances show a dynamic isotope effect that was found to rise to 1.3 and 1.4 at the lowest temperatures studied. This behavior is similar to a number of other simple liquids (HF, Classical theories for single particle motion in liquids suggest a dependence of on the square root of the inverse mass ratio, or the square root of the inverse ratio of the moments of inertia, if translationrotation coupling is dominant. should, however, be temperatureindependent. The strong temperaturedependence of and its high value at low temperatures found in many liquids can thus not be explained by single particle properties, but rather has to be viewed as a collective phenomenon. It was suggested earlier that the stronger hydrogen bonds expected in the deuterated liquids are responsible for this behavior. However, the fact that methane shows a similar dynamic isotope effect is an indication that more complex mechanisms are responsible for the deviations from classical models of liquid dynamics. Quantum mechanical calculations suggest that backscatteringeffects may describe this interesting phenomenon.

Vaporliquid equilibria of squarewell spheres
View Description Hide DescriptionResults of molecular dynamics (MD) simulations on squarewell fluids with λ=1.25, 1.375, 1.5, 1.75, and 2.0 are presented. The calculation of vaporliquid equilibrium was performed by isochoric integration of the liquid data to obtain the free energy of the liquid and equating this to the vapor free energy from a modified virial equation. The saturation pressure was investigated and compared with that from Monte Carlo simulation and secondorder analytical perturbation theory. The vapor pressures from the isochoric integration technique are shown to be smoother than previous results, permitting accurate estimation of the effect of the squarewell width on acentric factor. With the saturated properties from molecular dynamics, the f value used in Kofke’s GibbsDuhem integration was calculated and was found to be nearly constant. The related integration of the Clapeyron equation was implemented as a check on thermodynamic consistency. Vapor pressures presented here are consistent to within 2%.

Validation of molecular simulation by comparison with experiment: Rotational reorientation of tryptophan in water
View Description Hide DescriptionMolecular dynamics simulations aimed at analysis of the rotational reorientation of tryptophan and 3methylindole in water have been performed. The dependence of the rotational relaxation time of tryptophan on several simulation and model parameters has been evaluated. The considerable sensitivity found for particular parameters illustrates the necessity of a detailed analysis before jumping to conclusions regarding the validity of a molecular model and force field based on comparing simulation with experimental data. The best agreement with experimental data is obtained when using the extended simplepointcharge (SPC/E) model for water together with a reactionfield correction for the longrange electrostatic interactions.

Kinetic transitions in diffusionreaction space. II. Geometrical effects
View Description Hide DescriptionWe extend the stochastic master equation approach described earlier [J. J. Kozak and R. Davidson, J. Chem. Phys. 101, 6101 (1994)] to examine the influence on reaction efficiency of multipolar correlations between a fixed target molecule and a diffusing coreactant, the latter constrained to move on the surface of a host medium (e.g., a colloidal catalyst or molecular organizate) modeled as a Cartesian shell [Euler characteristic,]. Our most comprehensive results are for processes involving ion pairs, and we find that there exists a transition between two qualitatively different types of behavior in diffusionreaction space, viz., a regime where the coreactant’s motion is totally correlated with respect to the target ion, and a regime where the coreactant’s motion is effectively uncorrelated. This behavior emerges both in the situation where correlations between the ion pair are strictly confined to the surface of the host medium or where correlations can be propagated through the host medium. The effects of system size are also examined and comparisons with diffusionreaction processes taking place on surfaces characterized by Euler characteristic are made. In all cases studied, the most dramatic effects on the reaction efficiency are uncovered in the regime where the Onsager (thermalization) length is comparable to the mean displacement of the coreactant, a conclusion consistent with results reported in earlier work.

Chemical potential of model benzene fluids using expanded ensemble Monte Carlo simulations
View Description Hide DescriptionChemical potential for model benzene fluid at liquid densities is calculated using the expanded ensemble method, modified to permit continuous sampling in λspace. The density is varied from to Three different temperatures (T=300 K, 400 K, and 600 K) are considered to provide data below and above the critical temperature Two different potential models, the EvansWatts model and the Claessens’ model, are considered, both of which are rigid hexagonal models with six sites interacting by a LennardJones potential. Despite its simplicity, we found that the results obtained using Claessens’ model are in very good agreement with experimental data.

Structure of concentrated aqueous NaCl solution: A Monte Carlo study
View Description Hide DescriptionThe structure of aqueous NaCl 1 M solution was studied by Monte Carlo simulation data obtained with 2117 rigid water molecules and at 293 K. The structural features were determined from the usual radial distribution functions, angularradial distribution functions,angular correlations and the mean force potential. The ion hydration structure was obtained as such as the structure of ions associations. The first hydration shell structure is almost not affected by the finite concentration. The second shell is concentration dependent mainly with respect to the tilt angle. The cation hydration is less affected than the anion hydrated shell. Anion–cation, anion–anion and cation–cation pairs were detected. A fraction 0.46 of the cations and 0.32 of the anions are associated in pairs formed by two ions sharing, at least, two water molecules in their solvation shells. The idealized structures of all pairs include two to four water molecules located in such a way that the attractive energies are increased and the repulsive ones decreased. The structure of 1 M NaCl is also determined by recovering the water tetrahedral structure around the solute ions and by the stabilizing influence of water molecules that are shared by the ions. The last conclusion is that about 20% of the water molecules lose some degree of freedom because they solvate directly the solute. Almost all the water molecules are involved to some degree in the ion solvation.

Closedloop critical curves in simple hardsphere van der Waalsfluid models consistent with the packing fraction limit
View Description Hide DescriptionTwo new hardsphere equations are proposed which, in combination with a van der Waals attraction term, lead to a biquadratic, respectively a cubic, equation of state. The new equations show the correct limiting behavior at low as well as at high densities; their poles are close to the physical packing fraction of hard spheres. Both equations of state were extended towards mixtures by onefluid mixing rules, and their global phase behavior was investigated for the special case of equalsized molecules. Both equations are able to predict closedloop liquid–liquid immiscibility; the topology of the phenomenenon is the same as for the Carnahan–Starling equation. It appears the occurrence of closedloop liquid–liquid immiscibility does not depend on the location of the pole nor on the degree of the equation of state used.

The liquid–liquid phase transition in ionic solutions: Coexistence curves of tetranbutylammonium pricrate in alkyl alcohols
View Description Hide DescriptionWe report coexistence curves of the liquid–liquidphase transition in ionic solutions. The phase diagrams of tetranbutylammonium pricrate solutions in a series of alkanols (2propanol, 1decanol, 1dodecanol, 1tridecanol and 1tetradecanol) are determined either by measuring the refractive index in the two phase region in one sample of nearcritical composition as a function of the temperature, or by direct observation of the composition dependent phase separation temperatures. With the exception of the 2propanol system, the critical points are in accordance with the predictions by the restricted primitive model. The coexistence curves are analyzed in terms of different composition variables, of which the volume fraction seems to be the most appropriate one. For the volume fraction, deviations from asymptotic Ising behavior are observed which are equally well described by a critical exponent slightly different from the Ising value or by Wegner corrections. Although the deviations are quite small, they show a systematic increase with decreasing dielectric constant of the solvent, thus suggesting an approach to the meanfield case. The significance of this finding is, however, weakened by the fact that the corrections to scaling are also affected by the choice of the composition variable. For all investigated systems, the diameter of the coexistence curve shows a pronounced nonanalytic temperature dependence.

A density matrix description of overtone nuclear magnetic resonance in static and spinning solids
View Description Hide DescriptionOvertone NMR is an experiment introduced by LeGros, Bloom, Tycko, and Opella, capable of providing powder spectra devoid of firstorder quadrupole broadenings by irradiation and observation of the nuclear spins at twice their Larmor frequency. This technique constitutes one of the most promising alternatives for the acquisition of high resolution solid NMR spectra from random powders, particularly if it can be combined with strategies capable of removing the substantial secondorder quadrupole broadenings remaining in the overtone line shapes. In order to facilitate the search for these averaging manipulations, we present here a theoretical description of the overtone experiment based on the timedomain propagation of density matrices. It is shown that by combining perturbation methods with appropriate rotatingframe transformations and diagonalizations, overtone spin1 phenomena can be described using a single set of fictitious spin1/2 operators. By contrast to conventional spin1/2 irradiation and detection processes, however, overtone manipulations involve an unusual angular dependence on the azimuthal angle defining rotations about the main Zeemanmagnetic field. This behavior introduces unexpected complications toward the narrowing of overtone resonances by conventional sample spinning techniques. Nevertheless, it can still be shown that the removal of all spin1 anisotropies by certain forms of dynamicangle spinning overtone NMR remains feasible.
