Luís E. S. de Souza

Optimized perturbed hard sphere expressions for the structure and thermodynamics of Lennard-Jones fluids

First-order perturbed hard sphere fluid expressions are fitted to Lennard-Jones fluid compressibility factor, Z, and internal energy, U, data taking the two Lennard-Jones constants as adjustable parameters. The results are used to distinguish the utility of alternative perturbative algorithms over a wide density and temperature range. First-order Barker-Henderson perturbative expressions are found to systematically underestimate temperature dependent changes in thermodynamic properties while the Weeks-Chandler-Andersen model is found to reasonably reproduce simulation results throughout the liquid and supercritical fluid domain, with only a few per cent adjustment of the effective Lennard-Jones parameters. Closed analytical expressions for the Barker-Henderson and Weeks-Chandler-Andersen hard sphere diameters as well as a hard fluid reference system radial distribution function model are presented. These are shown to accurately reproduce hard sphere diameters and thermodynamic properties of Lennard-Jones ...

Hard fluid model for molecular solvation free energies

The hard fluid model, which approximates packing forces in molecular liquids using hard sphere reference fluids, is applied to the prediction of excess solvation free energies of hard spheres and cavity size distributions in water,carbon tetrachloride, chloroform, n‐hexane, n‐dodecane, and n‐undecyl alcohol. These are found to compare favorably with computer simulation measurements in these liquids, as well as experimental solubilities of rare gases in water,n‐hexane, and n‐dodecane (extrapolated to zero solutepolarizability). The results are used to determine repulsive contributions to solvation free energies of atomic and molecular solutes in water and n‐hexane. Attractive solvation free energies, determined from the difference between experimental and repulsive contributions, are found to correlate with solutepolarizability, and are compared with dispersion energy estimates. The success of the hard fluid model in describing aqueous solvation suggests that the small size of water molecules, rather than their unique hydrogen bonding structure, plays an important role in hydrophobic hydration.

CHEMICAL POTENTIALS OF HARD SPHERE SOLUTES IN HARD SPHERE SOLVENTS. MONTE CARLO SIMULATIONS AND ANALYTICAL APPROXIMATIONS

We report Monte Carlo simulation results for the excess chemical potentials of infinitely dilute hard spheres, and the distribution of cavity sizes, in a hard sphere fluid. The results are compared with previous simulations and analytical expressions derived from the Boublik–Mansoori–Carnahan–Starling–Leland equation of state and scaled particle theory.

Solvent mean force perturbations of diatomic dissociation reactions. Comparison of perturbed hard fluid and computer simulation results

The perturbed hard fluid model, which separates solute–solvent interactions into repulsive hard sphere and mean field attractive contributions, is applied to predict solvent effects on the thermodynamics of diatomic dissociation reactions. Theoretically predicted changes in excess Gibbs free energy (ΔG), entropy (ΔS), enthalpy (ΔH), and volume (ΔV) for the dissociation of a homonuclear diatomic dissolved in a monatomic solvent, with Lennard‐Jones solute atom–solvent atom and solvent–solvent interaction potentials, are compared with computer simulation results. The perturbed hard fluid model requires only one adjustable parameter, which is determined using simulation results at a single temperature and density. This parameter is used in the prediction of reaction thermodynamics over the entire vapor, liquid, and supercritical fluid regime. Furthermore, the thermodynamics of other reactions, in which the solute atom–solvent atom attractive well depth changes upon dissociation, can be predicted by including ...

Statistical mechanics of solvent induced forces and vibrational frequency shifts. Low density expansions and Monte Carlo simulations

Theoretical expressions are presented for the solvent configuration averaged force on a diatomic solute throughout the vapor–liquid density range. Analytical low density expansions and solvent configurational space averages are used to predict solvent induced changes in solute vibrational frequency. Purely classical Monte Carlo simulation results for a system representing bromine (Br2) dissolved in argon agree quantitatively with previous coupled quantum‐classical results of Herman and Berne, up to liquid densities. It is found to be impossible to obtain a red gas to liquid shift (such as that typically observed experimentally) in any realistic diatomic system with only binary solvent atom–solute atom interaction potentials. However, redshifts are predicted when a three‐atom potential, in which the solute–solvent interaction depends on solute bond length, is introduced.

Chemical potentials of hard molecular solutes in hard sphere fluids. Monte Carlo stimulations and analytical approximations

Monte Carlo measurements of the chemical potential of hard diatomics and polyatomics dissolved in hard sphere fluids are reported. These are performed as a function of density, solute size, and diatomic bond length. Bond length derivatives are used to determine the mean force along the diatomic bond axis. The results are compared with analytical expressions derived from the hard fluid (HF) model, a model proposed by Boublik, and a spherical approximation to diatomic and polyatomic chemical potentials.

Raman spectroscopy and theoretical modeling of HCl vibrational frequency shifts in high pressure argon

Raman vibrational frequencies of HCl in argon were measured at pressures up to 110 MPa. The mean frequency of the asymmetric Q‐branch is shown to accurately measure vibrational shifts through a density region where line shape changes due to motional narrowing render the peak maximum an inaccurate measure of pressure induced frequency shifts. A semiclassical, analytical expression utilizing Hutson’s HCl–Ar pair‐potentials is used to determine the derivative of the HCl vibrational frequency with respect to Ar density in the limit of zero density. The predictions are in reasonable agreement with experimental results, although the experimental frequency shifts are about 20% smaller (less redshifted) than theoretical predictions, which may represent the influence of multibody interactions. Experimental HCl Raman Q‐branch and S‐branch linewidths and peak shifts are compared qualitatively with previous R‐branch (IR absorption) results. Separation of the vibrational (Q‐branch) and rotational parts of the frequenc...

Pressure and temperature-dependent gauche-trans isomerization of 1-bromopropane: Raman measurement and statistical thermodynamic analysis

Raman measurements of the isomerization equilibrium in liquid 1-bromopropane are compared with perturbed hard-body fluid predictions. The integrated areas of the Raman bands arising from the C–Br stretch of the gauche and trans conformations are used to track the isomerization equilibrium as a function of pressure and temperature. Repulsive solvent–solute interactions are treated using the recently developed excluded-volume-anisotropy model (based on realistic molecular structures for the two isomers and the equation of state of liquid 1-bromopropane), and cohesive interactions are treated using the van der Waals mean field approximation. The results illustrate the delicate balance of attractive and repulsive solute–solvent interactions which underlie the effects of solvation on chemical equilibria. Comparison of the measured and predicted changes in ΔH with pressure, and ΔV with temperature, are used to determine parameters describing the attractive mean field and cavity formation energies of the two iso...

Vibrational frequency shift of H2 in rare gas clusters and solutions: Comparison of semi‐classical theory and experiment

A recently developed semi‐classical statistical mechanical formulation [de Souza et al., J. Chem. Phys. 99, 9954 (1993)] is combined with accurate H2‐rare gas potentials [Le Roy and Hutson, J. Chem. Phys. 86, 837 (1987)] to predict H2 vibrational frequency shifts in rare gas clusters and low density solutions. The results are compared with available experimental measurements as well as with predictions derived assuming a Lennard‐Jones (LJ) atom–atom potential. The Le Roy–Hutson potential has a minimum cluster energy and maximum H2 bond softening in the linear atom–diatom geometry, in contrast to the T geometry predicted using the LJ potential. The Le Roy–Hutson potential also yields better agreement with experimental temperature and density dependent H2 frequency shifts. A classical approximation to the ground state frequency of H2‐rare gas clusters is suggested which relates the probability density of the cluster configuration to the classical Boltzmann distribution at a temperature equal to the cluster ...

Solvent Mean Force Perturbations of Molecular Vibration, Isomerization and Dissociation

The mean force potential represents the effect of solvent-solute interactions on solvation thermodynamics, and thus on solute chemical potentials and equilibrium constants. Chemical reaction dynamics, on the other hand, may involve additional non-equilibrium contributions to the solvation of short-lived intermediates. Nevertheless, the solvent mean force potential places significant constraints on reaction dynamics as well as thermodynamics by defining the equilibrium structure of the entire reactive potential surface. Perturbed hard sphere fluid theories [1, 2, 3], which make optimal use of analytical Statistical mechanical expressions for the thermodynamic properties of hard sphere fluids in predicting the properties of real liquids, offer an appealing formalism for modeling such effects [4, 5, 6].