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Notes: The structure in four racemic fluids is explored using two integral equation theories: the reference interaction site method (RISM) [D. Chandler and H. C. Andersen, J. Chem. Phys. 57, 1930 (1972)] and the diagrammatically correct theory of Chandler, Silbey, and Ladanyi (CSL) [D. Chandler, R. Silbey, and B. M. Ladanyi, Mol. Phys. 46, 1335 (1982)]. Discrimination is measured by comparison of site pair distributions for sites on identical molecules with the corresponding distributions for sites on mirror-image molecules. We find that discrimination is largest for distributions between the smallest sites in the molecules. Between racemates, those consisting of more asymmetrical chiral molecules (i.e., with a bigger range of site sizes and bond lengths) show the largest discrimination. The indirect correlation function is shown to be nondiscriminating in racemates. Further, exact relationships between like–like and like–unlike differences in the other pair functions have been obtained. From these, the importance of the bridge functions in discrimination is evident. The CSL theory always satisfies the exact relationships, even with approximate bridge diagrams. RISM theory cannot satisfy these exact limits regardless of density and closure relation. We have found that RISM theory predicts qualitatively incorrect pair distributions at low densities, but that the difference in the distributions is more accurate. All bridge diagrams which contribute to O(ρo) have been enumerated and evaluated. Inclusion of these diagrams into the CSL theory leads to exact results at low density. However, we find that the inclusion of the ρo diagrams has dramatically improved the quality of the CSL theory at all densities. © 2001 American Institute of Physics.

Notes: The structure in eighteen racemates is explored at three temperatures and three densities. The enantiomers vary in shape from elongated, to nearly spherical, to flattened. Discrimination, as measured by the difference between like–like (LL) and like–unlike (LU) radial distributions, is assessed for these racemates. Elongated molecules show discrimination most readily with differences of up to 25% between the LL and LU distributions. However, the magnitude depends strongly on the orientation of the molecular dipole. Flattened molecules also show some discrimination but the magnitude is always quite small. The fluid structure is obtained from the molecule-based hypernetted chain theory (HNC) which has been applied, for the first time, to racemates. The incorporation of chirality into HNC theory is nontrivial. Specifically, for racemates, the number of nonzero coefficients in the rotational invariant expansions is very large, each coefficient is complex, and careful treatment of molecular shape into the closure relation is required. Our numerical procedures are discussed in detail. Bridge diagrams have also been evaluated for a reference system of hard ellipsoids. The impact of inclusion of these bridge diagrams has been considered for one racemate and found to be small. © 2001 American Institute of Physics.

Notes: An analysis of structure and discrimination in simple chiral fluids is presented. The chiral molecules consist of a central carbon bonded to four distinct groups. Molecular-dynamics simulations have been performed on a one-component chiral fluid and on two racemic mixtures. For the racemates, discrimination, as measured by differences in pair distribution functions, is present but found to be small. Intermolecular pair interaction energies are found to be good predictors of the magnitude and the sign (mirror-image pairs favored) of the differences observed in site–site distribution functions. For the one-component fluid, the quality of structural predictions from the reference-interaction-site method and Chandler–Silbey–Ladanyi (CSL) integral equation theories, with the hypernetted chain (HNC) and Percus–Yevick closures, has been examined. These theories generally provide a qualitatively correct description of the site–site distributions. Extensions beyond the HNC level have been explored: Two-field-point bridge diagrams have been explicitly evaluated and included in the CSL theory. The inclusion of these diagrams significantly improves the quality of the integral equation theories. Since the CSL theory has not been used extensively, and bridge diagrams have been evaluated in only a few instances, a detailed analysis of their impact is presented. For racemic mixtures, diagram evaluation is shown to be crucial. Specifically, the differences in site–site distributions for sites on identical and mirror-image molecules are found to originate from bridge diagrams which involve interactions between four-site, or larger, clusters. Discrimination cannot be predicted from an integral equation theory which neglects these diagrams. © 2000 American Institute of Physics.

Notes: A comprehensive study of integral equation theories for binary mixtures is presented. The mixture components differ primarily in size (the diameters differ by 10%, 20%, and 30%) and interact either via hard potentials or via Lennard-Jones potentials. For the latter, variation with energy parameter (ε) is considered. This article focuses on improving the accuracy of the theories by systematic inclusion of bridge diagrams into the closure relationships. Specifically, the first two orders of bridge diagrams are exactly evaluated for these mixtures. A general Monte Carlo integration scheme for diagram evaluation is discussed and applied. Comparisons with diagrams obtained from a Legendre expansion technique are made in order to assess whether this approach is practical. The approximation of higher order diagrams has been considered. Specifically, techniques for approximation of all higher order diagrams, which were successful for single component fluids, were found to be problematic for mixtures. However, a simple algorithm for approximate third order diagrams is presented and found to lead to improvements. A detailed analysis of the bridge diagram variation with the nature of the mixture is presented and may be useful in extending the present results to related mixtures. The spatial dependence of the diagrams has also been examined and found to be extremely well reproduced by simple polynomial expansions. In addition, physical arguments have been applied to extract large separation limits of the diagrams. The accuracy of the integral equation theories with order of bridge diagrams is assessed by comparing pressure estimates from the virial expansion and from the integration of compressibilities. With this measure, the quality of the integral equation theories for each mixture is assessed at 18 state points. In all cases, the thermodynamic consistency improves smoothly and rapidly with the order of bridge diagram included in the theory. This result, together with the general Monte Carlo algorithm and the detailed structural and spatial analysis, shows that direct bridge diagram evaluation is practical and consistently improves the quality of the theory for these mixtures. © 1999 American Institute of Physics.

Notes: In this paper we examine the influence of solute size and insertion conditions on solvent structural changes and excess thermodynamic properties in the infinite dilution limit. A general integral equation approach which can be applied under arbitrary conditions is given and isothermal-isochoric and isothermal-isobaric insertions are discussed in detail. Scaling relationships valid in the large solute limit are determined for both structural and thermodynamic properties. This is done by considering macroscopic thermodynamic relationships and explicit evaluation of low solvent density expansions of pair correlation functions. The hypernetted-chain and reference hypernetted-chain closure approximations are used to obtain numerical results for the insertion of hard sphere solutes of varying diameter into hard sphere, dipolar hard sphere and water-like solvents. The results obtained give a good deal of insight into the nature of solvation of inert solutes. It is shown that for all three solvents the excess properties are very well represented by a function obtained by summing terms proportional to the solute volume, surface area and diameter. One would expect such a result for large solutes, but here we show that this expression extrapolates all the way down to solutes comparable in size to the solvent particles. Further, it is shown that both the numerical value, and, more importantly, the physical interpretation of the excess thermodynamic properties strongly depend on the insertion conditions. Under all insertion conditions the chemical potential is a local property in the sense that it is completely determined by solute-solvent correlations which are important only in the immediate vicinity of the solute. However, this is not true of the excess energy, enthalpy and entropy which all contain nonlocal contributions arising essentially from changes in the actual or effective solvent density depending on the insertion conditions. We demonstrate that the nonlocal contributions can be very significant and therefore the excess energies, enthalpies and entropies often cannot provide useful information about solvent structure near solutes. This has significant implications for models which attempt to rationalize excess thermodynamics in terms of local solvent structure in the vicinity of solute particles. © 1997 American Institute of Physics.

Notes: Theoretical results are given for aqueous electrolyte solutions in contact with uncharged metallic surfaces. The metal is modeled as a jellium slab and is treated using local density functional theory. The solution structure is obtained using the reference hypernetted-chain theory. The two phases interact electrostatically and the coupled theories are iterated to obtain fully self-consistent results for the electron density of the metal and surface-particle correlation functions. The metal-induced structure of pure water and aqueous electrolyte solutions as well as the electrostatic potential drop across the interface are discussed in detail. The results are compared with those for ions in simple dipolar solvents. It is found that the water molecules are ordered by the metal field and that the surface-induced solvent structure strongly influences the ion distributions. © 1997 American Institute of Physics.