John S. Perkyns

A site-site theory for finite concentration saline solutions

A liquid state theory based on site–site integral equations is constructed to have the asymptotics given by angular expansion theory. This results in a theory which shows dielectric consistency, e.g., the dielectric constant as viewed from the solvent is the same as that viewed by the ions. Such consistency is lacking in other extended reference interaction site model (XRISM)‐based theories and leads to unrealistic structural predictions. The Kirkwood–Buff route to thermodynamics is used and allows a physical partitioning of the terms responsible for the solvation process. Sample results for a 1–1 salt are given.

A dielectrically consistent interaction site theory for solvent—electrolyte mixtures

Abstract A reformulation of reference interaction site model theory is proposed. The approach makes use of the formally correct asymptotic form of the correlations obtained from the one-center angular expansion technique. A modified closure, or equivalently, a modified propagation equation for site—site correlations is shown to incorporate the necessary information to allow dielectric consistency in finite-concentration salt solutions. Examples of the correlations and thermodynamics are given.

The behavior of ions near a charged wall-dependence on ion size, concentration, and surface charge.

A renormalization of the 3D-RISM-HNC integral equation is used to study the solvent and ion distributions at neutral and negatively charged planar atomistic surfaces. The charge density of the surfaces ranged from 0.0 to 0.4116 C/m(2), and the modeled electrolyte solutions consist of the salts NaCl, KCl, and CsCl at concentrations of 0.1, 0.25, and 1.0 M in SPC/E water. The results are qualitatively compared to the results from other integral equation methods and simulations for similar models. We find that the 3D-IEs predict an electric multilayer screening behavior in the solvent and ion distributions in contrast to the double layer anticipated from Poisson-Boltzmann theory. It is observed that the cation size has a significant effect on the distributions near the surface up to three solvation layers beyond which the behavior is the same among the different cations. The response of the distributions to the charged surface is described as an increase in ion and solvent density near the wall. The higher concentration solutions screen the electrostatic source more strongly at the wall as expected. The importance of ion-solvent and ion-ion correlations near the surface is shown through three-body correlation functions which are obtainable from the 3D-IEs in this study.

Integral equation approaches to structure and thermodynamics of aqueous salt solutions

Results for free energy, entropy, enthalpy and internal energy of solvation for monovalent ions in water have been studied by comparing DRISM theory results to those of RISM and ARISM theories. The greatly improved dielectric behavior in the DRISM case enabled the examination of realistically modeled salts at finite concentrations. The link between solvent structure and the entropy of solvent co-spheres was examined. Finally comparison with the Born free energy equation shows its virtues and flaws due to ignoring cavity formation and asymmetric solvation terms which together always contribute significantly to the free energy of hydration of ions.

A molecular site-site integral equation that yields the dielectric constant

Our recent derivation [K. M. Dyer et al., J. Chem. Phys. 127, 194506 (2007)] of a diagrammatically proper, site-site, integral equation theory using molecular angular expansions is extended to polar fluids. With the addition of atomic site charges we take advantage of the formal long-ranged potential field cancellations before renormalization to generate a set of numerically stable equations. Results for calculations in a minimal (spherical) angular basis set are presented for the radial distribution function, the first dipolar (110) projection, and the dielectric constant for two model diatomic systems. All results, when compared to experiment and simulation, are a significant quantitative and qualitative improvement over previous site-site theories. More importantly, the dielectric constant is not trivial and close to simulation and experiment.

Computationally useful bridge diagram series. II. Diagrams in h-bonds

Equations for calculating accurate 4-point and 5-point bridge diagrams in terms of h-bonds have been presented and solved for various phase points of the Lennard-Jones fluid. A method of finding a self-consistent solution for the bridge function and the radial distribution function is demonstrated. The significance of this result over bridge diagrams expressed as f-bonds, in terms of its applicability to charged and dipolar models is discussed. Two very simple phenomenological bridge diagram forms for the bridge function for this model are examined and found to give results almost as accurate and in some cases more accurate than previous forms in the literature. This work represents the first use of directly calculated 5-point bridge diagrams in terms of h-bonds, and the many extra orders of f-bond diagrams which they include, in an integral equation result.

A site-renormalized molecular fluid theory

The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335 (1982)]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.

Site-renormalised molecular fluid theory: on the utility of a two-site model of water

We propose a simple, two-site model of water, using the familiar three-site Simple Point Charge (SPC) model as a guide. We briefly examine the resulting dielectric and solvation properties of the bulk fluid, both pure and in a three component mixture of apolar or ionic simple fluid solutes, using integral equation methods. The results confirm a practical utility of this simplified model, and the essential predictive properties of the site-renormalised molecular fluid theory.

Structure and dynamics of α-MSH using DRISM integral equation theory and stochastic dynamics

The structural and dynamical features of the hormone α-MSH in solution have been examined over a 100 ns time scale by using free energy molecular mechanics models at room temperature. The free energy surface has been modeled using methods from integral equation theory and the dynamics by the Langevin equation. A modification of the accessible surface area friction drag model was used to calculate the atomic friction coefficients. The molecule shows a stable β-turn conformation in the message region and a close interaction between the side chains of His6, Phe7, and Trp9. A salt bridge between Glu5 and Arg8 was found not to be a preferred interaction, whereas a Glu5 and Lys11 salt bridge was not sampled, presumably due to relatively high free energy barriers. The message region was more conformationally rigid than the N-terminal region. Several structural features observed here agree well with experimental results. The conformational features suggest a receptor–hormone interaction model where the hydrophobic side chains of Phe7 and Trp9 interact with the transmembrane portion of the MC1 receptor. Also, the positively charged side chain of Arg8 and the imidazole side chain of His6 may interact with the negatively charged portions of the receptor which may even be on the receptors extracellular loops.

Computationally useful bridge diagram series. III. Lennard-Jones mixtures

The first two orders of bridge diagrams for the f-bond expansion and the h-bond expansion are calculated for a binary mixture of Lennard-Jones spheres. The method used follows the Legendre polynomial integration methods outlined in the first two papers of this series. As for the pure fluid cases, the thermodynamic results which follow from these methods are found to be in reasonable agreement with the simulation result. Analysis of the thermodynamic and structural results in comparison to the best current bridge function approximations indicate that accurate descriptions of higher order mixtures will require methods beyond the current mean field treatments which are of utility in simple fluids. The methods given are unfortunately not computationally convenient at highest order; however, the lower order diagrams are both accessible and give reasonable numerical results.