We have developed a self-consistent description of an interface between a metal and a molecular liquid by combination of the density functional theory in the Kohn–Sham formulation (KS DFT) for the electronic structure, and the three-dimensional generalization of the reference interaction site model (3D RISM) for the classical site distribution profiles of liquid. The electron and classical subsystems are coupled in the mean field approximation. The procedure takes account of many-body effects of dense fluid on the metal–liquid interactions by averaging the pseudopotentials of liquid molecules over the classical distributions of the liquid. The proposed approach is substantially less time-consuming as compared to a Car–Parrinello-type simulation since it replaces molecular dynamics with the integral equation theory of molecular liquids. The calculation has been performed for pure water at normal conditions in contact with the (100) face cubic centered (fcc) surface of a metal roughly modeled after copper. ...

Self-consistent description of a metal–water interface by the Kohn–Sham density functional theory and the three-dimensional reference interaction site model

Recent developments in models for the interface between a metal and an aqueous solution

The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is ∼1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decompos...

Molecular origin of the hydrophobic effect: analysis using the angle-dependent integral equation theory.

It has been experimentally shown that the folding of apoplastocyanin (apoPC) accompanies a very large enthalpic loss [N. Baden et al., J. Chem. Phys. 127, 175103 (2007)]. This implies that an even larger entropic gain occurs in stabilizing the folded structure to overcome the enthalpic loss. Here, we calculate the water-entropy gain upon the folding of apoPC using the angle-dependent integral equation theory combined with the multipolar water model and the recently developed morphometric approach. It is demonstrated that the calculated value is in quantitatively good accord with the value estimated from the experimental data by accounting for the conformational-entropy loss. According to a prevailing view, the water adjacent to a hydrophobic group is unstable especially in terms of the rotational entropy and the folding is driven primarily by the release of such unfavorable water to the bulk through the burial of nonpolar side chains. We show, however, that the resultant entropic gain is too small to elucidate the experimental result. The great entropic gain observed is ascribed to the reduction in the restriction for the translational motion of water molecules in the whole system.

Thermodynamics of apoplastocyanin folding: comparison between experimental and theoretical results.

We investigate the molecular mechanism of pressure denaturation of proteins using the angle-dependent integral equation theory combined with the multipole water model and the morphometric approach. We argue that the hydration entropy of a protein is the key quantity. It is verified that at an elevated pressure, a swelling structure--which has only moderately less compact than the native structure but has a much larger water-accessible surface area--turns more stable than the native structure in terms of the water entropy. The swelling structure is characterized by the penetration of water into the interior. The hydration entropy is decomposed into contributions from the translational and rotational restrictions for the molecular motions of water. Each contribution is further decomposed into the water-protein pair correlation component and the water-water-protein triplet and higher-order correlation components. The pair correlation component in the translational contribution is divided into two terms arising from the excluded volume and the water structure near the protein, respectively. It is found that pressure denaturation accompanies a loss of the translational and rotational entropies at the pair correlation level but a much larger gain of the translational entropy at the triplet and higher-order correlation levels. Although the translational and rotational motions of water molecules penetrating the protein interior and contacting the protein surface are constrained, the translational restriction for the water molecules well outside the protein is greatly reduced. The latter entropic gain dominates, leading to the denaturation.

Molecular mechanism of pressure denaturation of proteins.

An efficient algorithm, a hybrid of the Picard-type and Newton-Raphson (NR) methods, is developed for solving the reference hypernetted-chain (RHNC) theory for non-spherical particles near a uniform planar wall. The basic idea of the algorithm is also applicable to non-spherical particles near a large macroparticle at infinite dilution. The problem of dipolar hard spheres near a hard wall is chosen here as an example system. A feature of the algorithm is that the Jacobian matrix is determined in the bulk calculation and serves as part of the input data for the wall calculation. Hence, the convergence is achieved in only a single iteration in the inner NR loop regardless of the initial values of the iteration variables. It is shown that the great advantage of the constant Jacobian matrix can be preserved even for general cases of other particle-particle and wall-particle interactions. In the course of the study, we encounter a singular behaviour of the RHNC theory for bulk dipolar hard spheres. Keeping the...

Numerical solution of the RHNC theory for fluids of non-spherical particles near a uniform planar wall

We present a further study of Gillan's procedure for solving the HNC and related equations. We show that the jacobian matrix in the inner iterative loop is diagonally dominant in the absence of strong, long-range Coulomb potential and the matrix approaches the unit matrix when the density is low. Even in the presence of the Coulomb potential, for example in ionic systems other than aqueous electrolytes, the basic patterns of the matrix remain unchanged under a wide range of conditions. We consequently propose a more efficient iteration strategy based on the idea that the system matrix, defined as the negative inverse of the jacobian matrix calculated under a reference condition, can be used for all the iterations under many different conditions. Its power is demonstrated by solving the HNC equation for ionic systems where we present a simple but reliable way of initiating calculations. A P-V-T diagram is drawn for a symmetrical alkali halide system by solving the HNC equation. At relatively low temperatur...

Numerical solution of the HNC equation for ionic systems

An efficient algorithm is developed for solving the HNC and related equations for fluids characterized by non-spherical, angle-dependent pair interactions by choosing the dipolar hard spheres as an example system. The algorithm is a hybrid of the Picard type and Newton-Raphson (NR) methods. We note that the convergence properties are governed mainly by a few leading projections in the rotational-invariant expansion of η(12) (=h(12) - c(12); h and c are the total and direct correlation functions respectively) for the domain of r < d (d is the hard-sphere diameter) where the analytical expansion of the HNC closure reduces to a much simpler form, and apply the NR technique only to these variables. It is shown for the dipolar hard spheres that the Jacobian matrix can be split into two smaller independent matrices resulting in a considerable saving of computing time. A slightly modified version of the MSA procedure is proposed for setting the initial values of the iteration variables. It is demonstrated that o...

Numerical solution of the HNC equation for fluids of non-spherical particles. An efficient method with application to dipolar hard spheres

The characteristics of solutions of the HNC equation are studied for anion-cation systems that are distinguished by a strong long-range attractive Coulomb potential. The qualitative aspects of the discrepancies between the HNC and MC results for the 1–1 and 1–2 molten salts that have been tested and molten UO2 appear to be about the same as those for the other typical model potential systems. However, studies of the bridge functions for a 1–1 molten salt system reveal the unique nature of the bridge function for the anion-cation pair that cannot be explained in terms of previous approaches. It is shown that the HNC equation possesses no solutions for a model system of molten SiO2 or alkali-halide vapour, characterized by the SiO4 tetrahedral structure and the clustering of ions respectively. It is suggested that a correct description of these ‘strongly’ ordered structures in the relatively short-range domain is possible only if account is taken of three-body and higher-order density correlations. All prev...

Characteristics of solutions of the HNC equation applied to anion-cation systems interacting through a strong long-range Coulomb potential

Algorithms, previously reported for solving integral equation theories for fluids of non-spherical particles, are now extended to water-like fluids (bulk fluids and fluids near a macroparticle and a planar wall) modelled as hard spheres embedded with point dipoles and tetrahedral quadrupoles. Alternative algorithms are reviewed in detail, and the unique advantages of the present methods are emphasized. These advantages include compactness of the analytically derived expressions for the Jacobian matrix, remarkable reduction in the matrix size and complere constancy of the matrix during the whole computation. In the macroparticle and wall cases, for instance, convergence is achieved in about ten iterations starting from the ideal gas condition, even for strongly interacting water-like fluids. The density and orientational structures of water-like fluids near a large macroparticle (its diameter is 30 times larger than that of the water molecule) and a planar wall are also investigated by employing the refere...

Numerical solution of the RHNC theory for water-like fluids near a macroparticle and a planar wall

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