Site-site Direct Correlation Function Research Articles

Extraction of site–site bridge functions and effective pair potentials from simulations of polar molecular liquids

We develop an efficient method to extract site-site bridge functions from molecular simulations. The method is based on the inverse solution of the reference site interaction model. Using the exact long-range asymptotics of site-site direct correlation functions defined by the site-site Ornstein-Zernike equations, we regularize the ill-posed inverse problem, and then calculate site-site bridge functions and effective pair potentials for ambient water, methanol, and ethanol. We have tested the proposed algorithm and checked its performance. Our study has revealed various peculiarities of the site-site bridge functions, such as long-range behavior, strong dependence on the electrostatic interactions. Using the obtained data, we have calculated thermodynamic properties of the solvents, namely, isothermal compressibility, internal energy, and Kirkwood-Buff integrals. The obtained values are in excellent agreement not only with molecular simulations but also with available experimental data. Further extensions of the method are discussed.

Site-site direct correlation functions for three popular molecular models of liquid water

Direct correlation functions (DCFs) play a pivotal role in the applications of classical density functional theory (DFT) to addressing the thermodynamic properties of inhomogeneous systems beyond the local-density or mean-field approximations. Whereas numerous studies have been dedicated to the radial distribution functions of liquid water--the most important solvent on earth, relatively little attention has been given to the site-site DCFs. The water DCFs are long-ranged and difficult to calculate directly by simulation, and the predictions from conventional liquid-state theories have been rarely calibrated. Here we report a computational procedure for accurate evaluation of the site-site DCFs of liquid water based on three popular molecular models (viz., SPC, SPC∕E, and TIP3P). The numerical results provide a benchmark for calibration of conventional liquid-state theories and fresh insights into development of new DFT methods. We show that: (1) the long-range behavior of the site-site DCFs depends on both the molecular model and the thermodynamic condition; (2) the asymptotic limit of DCFs at large distance does not follow the mean-spherical approximation (MSA); (3) individual site-site DCFs are long ranged (~40 nm) but a summation of all DCF pairs exhibits only short-range behavior (~1 nm or a few water diameters); (4) the site-site bridge correlation functions behave as the DCFs, i.e., they are also long-ranged while the summation of all bridge correlation functions is short ranged. Our analytical and numerical analyses of the DCFs provide some simple strategies for possible improvement of the numerical performance of conventional liquid-state theories.

The dielectric constant and the site-site direct correlation function of the RISM-2 theory for polar polyatomic molecular fluids

The exact expression of the dielectric constant for polar polyatomic molecular fluids is obtained in terms of the site-site direct correlation function. This equation is closely related to the formula of the dielectric constant in terms of the molecular direct correlation function (the Ramshaw equation, Ramshaw, 1972, J. chem. Phys., 57, 2684). We discuss why RISM-1 theory gives a trivial expression for the dielectric constant using equations obtained here, and show that RISM-2 theory leads to a non-trivial result for the dielectric constant of molecular liquids.

The Asymptotic Behavior of the Site-Site Ornstein-Zernike Equation and RISM-2 Approximations for Polyatomic Molecular Fluids

It is shown that the asymptotic properties of the reference interaction site model (RISM)-2 type integral equations for polyatomic molecular fluids are quite similar to those of simple fluids. The exact asymptotic form of the new site-site direct correlation function C αγ ( r ), which is defined by the site-site Ornstein-Zernike equation, is given by using the exact asymptotic form of the site-site total correlation function. The result is C αγ ( r )≃- U (1, 2)/ k B T for nonpolar fluids composed of homonuclear diatomic molecules as well as heteronuclear diatomic molecules, where U (1, 2) is an intermolecular potential, k B the Boltzmann constant and T the absolute temperature. The asymptotic form of C αγ ( r ) given by the RISM-2 approximations is found to be in accordance with the exact result. Thus, the RISM-2 theory is concluded to have no theoretical inconsistency like that in the RISM-1 theory.

The coupling of long and short range correlations in ISM liquids

A simple modification of the HNC-like closure within the extended RISM equation formalism is considered which assures that the asymptotic form of the site-site direct correlation functions is consistent with the dielectric constant. The short ranged structural results obtained with the modification are compared to those following from the original closure for three strongly polar diatomic models, with the result that only very small differences are found. These results demonstrate both that the short ranged results are only weakly coupled to the asymptotic amplitudes, and that the latter can potentially be corrected in a relatively straightforward manner.

New and proper integral equations for site-site equilibrium correlations in molecular fluids

We show that the often used site-site direct correlation function cannot be defined in terms of a sum over a subset of the diagrams in the interaction site cluster series for the equilibrium pair correlation functions of a molecular fluid. However, from an exact topological reduction, we arrive at a new class of site-site direct correct correlation functions that are properly defined in the diagrammatic sense. The class is composed of four topologically distinct functions which are related to each other and the pair correlation function through four coupled Ornstein-Zernike-like equations. These new integral equations are exact and provide a rigorous foundation for integral equation theories of molecular fluids. The formal solutions to the equations are constructed, and the utility of the formulation is illustrated by discussing one example of an approximate closure to the integral equations.

Exact asymptotic form of the site-site direct correlation function for linear triatomic molecules

(1982). Exact asymptotic form of the site-site direct correlation function for linear triatomic molecules. Molecular Physics: Vol. 46, No. 3, pp. 665-670.

Interaction site models for molecular fluids

A detailed study is made of the atom-atom (i.e. site-site) correlation functions—especially the direct correlation function—for the interaction site model (ISM) of Andersen and Chandler. The work is based on the observation of Høye and Stell that the site-site Ornstein-Zernike-like equation of Chandler and Andersen can be regarded as a rewritten version of the usual Ornstein-Zernike equation for particle-particle correlations, where the particles are identified with the atoms that constitute the ISM molecules. Our new results include (i) new compressibility theorems in terms of the site-site direct correlation functions, and (ii) for ISM diatomics (both polar and non-polar) full asymptotic (i.e. large-r) characterization of the site-site direct correlation function based on the assumption that the corresponding particle-particle direct correlation function behaves asymptotically like the particle-particle potential times -1/k B T (k B = Boltzmann's constant and T = absolute temperature). Further asymptotic results are also given for a wider class of ISMs, in particular for triatomics. All our asymptotic results (except those for two classes of homonuclear symmetric n-atomics) are in fundamental disagreement with assumptions of the reference interaction site approximation (RISA) and the more general interaction site approximation (ISA), both originally proposed by Chandler and Andersen, as well as with all subsequently proposed approximations of which we are aware. (iii) A characterization is given of a family of ISMs containing point charges that is solvable in a class of linear approximations, including the ISA, as well as an approximation that is asymptotically faithful to the results noted in the preceding item. The family of ISMs considered includes models that have heretofore lacked analytic solution. (iv) The relation between the exact analytic solution of the Chandler-Andersen RISA and its approximate solution according to the widely-used Lowden-Chandler ansatz is examined on the basis of the particle-particle picture. It is pointed out how the relatively good liquid density agreement and the relatively poor low density agreement between the two solutions can be easily understood within this framework.

Exact asymptotic form of the site-site direct correlation function for rigid polar molecules

Exact asymptotic form of the site-site direct correlation function for rigid polar molecules

Analytic solution of the RISM equation for symmetric diatomics with Yukawa closure

We present the site-site direct correlation function c(r) for a fluid of hard diatomic symmetric molecules obtained from Monte Carlo simulation data via the RISM integral equation. This c(r) ensures that the site-site correlation function given by the RISM equation is exact, and thus provides a basis for critically examining the usual closure for the RISM equation. As an example of an improved closure we present the analytic solution of the RISM integral equation with a Yukawa closure for c(r).

Correlation Functions Calculated by Using Reference Interaction Site Model Equations for Diatomic Molecular Fluids

Abstract The reference interaction site model (RISM) theory was applied to diatomic molecular fluids, by using three different forms of approximation for site-site direct correlation function. Applicability of the three forms of RISM equation, RISM-1, RISM-2, and RISM-3, was examined, site-site pair correlation functions being calculated from them and a comparison of the results with those of computer simulations being made. Structure factor for liquid nitrogen, oxygen, and bromine were obtained from the solution of the RISM-2 equation and compared with experimental results.

The solution of the RISM equation for diatomic symmetric molecules

The RISM equation for diatomic symmetric molecules is solved using a Weiner-Hopf factorization technique. This procedure introduces a function Q(r) which is related to both the site-site total correlation function h(r) and the site-site direct correlation function c(r). Determining Q(r) effectively solves the RISM equation. We show that Q(r) can be written as an infinite sum, for r greater than the hard sphere diameter R, and using this form, solve for Q(r) when 0 < r < R. To generate a solution, this infinite series must be truncated. A method to determine the coefficients in the truncated series is outlined.