Pair correlation function integrals: Computation and use

Abstract

We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long-distance behavior of radial distribution functions is determined by requiring that the corresponding direct correlation functions follow certain approximations at long distances. We have briefly described the method and tested its performance in previous communications [R. Wedberg, J. P. O'Connell, G. H. Peters, and J. Abildskov, Mol. Simul. 36, 1243 (2010); Fluid Phase Equilib. 302, 32 (2011)], but describe here its theoretical basis more thoroughly and derive long-distance approximations for the direct correlation functions. We describe the numerical implementation of the method in detail, and report numerical tests complementing previous results. Pure molecular fluids are here studied in the isothermal-isobaric ensemble with isothermal compressibilities evaluated from the total correlation function integrals and compared with values derived from volume fluctuations. For systems where the radial distribution function has structure beyond the sampling limit imposed by the system size, the integration is more reliable, and usually more accurate, than simple integral truncation.

Experimental investigation of triplet correlation approximations for fluid water

“…The a and b parameters were obtained after fitting k values between 10–20 nm −1 . Other approaches are available to ensure correct behavior of the structure factors and/or rdfs [51, 54–56], although many of these require a knowledge of the intermolecular potential. As the above equation resulted in good fits to the experimental structure factors for all but the T = 673 K and p = 500 bar state point, which lies closest to the critical point ( T = 647.096 K and p = 220.64 bar) [45], we adopted the simple approach provided by Eq.…”

- Global and Local Properties of Mixtures: An Expanded Paradigm for the Study of Mixtures

“…For potentials that decay faster than r -3 , the asymptotic behavior of the DCF is (Lebowitz and is employed to express c explicitly in terms of h. This transforms the integral equation into a system of nonlinear equations for which a numerical solution is found using Newton's method (Wedberg et al 2011a). The Jacobian is evaluated analytically and 5-15 iterations are normally required for convergence.…”

“…The truncation (Weerasinghe and Smith 2003b) integration approaches, caution is advised regarding activity coefficient derivatives when a system is nearly ideal or when the mole fraction of a component is less than approximately 15%, as discussed by Wedberg et al (Wedberg et al 2011a). …”

“…Recently we (Wedberg et al 2010;Wedberg 2011;Wedberg et al 2011aWedberg et al , 2011b have investigated more thoroughly the extension method of Verlet (Verlet 1968) for mixtures with polyatomic molecules. This section gives a more complete description of our implementation, including some results not previously published.…”

“…This section gives a more complete description of our implementation, including some results not previously published. We have analyzed MD simulations of both pure (Wedberg et al 2010) and mixed (Wedberg et al 2011a(Wedberg et al , 2011b …”