Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation

Abstract

We report coefficients of the h-bond expansion of the bridge function of the hard-sphere system up to order ρ4 (where ρ is the density in units of the hard-sphere diameter), which in the highest-order term includes 88 cluster diagrams with bonds representing the total correlation function h(r). Calculations are performed using the recently introduced Mayer-sampling method for evaluation of cluster integrals, and an iterative scheme is applied in which the h(r) used in the cluster integrals is determined by solution of the Ornstein–Zernike equation with a closure given by the calculated clusters. Calculations are performed for reduced densities from 0.1 to 0.9 in increments of 0.1. Comparison with molecular simulation data shows that the convergence is very slow for the density expansion of the bridge function calculated this way.

Study of integral equation theory and human beta defensin 28

“…proposed to calculate cluster integrals by Singh and Kofke [28] and applied to h-bond bridge diagrams up to order ρ 4 by Kwak and Kofke [29]. for clarity, which is 1/2 5 th .…”

“…A third way to obtain a nonempirical or nonanalytical representation of is to evaluate diagrammatic expansion of b(r) directly and truncate the infinite series at some point [24,[26][27][28][29]49]. The bridge function can be expressed as a series in powers of density, where the coefficient b n (r) are multi-dimensional integrals, which can be written in terms of bridge diagrams.…”

“…So far, the 2 nd to 5 th coefficients in terms of f(r) have been found by Labik et al [27] and up to 6 th coefficient by Kolafa and Labik [50] for hard sphere systems. Recently, Kwak and Kofke calculated bridge diagrams of a hard sphere fluid up to order ρ 4 in terms of h(r) [29]. Their results at high density are better than those using the f(r) representation and classical closures (i.e.…”

“…Furthermore, the true characteristic of the bridge function is still on debate. In contrast to these empirical approaches, the second route is the direct evaluation of the bridge function by its definition that is expressed as an infinite sum of highly connected bridge diagrams [24,[26][27][28][29].…”

“…To date, one of the successful methods to compute the high-dimensional integrals of bridge function is the biased Monte Carlo sampling, which is proposed by Rast et al [24] and improved by Labik et al [27]. Another successful approach is a free energy perturbation method, so-called Mayersampling, which is first introduced to evaluate accurate virial coefficients represented as cluster diagrams by Singh and Kofke [28] and later applied to calculate the bridge diagrams by Kwak and Kofke [29]. However, the bridge function calculated from these approaches converges very slowly.…”