Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas

Abstract

It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.

Bridge functions of classical one-component plasmas

“…This still remains a cumbersome task, but it is much less formidable than the computation through the formal definition and it is rather feasible with modern computational resources. Part of the complexity stems from the fact that two simulation methods need to be simultaneously employed to indirectly extract bridge functions in the full range [15,23].…”

“…The OZ inversion method is rather straightforward and requires input from standard equilibrium simulations. However, the omnipresent uncertainties in the extraction of the radial distribution function propagate largely augmented to the computation of the bridge function, which necessitates very accurate simulations with a large num-ber of particles and statistically independent configurations [23]. Furthermore, the OZ inversion method cannot be employed for the reliable computation of bridge functions within the entire range.…”

“…The extraction of the radial distribution functions with the histogram method unavoidably leads to poor collected statistics at short distances that lie within the so-called correlation void, that can be loosely defined as arg r {g(r) ≪ 1} or arg r {g(r) ≃ 0}. This issue does not bear any consequences for the radial distribution function (which is practically zero) or the direct correlation function [which cannot be affected by uncertainties in the infinitesimally small g(r) values], but is crucial for the bridge function courtesy of the presence of the logarithmic term in the closure condition [23].…”

“…The cavity distribution method is based on the fact that the cavity distribution function can be directly extracted from computer simulations, being equal to the radial distribution function for a tagged particle pair whose mutual interaction is suppressed that are dissolved at infinite dilution in a system where all other pair interactions remain the same [4,6]. The cavity distribution function remains continuous even if the interaction potential is discontinuous or diverges and acquires large but finite values near the origin r = 0 [7,23]. In other words, by merging the radial distribution function and the interaction potential in its definition, the cavity distribution function eliminates their inherent pathologies close to the contact point.…”

“…The computation of bridge functions with structural input from computer simulations presents the only viable alternative to the seemingly endless parade of approximations of integral equation theory. In spite of the rather demanding design of the bridge function extraction simulations, the heavy computational cost and the necessity for meticulous uncertainty propagation analysis, "exact" bridge functions have been computed with structural input from Monte Carlo or molecular dynamics (MD) simulations for numerous liquid systems which include established model interactions such as hard spheres [10][11][12][13] and their binary mixtures [11,13], Lennard-Jones interactions [15][16][17][18], inverse power law interactions [19], onecomponent plasmas [20][21][22] and Yukawa one-component plasmas [23] as well as more realistic model interactions such as hard spheroids [24], liquid metal interionic potentials [25], model 2-2 electrolytes [26], molten salts [27], Lennard-Jones dipolar fluids [28] and even the extended simple point charge (SPC/E) site-site model of water [29]. Unfortunately, the state-of-affairs is quite discouraging, since many bridge function extraction investigations concern the intermediate and long range exclusively, contain uncontrolled uncertainties and are restricted to a single or to few thermodynamic states.…”