Perturbation Theory for Fluids

Abstract

Recently, Barker and Henderson have introduced a semimacroscopic approximation to the second order in the expansion of the configuration integral by considering the pair potential as the sum of a strong (repulsive) part and a weaker (long-range) part. We analyze this approximation and show that the essential part of it is to reduce the higher-order distribution functions to a second-order nonuniform distribution function, the nonuniformity coming from fixing a particle at the origin. The approximation can be done to all orders, and the series can be summed to give an expression for the free energy and pressure. The expression involves the grand partition function for the nonuniform system taken at the chemical potential for the reference system minus the perturbing potential. The functions of the nonuniform system are approximated by taking the functional form they have at uniformity and by using the product of the density and the radial distribution function of the reference system for the nonuniform density. The summed series can then be computed. For the three-dimensional square-well fluid it is confirmed that the convergence is very rapid down to reduced temperatures about 0.5. Comparison with the one-dimensional square-well fluid shows that below this temperature the convergence is slow and it is necessary to use the whole seri~

Liquid theory with high accuracy and broad applicability: Coupling parameter series expansion and non hard sphere perturbation strategy

“…It is recognized that the Barker and Henderson approximation can be used in any order of the HTSE, and the complete series can be summed to obtain an expression involving only the two-particle distribution function of the reference system. 16 However, it is noted that the summed series results practically the same as those obtained from the second-order theory. Consequently, the summed series has rarely been used since it is first introduced in literature.…”

The First Three Coefficients in the High Temperature Series Expansion of Free Energy for Simple Potential Models with Hard-Sphere Cores and Continuous Tails

“…In contrast, as the MCA provides poor results for the second-order term, it is not expected that it will work better for the third-and higher-order terms. As a matter of fact, Praestgaard and Toxvaerd 19 resummed the perturbation expansion in the MCA approximation and reported expressions for the resulting free energy and pressure. Their results reveal that the resummed expansion considerably underestimates the contribution of the terms beyond the first-order one.…”

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

“…Recently, we developed a thermodynamic perturbation theory for classical fluids which combines the classical integral equation theory with the perturbation theory [13][14][15]. However, it was seen that the method doesn't bring in much improvement for short-ranged potentials [17]. This is an advantage over traditional perturbation theories as they allow exact calculation of the terms of the perturbation series only up to the first order.…”

“…To obtain the higher order terms, Barker and Henderson introduced an approximation called the Macroscopic Compressibility Approximation(MCA) [16]. However, it was seen that the method doesn't bring in much improvement for short-ranged potentials [17]. Another advantage of our method is that it works in a broader region of thermodynamic phase space including the region of phase transitions whereas solving the integral equation and closure is possible only in some domain of the phase space.…”