### Abstract

Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamicperturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. *J. Chem. Phys.* **1954**, *22*, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. *J. Chem. Phys.* **1967**, *47*, 2856-2861), have some serious shortcomings: (i) the *n*th-order term of the HTSE is involved with reference fluid distribution functions of order up to 2*n*, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence speed of the CPSE in both the HS and non HS perturbation schemes is certainly faster than that of the HTSE and the HS perturbation scheme. (iii) We illustrate applications of the CPSE TPT in both the HS and non HS perturbation schemes in calculating thermodynamic properties of various coarse-grained potential function models and as input information of other liquid state theories such as a classical density functional theory(DFT), and also discuss, in the framework of classical DFT, the potential of our CPSE scheme in several typical problems of chemical physics interest. (iv) Finally, we consider several topics which are possibly expected to be settled in the immediate future and possible integration with other liquid state theory frameworks aiming to solve problems in complex fluids in both bulk and inhomogeneous states.

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