Correctness of certain integral equation theories for core-softened fluids

Area of Science:

• Statistical mechanics
• Computational physics
• Physical chemistry

Background:

• Integral equation theory provides a computationally efficient method for determining thermodynamic properties and phase diagrams.
• The Ornstein-Zernike equation requires approximations (closures) to solve for the relationship between direct (c(r)) and total (h(r)) correlation functions.
• Various closure approximations exist, each with distinct advantages and limitations.

Purpose of the Study:

• To evaluate the performance of four common integral equation closures: hyper-netted chain (HNC), Percus-Yevick (PY), Kovalenko-Hirata (KH), and Rogers-Young (RY).
• To establish the convergence domains for each closure when applied to a system with a core-softened potential.
• To compare the accuracy of these integral equation methods against established simulation techniques.

Main Methods:

• Application of HNC, PY, KH, and RY closures to the Ornstein-Zernike equation for a core-softened potential model.
• Determination of convergence criteria and domains for each closure approximation.
• Calculation of equilibrium thermodynamic properties including pair distribution functions, pressure, and excess energy.

Main Results:

• The study successfully established convergence domains for all tested integral equation closures.
• Calculated pair distribution functions, pressure, and excess energy were compared across the different closures.
• Results from integral equation methods were benchmarked against data from Monte Carlo and molecular dynamics simulations.

Conclusions:

• Integral equation theory, particularly with appropriate closures, offers a viable and efficient alternative to computationally intensive simulations for certain systems.
• The choice of closure significantly impacts the accuracy and convergence behavior of integral equation calculations.
• This work provides valuable insights into the applicability and limitations of different integral equation closures for systems with complex potentials.