Potential-energy-landscape-based extended van der Waals equation.

Area of Science:

• Thermodynamics and Statistical Mechanics
• Computational Chemistry
• Physical Chemistry

Background:

• Inherent structures (IS) represent local minima on a potential energy landscape for N-atom systems.
• A prior formulation by Stillinger established an exact IS framework for thermodynamics.
• Investigating the implications of IS for the equation of state is crucial for understanding fluid behavior.

Purpose of the Study:

• To explore the equation of state derived from the inherent structure formulation of thermodynamics.
• To determine if an extended van der Waals (vdW) equation can capture complex fluid properties.
• To simulate and analyze key IS parameters in a Lennard-Jones fluid.

Main Methods:

• Analyzing the conditions under which the van der Waals equation holds using density-dependent coefficients.
• Introducing a "landscape" contribution to pressure at lower temperatures.
• Simulating inherent structure energy, distribution width, and the "top of the landscape" temperature (TOL) across a wide density range.

Main Results:

• The van der Waals equation with density-dependent coefficients is valid when averaged inherent structure energy approaches its high-temperature plateau.
• An extended vdW equation incorporating landscape contributions exhibits waterlike density anomalies and flat isotherms.
• Simulations in Lennard-Jones fluid provide data for an explicit equation of state, showing good agreement with critical point parameters.

Conclusions:

• The inherent structure formulation provides a robust framework for developing advanced equations of state.
• The extended van der Waals equation derived from IS successfully reproduces key features of real fluid behavior.
• This approach offers a physically grounded method for modeling complex thermodynamic properties.