Single-random-valley approximation in vibration-transit theory of liquid dynamics

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Materials Science

Background:

• Current theories struggle to calculate thermodynamic properties of elemental monatomic liquids without adjustable parameters.
• Vibration-transit theory proposes that random potential energy valleys dominate liquid behavior above melting.
• This hypothesis suggests these valleys are uniform, simplifying statistical mechanics calculations.

Purpose of the Study:

• To test the vibration-transit theory's single random valley approximation for calculating liquid thermodynamic properties.
• To validate the theory's applicability to elemental monatomic liquids using a realistic interatomic potential.
• To assess the accuracy of the approximation for liquid sodium (Na) at various temperatures.

Main Methods:

• Employed molecular dynamics simulations for liquid Na (N=500) at temperatures from 0.90Tm to 3.31Tm.
• Utilized steepest descent quenches to identify potential energy valleys.
• Calculated six potential parameters (potential energy, five principal moments of vibrational frequency distribution) for each structure.

Main Results:

• Observed temperature-independent means and small standard deviations for all potential parameters.
• Results align with the hypothesis of random valley uniformity in the thermodynamic limit and finite-N broadening.
• The single random valley approximation showed negligible expected errors for entropy (0.1%) and internal energy (0.5%) for liquid Na.

Conclusions:

• The single random valley approximation provides accurate thermodynamic property calculations for elemental liquids.
• The theory is validated for liquid Na, demonstrating its potential for broader applications.
• Findings suggest the approximation may extend to more complex systems beyond elemental liquids.