Rahman's 1964 Liquid Argon Simulation Replication

Abstract

Replicated Rahman’s landmark 1964 molecular dynamics simulation of liquid argon using LAMMPS and Python. Recreated all eight original figures with excellent agreement: diffusion coefficients within 2%, structural peaks within 0.1 Å, and velocity distributions matching to three significant figures.

What I Built

Simulation Setup

Replicated Rahman’s exact conditions:

• System: 864 argon atoms at 94.4 K and 1.374 g/cm³ density
• Interaction: Lennard-Jones potential with Rahman’s parameters
• Improvements: Energy minimization, equilibration, and Velocity Verlet integration
• Production run: 10 ps in NVE ensemble, 5,001 trajectory frames

Analysis Tools

Built Python package to recreate every figure:

• Thermodynamic properties: Temperature control and Maxwell-Boltzmann distributions
• Structure: Radial distribution functions and static structure factors
• Dynamics: Mean square displacement and diffusion coefficients
• Correlations: Velocity autocorrelation and Van Hove correlation functions
• Non-Gaussian analysis: Deviations from simple diffusion

Key Results

Quantitative Agreement

Replication matched Rahman’s 1964 results closely:

Physical Validation

Simulation confirmed Rahman’s discoveries:

• Cage effect: Atoms trapped by neighbors bounce backward, creating negative velocity correlations
• Liquid structure: Short-range order persists, long-range order disappears
• Non-Gaussian motion: Atomic displacements deviate from random walks
• Structural evolution: Local coordination shells gradually “melt”

Technical Implementation

Modern Advantages

What took months on Rahman’s IBM mainframe now runs in under an hour:

• Better integration: Velocity Verlet with 2 fs timesteps vs Rahman’s 10 fs
• Improved equilibration: 500 ps NVT equilibration to melt the crystal
• Enhanced stability: Temperature control within 1% vs Rahman’s larger fluctuations
• Better statistics: 5,001 frames vs Rahman’s limited sampling

Implementation

Code follows modern best practices:

• Modular design: Separate modules for thermodynamics, dynamics, and structure
• Caching: Expensive calculations cached to prevent redundant computation
• Memory optimization: Large datasets processed in chunks
• Reproducibility: Single-command workflow from simulation to figures

Why This Matters

Historical Significance

Rahman’s 1964 paper invented molecular dynamics and discovered fundamental physics:

• First atomic-scale view of liquid dynamics
• Discovery of the cage effect in liquids
• Proof that computer simulation could reveal new physics

Method Validation

Quantitative agreement after 60 years validates:

• Rahman’s Lennard-Jones model accurately captures liquid argon
• His methodology was sound despite 1960s computing limitations
• Observed phenomena are real physics, not computational artifacts

Modern Relevance

This replication shows how classical physics connects to current methods:

• Molecular dynamics scaled from 864 atoms to millions, but core principles remain
• Modern tools enable better accuracy and faster computation
• Historical papers provide benchmarks for new approaches

Technical Notes

Work required careful attention to:

• Parameter conversion: Translating Rahman’s units to LAMMPS conventions
• Statistical analysis: Implementing error bars and correlation functions
• Visualization: Recreating Rahman’s plotting styles for comparison
• Documentation: Notes on methodology and implementation choices

Analysis package handles computational complexity while maintaining clarity about calculations and their purpose.

Impact

This replication:

• Educational: Shows how foundational physics translates to modern tools
• Methodological: Provides tested analysis code for liquid simulations
• Historical: Preserves and validates important computational physics history
• Practical: Demonstrates high accuracy with straightforward molecular dynamics

Work bridges six decades of computational physics while confirming that fundamental insights about matter remain unchanged.

Related Work

This replication is documented in detail in:

• Replicating Rahman’s 1964 Liquid Argon Simulation