HPC Tier Module
Lennard-Jones Molecular Dynamics
Velocity-Verlet Lennard-Jones molecular dynamics with measured energy conservation as the trust verdict.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
The problem
Many-body trajectories are chaotic, so a long MD run cannot certify the exact microstate - yet engineers still need confidence that the simulation conserved the invariant a symplectic integrator is built to hold.
The local-first solution
This plugin runs N-particle Lennard-Jones dynamics with the velocity-Verlet integrator in a periodic minimum-image box in your browser, measures the max relative drift of total energy, and maps that residual to the trust ladder - certifying the conserved quantity, not the long-term microstate. Deterministic f64 math, nothing uploaded.
What it does
Lennard-Jones 12-6 pair potential and its exact analytic force
Velocity-Verlet symplectic, time-reversible integration with O(dt^2) bounded drift
Periodic boundary with minimum-image convention and a smooth shifted cutoff
Two-body validation anchor at r_min=2^(1/6) sigma where the force is exactly zero
Measured total-energy and total-momentum conservation diagnostics
GeoNum conditioning probe of the cancelling KE+PE energy summation
Honest scope
EXACT: the LJ potential/force algebra, velocity-Verlet update, minimum-image displacement, and conservation diagnostics in f64. Runs in reduced LJ units by default; mapping to a real substance uses dated eps/sig inputs (the argon preset cites Rahman 1964), all echoed back. NOT modeled: long-range tail corrections, thermostat/barostat (this is microcanonical NVE - temperature is reported, not controlled), neighbor lists (direct O(N^2), so N is kept modest), or electrostatics. A prototype, not production MD.
Authorities cited
- Lennard-Jones, J. E. (1924). On the Determination of Molecular Fields. II. From the Equation of State of a Gas. Proc. R. Soc. Lond. A 106(738), 463-477. DOI 10.1098/rspa.1924.0082 - the 12-6 pair potential U(r) = 4 eps[(sig/r)^12 - (sig/r)^6].
- Verlet, L. (1967). Computer Experiments on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Phys. Rev. 159(1), 98-103. DOI 10.1103/PhysRev.159.98 - the Verlet / velocity-Verlet integrator and the first LJ MD of liquid argon.
- Rahman, A. (1964). Correlations in the Motion of Atoms in Liquid Argon. Phys. Rev. 136(2A), A405-A411. DOI 10.1103/PhysRev.136.A405 - LJ-argon parameters eps/k_B = 120 K, sigma = 3.40 angstrom (the bundled argon preset; confirm for your substance).
- Allen, M. P. & Tildesley, D. J. (1987, 2nd ed. 2017). Computer Simulation of Liquids. Oxford University Press. DOI 10.1093/oso/9780198803195.001.0001 - minimum-image convention, periodic boundaries, potential truncation/shift, and the velocity-Verlet algorithm (Ch. 3-4).
- Frenkel, D. & Smit, B. (2002). Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed. Academic Press. ISBN 978-0-12-267351-1 - NVE microcanonical MD, energy conservation as the integrator-correctness diagnostic, reduced units.
- Swope, W. C., Andersen, H. C., Berens, P. H. & Wilson, K. R. (1982). A computer simulation method... J. Chem. Phys. 76(1), 637-649. DOI 10.1063/1.442716 - the explicit velocity-Verlet form used here.
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Run MD with conservation certified
Run the simulation in your browser with nothing uploaded, then route the energy-drift verdict and trajectory diagnostics into a Sandbox workspace or attach them to a Worklog case.