  The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD)
simulations and among the most widely used computational kernels in science.
The potential models atomistic attraction and repulsion with century old
prescribed parameters ($q=6, \; p=12$, respectively), originally related by a
factor of two for simplicity of calculations. We re-examine the value of the
repulsion exponent through data driven uncertainty quantification. We perform
Hierarchical Bayesian inference on MD simulations of argon using experimental
data of the radial distribution function (RDF) for a range of thermodynamic
conditions, as well as dimer interaction energies from quantum mechanics
simulations. The experimental data suggest a repulsion exponent ($p \approx
6.5$), in contrast to the quantum simulations data that support values closer
to the original ($p=12$) exponent. Most notably, we find that predictions of
RDF, diffusion coefficient and density of argon are more accurate and robust in
producing the correct argon phase around its triple point, when using the
values inferred from experimental data over those from quantum mechanics
simulations. The present results suggest the need for data driven recalibration
of the LJ potential across MD simulations.
