Abstract
The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD) simulations and among the most widely used computational kernels in science. The LJ 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 propose the inference of the repulsion exponent through Hierarchical Bayesian uncertainty quantification We use experimental data of the radial distribution function and dimer interaction energies from quantum mechanics simulations. We find that the repulsion exponent p ≈ 6.5 provides an excellent fit for the experimental data of liquid argon, for a range of thermodynamic conditions, as well as for saturated argon vapour. Calibration using the quantum simulation data did not provide a good fit in these cases. However, values p ≈ 12.7 obtained by dimer quantum simulations are preferred for the argon gas while lower values are promoted by experimental data. These results show that the proposed LJ 6-p potential applies to a wider range of thermodynamic conditions, than the classical LJ 6-12 potential. We suggest that calibration of the repulsive exponent in the LJ potential widens the range of applicability and accuracy of MD simulations.
Highlights
The Lennard-Jones (LJ) potential is one of the centerpieces in Molecular Dynamics (MD) simulations, the key computational method for studying atomistic phenomena across Chemistry, Physics, Biology and Mechanics
We find that the most likely values for the LJ repulsive exponent for liquid argon are p ≈ 6.5, strongly differing from the value of p = 12 that is being used, while the gaseous argon is simulated best with the exponent p ≈ 12.7, much closer to the conventional one
We have performed a systematic study of the modified 6-p Lennard-Jones potential for liquid and gaseous argon using Hierarchical Bayesian inference with data from experiments and quantum mechanics simulations
Summary
The Lennard-Jones (LJ) potential is one of the centerpieces in Molecular Dynamics (MD) simulations, the key computational method for studying atomistic phenomena across Chemistry, Physics, Biology and Mechanics. Bayesian Uncertainty Quantification (UQ) employs experimental data and provides a probability distribution of the parameters. In cases where the data sets correspond to different inputs for the system, e.g. different thermodynamic conditions, the use of Hierarchical Bayesian (HB) methods provides a stable method for UQ9,10. The authors calibrated using pressure and viscosity data for various thermodynamic conditions and concluded that the exponent 12 is the best choice. We perform the HB inference for the LJ 6-12 and LJ 6-p parameters of argon based on experimental RDFs of liquid argon and saturated argon vapor for six different temperature and pressure pairs, as well as on one dataset www.nature.com/scientificreports/. We present a rigorous model selection process for the LJ 6-12 vs LJ 6-p potentials for each of the cases and perform robust posterior predictions for the diffusion coefficient and density
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