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.
Fusing heterogeneous data for the calibration of molecular dynamics force fields using hierarchical Bayesian models
We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierar- chical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.
2017
- L. Kulakova, G. Arampatzis, P. Angelikopoulos, P. Hadjidoukas, C. Papadimitriou, and P. Koumoutsakos, “Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations,” Sci. Rep.-UK, vol. 7, iss. 1, p. 16576, 2017.