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Rigid bodies, made of smaller composite beads, are commonly used to simulate anisotropic particles with molecular dynamics or Monte Carlo methods. To accurately represent the particle shape and to obtain smooth and realistic effective pair interactions between two rigid bodies, each body may need to contain hundreds of spherical beads. Given an interacting pair of particles, traditional molecular dynamics methods calculate all the inter-body distances between the beads of the rigid bodies within a certain distance. For a system containing many anisotropic particles, these distance calculations are computationally costly and limit the attainable system size and simulation time. However, the effective interaction between two rigid particles should only depend on the distance between their center of masses and their relative orientation. Therefore, a function capable of directly mapping the center of mass distance and orientation to the interaction energy between the two rigid bodies would completely bypass inter-bead distance calculations. It is challenging to derive such a general function analytically for almost any non-spherical rigid body. In this study, we have trained neural nets, powerful tools to fit nonlinear functions to complex datasets, to achieve this task. The pair configuration (center of mass distance and relative orientation) is taken as an input, and the energy, forces, and torques between two rigid particles are predicted directly. We show that molecular dynamics simulations of cubes and cylinders performed with forces and torques obtained from the gradients of the energy neural-nets quantitatively match traditional simulations that use composite rigid bodies. Both structural quantities and dynamic measures are in agreement, while achieving up to 23 times speedup over traditional molecular dynamics, depending on hardware and system size. The method presented here can, in principle, be applied to any irregular concave or convex shape with any pair interaction, provided that sufficient training data can be obtained.
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This content will become publicly available on July 10, 2026
Approximation of Anisotropic Pair Potentials Using Multivariate Interpolation
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to mathematically formulate. Data-driven approaches for approximating anisotropic pair potentials have gained significant interest due to their flexibility and generality but often require large sets of training data, potentially limiting their feasibility when training data is computationally demanding to collect. Here, we investigate the use of multivariate polynomial interpolation to approximate anisotropic pair potentials from a limited set of prescribed particle configurations. We consider both standard Chebyshev polynomial interpolation as well as mixed-basis polynomial interpolation that uses trigonometric polynomials for coordinates along which the pair potential is known to be periodic. We exploit mathematical reasoning and physical knowledge to refine the interpolation domain and to design our interpolants. We test our approach on two-dimensional and three-dimensional model anisotropic nanoparticles, finding satisfactory approximations can be constructed in all cases.
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- Award ID(s):
- 2223084
- PAR ID:
- 10627955
- Publisher / Repository:
- American Chemical Society
- Date Published:
- Journal Name:
- The Journal of Physical Chemistry B
- Volume:
- 129
- Issue:
- 27
- ISSN:
- 1520-6106
- Page Range / eLocation ID:
- 6985-6996
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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