- Title
- New alternatives to the Lennard-Jones potential
- Creator
- Moscato, Pablo; Haque, Mohammad Nazmul
- Relation
- ARC.DP200102364 http://purl.org/au-research/grants/arc/DP200102364
- Relation
- Scientific Reports Vol. 14, no. 11169
- Publisher Link
- http://dx.doi.org/10.1038/s41598-024-60835-8
- Publisher
- Nature Publishing Group
- Resource Type
- journal article
- Date
- 2024
- Description
- We present a new method for approximating two-body interatomic potentials from existing ab initio data based on representing the unknown function as an analytic continued fraction. In this study, our method was first inspired by a representation of the unknown potential as a Dirichlet polynomial, i.e., the partial sum of some terms of a Dirichlet series. Our method allows for a close and computationally efficient approximation of the ab initio data for the noble gases Xenon (Xe), Krypton (Kr), Argon (Ar), and Neon (Ne), which are proportional to r-6 and to a very simple depth=1 truncated continued fraction with integer coefficients and depending on n-r only, where n is a natural number (with n=13 for Xe, n=16 for Kr, n=17 for Ar, and n=27 for Neon). For Helium (He), the data is well approximated with a function having only one variable n-r with n=31 and a truncated continued fraction with depth=2 (i.e., the third convergent of the expansion). Also, for He, we have found an interesting depth=0 result, a Dirichlet polynomial of the form k16-r+k248-r+k372-r (with k1,k2,k3 all integers), which provides a surprisingly good fit, not only in the attractive but also in the repulsive region. We also discuss lessons learned while facing the surprisingly challenging non-linear optimisation tasks in fitting these approximations and opportunities for parallelisation.
- Subject
- Lennard-Jones potential; Dirichlet polynomial; analytic continued fraction; symbolic regression; Memetic algorithm
- Identifier
- http://hdl.handle.net/1959.13/1504857
- Identifier
- uon:55584
- Identifier
- ISSN:2045-2322
- Rights
- © Crown 2024. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Language
- eng
- Full Text
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