- 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
- x
- Language
- eng
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