New alternatives to the Lennard-Jones potential.
Sci Rep
; 14(1): 11169, 2024 May 15.
Article
en En
| MEDLINE
| ID: mdl-38750117
ABSTRACT
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 d e p t h = 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 d e p t h = 2 (i.e., the third convergent of the expansion). Also, for He, we have found an interesting d e p t h = 0 result, a Dirichlet polynomial of the form k 1 6 - r + k 2 48 - r + k 3 72 - r (with k 1 , k 2 , k 3 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.
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1
Colección:
01-internacional
Base de datos:
MEDLINE
Idioma:
En
Revista:
Sci Rep
Año:
2024
Tipo del documento:
Article
País de afiliación:
Australia
Pais de publicación:
Reino Unido