The oLJ13_N13IC Cluster Is the Global Minimum Cluster of Lennard Jones' Potential for 13 Particles

EasyChair Preprint 9385

Abstract

The oLJ13_N13IC is the name of the minimal icosahedral cluster with 13 particles where "oLJ" states that it is the global minimum for the Lennard Jones potential, and the suffix "N13IC" represents the family of the particle-centered icosahedral lattice. It is well known from the early work M. R. Hoare and P. Pal (1975, Physical cluster mechanics: statistical thermodynamics and nucleation theory for monatomic systems) and J. A. Northby (1987, Structure and binding of Lennard-Jones clusters: 13 ≤ n ≤ 147)) and has been found experimentally in xenon clusters (1981, Echt, et al.) and sodium clusters (2005, Haberland, et al.), and is related with so-called magic numbers. It has been considered as a plausible global minimum but not a true global minimum. As far as I know, this is the first formal proof of global optimization of it.

Except for the global optimal clusters of 2, 3 and 4 particles that satisfy the classic strong criterion of global optimality, the clusters with more particles are just putative global minimal clusters due to the lack of criteria or techniques that determine their global optimality.

The article proofs the global optimality for the oLJ13_N13IC cluster by using a novel discrete combinatorial approach on the Euler characteristic and a linear prediction of the good pair potential of Lennard Jones.

Keyphrases: Operational Research, Optimization, combinatorial optimization, discrete, formal methods, minimization, modelling, numerical methods

@booklet{EasyChair:9385,
  author    = {Carlos Barron-Romero},
  title     = {The oLJ13_N13IC Cluster Is the Global Minimum Cluster of Lennard Jones' Potential for 13 Particles},
  howpublished = {EasyChair Preprint 9385},
  year      = {EasyChair, 2022}}