{"paper":{"title":"A Brief Review on Results and Computational Algorithms for Minimizing the Lennard-Jones Potential","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.DS","physics.chem-ph"],"primary_cat":"physics.comp-ph","authors_text":"Jiapu Zhang","submitted_at":"2010-12-30T06:30:03Z","abstract_excerpt":"The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of $N$ atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form  $f(x) = 4\\sum_{i=1}^N \\sum_{j=1,j<i}^N (\\frac{1}{\\tau_{ij}^6} - \\frac{1}{\\tau_{ij}^3} {subject to} x\\in \\mathbb{R}^n$, where $\\tau_{ij} = (x_{3i-2} - x_{3j-2})^2 + (x_{3i-1} - x_{3j-1})^2 + (x_{3i} - x_{3j})^2$, $(x_{3i-2},x_{3i-1},x_{3i})$ is the coordinates of atom $i$ in $\\mathbb{R}^3$, $i,j=1,2,...,N(\\geq 2 \\quad \\text{integer})$, and $n=3N$; however it is a challenging and difficult problem for ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0039","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}