{"paper":{"title":"From Sticky-Hard-Sphere to Lennard-Jones-Type Clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.atm-clus","authors_text":"David J. Wales, Lukas Trombach, Peter Schwerdtfeger, Robert S. Hoy","submitted_at":"2018-01-31T03:42:22Z","abstract_excerpt":"A relation $\\mathcal{M}_{\\mathrm{SHS}\\to\\mathrm{LJ}}$ between the set of non-isomorphic sticky hard sphere clusters $\\mathcal{M}_\\mathrm{SHS}$ and the sets of local energy minima $\\mathcal{M}_{LJ}$ of the $(m,n)$-Lennard-Jones potential $V^\\mathrm{LJ}_{mn}(r) = \\frac{\\varepsilon}{n-m} [ m r^{-n} - n r^{-m} ]$ is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both $m$ and $n$, and increases exponentially with increasing cluster size $N$ for $N \\gtrsim 10$. While the map from $\\mathcal{M}_\\mathrm{SHS}\\to \\mathcal{M}_{\\mathrm{SHS}\\to\\mathrm{LJ}}$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10290","kind":"arxiv","version":2},"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"}