{"paper":{"title":"The Green's Function for the H\\\"uckel (Tight Binding) Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Gilbert Strang, Ramis Movassagh, Roald Hoffmann, Yuta Tsuji","submitted_at":"2014-07-17T19:12:54Z","abstract_excerpt":"Applications of the H\\\"uckel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is also the Laplacian matrix plus twice the identity. In this paper, we analytically calculate the determinant and, when it exists, the inverse of this matrix in connection with the Green's function, $\\mathbf{G}$, of the $N\\times N$ H\\\"uckel matrix. A corollary is a closed form expression for a Harmonic sum (Eq. 12). We then extend the results to $d-$dimensional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4780","kind":"arxiv","version":4},"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"}