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Scaling behavior of ground‐state energy cluster expansion for linear polyenes
Author(s) -
Griffin L. L.,
Wu Jian,
Klein D. J.,
Schmalz T. G.,
Bytautas L.
Publication year - 2004
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20300
Subject(s) - limit (mathematics) , ground state , scaling , statistical physics , coupled cluster , convergence (economics) , cluster expansion , chemistry , cluster (spacecraft) , physics , ab initio , computational chemistry , quantum mechanics , mathematics , geometry , mathematical analysis , molecule , computer science , economic growth , economics , programming language
Ground‐state energies for linear‐chain polyenes are additively expanded in a sequence of terms for chemically relevant conjugated substructures of increasing size. The asymptotic behavior of the large‐substructure limit (i.e., high‐polymer limit) is investigated as a means of characterizing the rapidity of convergence and consequent utility of this energy cluster expansion. Consideration is directed to computations via: simple Hückel theory, a refined Hückel scheme with geometry optimization, restricted Hartree–Fock self‐consistent field (RHF‐SCF) solutions of fixed bond‐length Parisier–Parr–Pople (PPP)/Hubbard models, and ab initio SCF approaches with and without geometry optimization. The cluster expansion in what might be described as the more “refined” approaches appears to lead to qualitatively more rapid convergence: exponentially fast as opposed to an inverse power at the simple Hückel or SCF–Hubbard levels. The substructural energy cluster expansion then seems to merit special attention. Its possible utility in making accurate extrapolations from finite systems to extended polymers is noted. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005