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Discussion on the variable Wolfsberg–Helmholtz parameter, a new simplified Löwdin transformation and the characteristic structure of the transformed EHT Hamiltonian matrices
Author(s) -
CarbóDorca Ramon
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.20011
Subject(s) - hamiltonian (control theory) , eigenvalues and eigenvectors , helmholtz free energy , transformation (genetics) , mathematical physics , helmholtz equation , hamiltonian matrix , mathematics , matrix (chemical analysis) , quantum , physics , quantum mechanics , mathematical analysis , chemistry , symmetric matrix , mathematical optimization , biochemistry , chromatography , gene , boundary value problem
Three related problems are discussed: (1) the variable nature of the Wolfsberg–Helmholtz parameter and its relationship with the overlap eigenvalue range; (2) the possibility of deriving an efficient framework, describing a simplified Löwdin transformation to solve generalized secular equations; and (3) the structure of the transformed classical EHT Hamiltonian. This work shows how the simplified Löwdin transformation permits expression of the resulting transformed Hamiltonian elements by means of inward matrix products and total matrix sums. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004