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“Neglect of Diatomic Differential Overlap” in nonempirical quantum chemical orbital theories. II. A polynomial expansion for Δ −1/2 in terms of Legendre and Chebyshev polynomials
Author(s) -
Neymeyr Klaus,
Seelig Friedrich Franz
Publication year - 1995
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.560530509
Subject(s) - legendre polynomials , diatomic molecule , associated legendre polynomials , mathematics , chebyshev polynomials , legendre function , polynomial , matrix (chemical analysis) , approximation theory , differential (mechanical device) , mathematical analysis , gegenbauer polynomials , quantum mechanics , physics , chemistry , classical orthogonal polynomials , orthogonal polynomials , molecule , thermodynamics , chromatography
Several attempts to justify the Neglect of Diatomic Differential Overlap ( NDDO ) approximation in terms of a power series expansion for Δ −1/2 (Δ is the overlap matrix) have been made (cf. Part I). The new approach for attaining an optimal approximation of Δ −1/2 represented here transfers the problem of finding an optimal matrix polynomial to an approximation problem of real functions within the spectrum of Δ. Best approximations are derived by use of Legendre and Chebyshev polynomials. © 1995 John Wiley & Sons, Inc.