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Normalized irreducible tensorial matrix expansions applied to an effective sp ‐type Hamiltonian for the PES of water
Author(s) -
Ellzey M. L.
Publication year - 1991
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.560400307
Subject(s) - basis (linear algebra) , hamiltonian (control theory) , matrix (chemical analysis) , mathematics , chemistry , geometry , mathematical optimization , chromatography
Abstract Any matrix can be expanded on a basis of SU(2) normalized irreducible tensorial matrices, NITM , defined in terms of 3‐ j symbols or coupling coefficients of SU (2). The NITM transform under rotations according to Wigner's matrices. If one dimension of an NITM is odd and the other even, the tensor has half‐integer rank. A simple NITM basis consists of all NITM having the same numbers of rows and columns as the expanded matrix. A compound NITM basis consists of two or more simple bases, each spanning a corresponding block in the expanded matrix. The choice of NITM basis for expanding an effective Hamiltonian matrix is a crucial step in formulating a model. To illustrate the use of a compound NITM basis, including nonsquare NITM , an effective sp ‐type overlap‐free superposition Hamiltonian is constructed and applied to the photoelectron ionization potential spectrum of water.