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Valence bond approach exploiting Clifford algebra realization of Rumer–Weyl basis
Author(s) -
Li Xiangzhu,
Paldus Josef
Publication year - 1992
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.560410112
Subject(s) - basis set , hamiltonian (control theory) , unitary group , basis (linear algebra) , clifford algebra , mathematics , unitary state , basis function , quantum mechanics , algebra over a field , computational chemistry , physics , pure mathematics , chemistry , geometry , molecule , mathematical optimization , political science , law
A detailed algorithm is described that enables an implementation of a general valence bond ( VB ) method using the Clifford algebra unitary group approach ( CAUGA ). In particular, a convenient scheme for the generation and labeling of classical Rumer–Weyl basis (up to a phase) is formulated, and simple rules are given for the evaluation of matrix elements of unitary group generators, and thus of any spin‐independent operator, in this basis. The case of both orthogonal and nonrothogonal atomic orbital bases is considered, so that the proposed algorithm can also be exploited in molecular orbital configuration interaction calculations, if desired, enabling a greater flexibility for N ‐electron basis‐set truncation than is possible with the standard Gel'fand–Tsetlin basis. Finally, an exploitation of this formalism for the VB method, based on semiempirical Pariser–Parr–Pople ( PPP )‐type Hamiltonian and nonorthogonal overlap‐enhanced atomic orbital basis, and its computer implementation, enabling us to carry out arbitrarily truncated or full VB calculations, is described in detail.