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Recurrence relations for matrix elements of few‐body correlated wave functions
Author(s) -
Harris Frank E.
Publication year - 2005
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.20682
Subject(s) - recursion (computer science) , wave function , basis (linear algebra) , matrix (chemical analysis) , complement (music) , recurrence relation , exponential function , function (biology) , pure mathematics , mathematics , quantum , quantum mechanics , physics , combinatorics , mathematical analysis , chemistry , algorithm , geometry , biochemistry , chromatography , complementation , evolutionary biology , biology , gene , phenotype
Abstract This article considers the matrix elements arising from the use of wave functions containing exponentials in all the interparticle distances. Special cases (with some vanishing parameters) correspond to the use of the Hylleraas basis. For the three‐body (sometimes called two‐electron) correlated wave function, we present new recurrence relations that complement the formula of Sack, Roothaan, and Kolos. One of these is a sum rule that could also be used for downward recursion; the other is suitable for recursion in the usual (upward) recursive process. Formulas connecting matrix elements in the four‐body (three‐electron) problem are also derived; their use confirms the recurrence relations recently published by Pachucki, Puchalski, and Remiddi for the Hylleraas basis and provides a new sum rule for matrix elements in the general correlated exponential basis. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005