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Configuration interaction matrix elements for atoms using permutation group algebra
Author(s) -
Dinesha K. V.,
Hinze Juergen
Publication year - 1984
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.560260409
Subject(s) - permutation matrix , eigenvalues and eigenvectors , permutation group , unitary group , group (periodic table) , hamiltonian (control theory) , hamiltonian matrix , configuration interaction , angular momentum , matrix (chemical analysis) , irreducible representation , physics , unitary state , spin (aerodynamics) , algebra over a field , chemistry , quantum mechanics , permutation (music) , mathematics , pure mathematics , symmetric matrix , molecule , mathematical optimization , chromatography , acoustics , political science , law , thermodynamics
A procedure is described for the efficient evaluation of the energy matrix elements necessary for atomic configuration‐interaction calculations. With the orbital configurations of an N electron system in spin state S written as the irreducible representations [2 1/2 N − S , 1 2 S ] of the permutation group S ( N ), it is possible to evaluate readily the energy matrix elements of a spin‐free Hamiltonian expressed in terms of the generators of the unitary group. We show how the use of angular momentum ladder operators permits the effective generation of a basis of eigenstates of ℒ 2 , ℒ z as well as 2 and z , for which the energy matrix elements may be evaluated with ease.