Configuration interaction matrix elements for atoms using permutation group algebra | Zendy

Dinesha K. V. | Zendy; Hinze Juergen | Zendy

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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.

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