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Symmetry properties of natural orbitals and geminals I. Construction of spin‐ and symmetry‐adapted functions
Author(s) -
McWeeny R.,
Kutzelnigg W.
Publication year - 1968
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.560020203
Subject(s) - atomic orbital , hamiltonian (control theory) , physics , eigenfunction , tensor (intrinsic definition) , symmetry (geometry) , quantum mechanics , symmetry group , spin (aerodynamics) , theoretical physics , eigenvalues and eigenvectors , mathematics , pure mathematics , mathematical optimization , geometry , thermodynamics , electron
Natural spin‐orbitals ( NSO ), natural spin‐geminals ( NSG ) and their spinless counterparts are not always adapted to the symmetry group of the Hamiltonian. Alternative orbitals and geminals that are always symmetry adapted and as close as possible to the NSO and NSG are defined and their properties are discussed. The expansion of the one‐ and two‐ particle density matrices ρ 1 and ρ 2 in irreducible tensor components is considered and the relations between the tensor components of ρ 2 and the spin coupling functions introduced previously are established. The totally symmetric components ρ 1 0and ρ 2 0of ρ 1 and ρ 2 are of particular interest, because their eigenfunctions are the required symmetry‐adapted NSO'S and NSG'S , respectively.