Symmetry properties of natural orbitals and geminals I. Construction of spin‐ and symmetry‐adapted functions

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 ρ1 and ρ2 in irreducible tensor components is considered and the relations between the tensor components of ρ2 and the spin coupling functions introduced previously are established. The totally symmetric components ρ and ρ of ρ1 and ρ2 are of particular interest, because their eigenfunctions are the required symmetry‐adapted NSO'S and NSG'S, respectively.