FORM OF SPINLESS FIRST-ORDER AND 2ND-ORDER DENSITY-MATRICES IN ATOMS AND MOLECULES, DERIVED FROM EIGEN FUNCTIONS OF S-2 AND S-Z

Many-electron theory of atoms and molecules starts out from a spin-ind ependent Hamiltonian H. In principle, therefore, one can solve for sim ultaneous eigenfunctions Psi of H and the spin operators S-2 and S-z. The fullest possible factorization into space and spin parts is here e xploited to construct the spinless second-order density matrix Gamma, and hence also the first-order density matrix. After invoking orthonor mality of spin functions, and independently of the total number of ele ctrons, the factorized form of Psi is shown to lead to Gamma as a sum of only two terms for S = 0, a maximum of three terms for S = 1/2 and four terms for S greater than or equal to 1. These individual terms ar e characterized by their permutational symmetry. As an example, the gr ound state of the Be atom is discussed.