Form of spinless first- and second-order density matrices in atoms and molecules, derived from eigenfunctions of S2 and Sz

Many-electron theory of atoms and molecules starts out from a spin-independent Hamiltonian H. In principle, therefore, one can solve for simultaneous eigenfunctions Ψ of Hand the spin operators S² and S_z. The fullest possible factorization into space and spin parts is here exploited to construct the spinless second-order density matrix Γ, and hence also the first-order density matrix. After invoking orthonormality of spin functions, and independently of the total number of electrons, the factorized form of Ψ is shown to lead to Γ as a sum of only two terms for S = 0, a maximum of three terms for S = 1/2 and four terms for S ≥ 1. These individual terms are characterized by their permutational symmetry. As an example, theground state of the Be atom is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.