derived from Eigen functions of S-2 and S-z Form of spinless first- and second-order density matrices in atoms and molecules - Texas A&M University (TAMU) Scholar

Form of spinless first- and second-order density matrices in atoms and molecules, derived from Eigen functions of S-2 and S-z
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Many-electron theory of atoms and molecules starts out from a spin-independent Hamiltonian H. In principle, therefore, one can solve for simultaneous eigenfunctions of H and the spin operators S2 and Sz. The fullest possible factorization into space and spin parts is here exploited to construct the spinless second-order density matrix , 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 is shown to lead to F 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, the ground state of the Be atom is discussed.