No abstract

The general theoretical background for solving approximately the contracted Schrodinger equation (CSchE) in a self-consistent (SC) way has recently been proposed [F. Colmenero and C. Valdemoro, Phys. Rev. A 47, 979 (1993)Here, a spin-free procedure is developed and the convergence of the sc iterative process is analyzed using as test cases the beryllium atom and four isoelectronic ions in their ground states. Damping and extrapolation procedures are employed to improve and accelerate the convergence. The results obtained are in very close agreement with those obtained by means of the full configuration-interaction (FCI) method.

The commutation-anticommutation relations of q-electron operators imply a set of N representability conditions [A. J. Coleman, Rev. Mod. Phys. 31, 668 (1963)]for the corresponding q-order reduced density matrices (q-RDM) [C. Valdemoro, An. Fis. 79, 95 (1983);in Structure, Interaction and Reactivity, edited by S. Fraga (Elsevier, Amsterdam, 1992)]. From these conditions, a general and closed-form relation is obtained here. In this equation the part involving RDM's has the same structure as that involving hole reduced density matrices. This relation is the basis of a method for approximating a q-RDM in terms of the r-RDM's [C. Valdemoro, Phys. Rev. A 45, 4462 (1992)] with r & q. The derivation of this relation can be simplified significantly by employing a graph method which is described here. These graphs are in a one-to-one correspondence with the elements of the symmetric group of permutations.