3,5-CONTRACTED SCHRODINGER-EQUATION - DETERMINING QUANTUM ENERGIES AND REDUCED DENSITY-MATRICES WITHOUT WAVE-FUNCTIONS

Through the 3,5-contracted Schrodinger equation (3,5-CSchE) quantum en ergies and 3-particle reduced density matrices (3-RDMs) are determined directly without wave functions. Since the 3,5-CSchE involves the 5-R DM, its solution is indeterminate without N-representability condition s. However, the indeterminacy of the 3,5-CSchE may be removed through a reconstruction strategy for building the 4- and 5-RDMs from the 3-RD M. We present a systematic procedure for obtaining corrections for Val demoro's reconstruction functionals from two complementary approaches, the particle-hole duality and the theory of cumulants. With the cumul ants we are able to demonstrate that we have obtained all terms in the reconstruction functionals which may be written as antisymmetric prod ucts of the lower rdms. The cumulants allow us to understand the recon struction functionals in terms of a renormalized many-body perturbatio n theory. The reconstruction functionals also lead to a natural genera lization of Wick's theorem for evaluating expectation values of fermio nic annihilation and creation operators with respect to correlated ref erence states. Previous work [Phys. Rev. A 57, 4219 (1998)] has explor ed the determination of correlation energy and 2-RDMs through the 2,4- CSchE, also known as the density equation. Because the reconstruction functionals employed with the 3,5-CSchE depend only on the antisymmetr ic products of lower RDMs in constrast to those used with the 2,4-CSch E, the 3,5-CSchE method presented here does not require the solution o f systems of linear equations during reconstruction or the storage of the reconstructed RDMs. Application of the 3,5-CSchE technique to a qu asi-spin model generates ground-state energies and 2-RDMs similar in a ccuracy to single-double configuration interaction (SDCl). We employ a simple iterative procedure for the solution of the 3,5-CSchE without traditional diagonalization. The CSchE techniques offer an approximate solution of the N-representability problem and a new approach to elec tron correlation. (C) 1998 John Wiley & Sons, Inc.