Pursuit of N-representability for the contracted Schrodinger equation through density-matrix reconstruction

The solution of N-representability for the two-particle reduced density mat rix (2-RDM) is intimately connected through the contracted Schrodinger equa tion with the problem of reconstructing the 3- and 4-RDM's from the 2-RDM [ D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998)]. We derive an explicit formu la for building the 3-RDM from the 2-RDM which significantly improves the a ccuracy of the 3-RDM cumulant expansion. Calculations indicate that the imp rovement is better than that achieved by the correction of Nakatsuji and Ya suda (NY) [Phys. Rev. Lett. 76, 1039 (1996); Phys. Rev. A 56, 2648 (1997)]. We also present a more efficient formulation of the NY correction. Both th e present and NY reconstructions are shown to satisfy the particle-hole dua lity. Comparison of the reconstruction methods is made through several mole cules LIH, BeH2 BH3, H2O, and CH4, as well as systems with more general pai rwise correlation. [S1050-2947(99)06811-0].