Pursuit ofN-representability for the contracted Schrödinger equation through density-matrix reconstruction

The solution of N-representability for the two-particle reduced density matrix (2-RDM) is intimately connected through the contracted Schrödinger equation 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 formula for building the 3-RDM from the 2-RDM which significantly improves the accuracy of the 3-RDM cumulant expansion. Calculations indicate that the improvement is better than that achieved by the correction of Nakatsuji and Yasuda (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 the present and NY reconstructions are shown to satisfy the particle-hole duality. Comparison of the reconstruction methods is made through several molecules LiH, ${\mathrm{BeH}}_2,$ ${\mathrm{BH}}_3,$ ${\mathrm{H}}_2\mathrm{O},$ and ${\mathrm{CH}}_4,$ as well as systems with more general pairwise correlation.