Controlling the N - and S -representability of the second-order reduced density matrix: The doublet-state case

Abstract

A purification procedure that simultaneously corrects the N- and S-representability main defects of a second-order reduced density matrix (2RDM), second-order hole reduced density matrix (2HRDM), and second-order G matrix is presented here. In this purifying procedure, the generalized unitarily invariant second-order matrix decomposition [D. R. Alcoba, Int. J. Quantum Chem. 97, 776 (2004)] for the 2RDM and the 2HRDM as well as for the G matrix is combined with the S-representability conditions. In particular, here we will focus our attention on the RDMs corresponding to doublet states. We will thus explicitly give the S-representability conditions that a two-body correlation matrix has to satisfy when an N-electron system is in a doublet spin-state in the spin-component of maximum projection. Furthermore, as a consequence of the G-matrix spin properties (which directly affect the S-representability of the 2RDM), we show that a different contracting form for the 2RDM is possible. The numerical results presented in this work confirm the efficiency of our purifying procedure.