Approximatingq-order reduced density matrices in terms of the lower-order ones. II. Applications
Francisco Colmenero, Carmela Valdemoro · Physical Review A · 1993
The general equation linking a q-order reduced density matrix (q-RDM) with the corresponding q-order hole reduced density matrix (q-HRDM) has been reported in the preceding paper [F. Colmenero, C. Perez del Valle, and C. Valdemoro, preceding paper, Phys. Rev. A 47, 971 (1993)]. In this equation, neither Kronecker \ensuremath{\delta} functions nor mixed products of elements of RDM's and HRDM's appear, and the part involving hole terms has the same structure as that involving particle terms. Recently [C. Valdemoro, Phys. Rev. A 45, 4462 (1992)], a similar equation for q=2 has been used to approximate the 2-RDM from the knowledge of the 1-RDM. Here, the 3-RDM and the 4-RDM are approximated by using the 2-RDM as an initial datum. The ultimate aim of this research is to develop an iterative method for solving the contracted form of the Schr\"odinger equation [L. Cohen and C. Frishberg, Phys. Rev. A 13, 927 (1976); H. Nakatsuji, ibid. 14, 41 (1976)]. A matrix form in the orbital representation of this equation is reported here. Finally, the second-order hypervirial equation, also in its matrix form, has been derived so that the quality of the results can be judged.