Recent article by Prof. David Sherrill "Frontiers in electronic structure theory", J. Chem. Phys 132, 110902 (2010) lacks important citation on the direct determination of second-order reduced density matrix.
Following part is not appropriate.
> Fortunately, the discovery
> of additional N-representability constraints is now allowing
> accurate computations of molecular energies directly from
> linear functionals of the 2-RDM.
...cites Mazziotti's paper.
There are two important papers on this topic. One is ours,
J. Chem. Phys. 114, 8282 (2001)
maho nakata, hiroshi nakatsuji, masahiro ehara, mituhiro fukuda, kazuhide nakata, and katsuki fujisawa
"Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm."
We first formulated the RDM method - variational calculations with some N-rep. conditions - as the standard type semidefinite programming. It is not trivial that the RDM method can be formulated as the standard type SDP. Our finding was: 100-120% correlation energy for small molecules.
After that, at least Mazziotti, Braams, Canses, and Ayers are followed this approach. A lot of papers based on JCP 114, 8282 (2001) have been published. And the citation count by web of science is 105. Somehow, Mazziotti's papers do not cite appropriately (IMHO).
Second paper, which is not ours but this one is also very important.
J. Chem. Phys. 120, 2095 (2004)
They implemented other N-repeatability conditions called T1 and T2 conditions. With them, the results are comparable with CCSD(T) which is a breakthrough on this topic.
I believe above two articles are recent breakthrough on the RDM method.
Nakata Maho is a scientist and interested in reduced density matrix related theories, optimization and multiple precision arithmetics.