Electronic structure calculations based on the two-body reduced density matrix, semidefinite programming, and three-index representability conditions

For nonrelativistic electrons in an external potential the ground state energy depends only upon the two-body reduced density matrix (2-RDM) and a lower-bound approximation may be obtained by minimizing the energy with respect to the 2-RDM subject to some representability conditions. Work going back to the 1970s and the recent work [1] showed that by imposing the well-known $P$, $Q$, and $G$ conditions an accuracy is obtained that compares favorably to Hartree-Fock. In our work [2] we impose additional ``three-index'' representability conditions and demonstrate an accuracy that is fully competitive with CISD or CCSD(T) on the same model space for a variety of small molecules. The approximation has a well-defined solution - there are no local minima - and is size consistent. The poster will present further results and experience and will discuss remaining computational challenges. [1] Nakata, M.\ et al., J.\ Chem.\ Phys.\ 114 (2001) 8282--8292. [2] Zhao, Z.\ et al., J.\ Chem.\ Phys.\ 120 (2004) 2095--2104.