Employing the variational approach having the two-body reduced density matrix (RDM) as variables to compute the ground state energies of atomic-molecular systems has been a long time dream in electronic structure theory in chemical physics/physical chemistry. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large.
Research Report B-413, Dept. Mathematical and Computing Sciences, Tokyo Institute of Technology, February, 2005.