, Volume 109, Issue 2-3, pp 553-580

Large-scale semidefinite programs in electronic structure calculation

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Abstract

It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. 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.

In memory of Jos Sturm who made many contributions to the theory and practice of semidefinite programming, including the widely used SeDuMi software package, and whose tragic early death is a great loss to our community.
The work of Mituhiro Fukuda was primarily conducted at the Courant Institute of Mathematical Sciences, New York University.