Large-scale semidefinite programs in electronic structure calculation

  • Authors:

  • Mituhiro Fukuda;Bastiaan J. Braams;Maho Nakata;Michael L. Overton;Jerome K. Percus;Makoto Yamashita;Zhengji Zhao

  • Affiliations:

  • Tokyo Institute of Technology, Department of Mathematical and Computing Sciences, 2-12-1-W8-29 Oh-okayama, 152-8552, Meguro-ku, Tokyo, Japan;Emory University, Department of Mathematics and Computer Science, 2-12-1-W8-29 Oh-okayama, 30322, Atlanta, GA, USA;The University of Tokyo, Department of Applied Chemistry, 7-3-1 Hongo, 113-8656, Bunkyo-ku, Tokyo, Japan;New York University, Department of Computer Science, Courant Institute of Mathematical Sciences, 7-3-1 Hongo, 10012, New York, NY, USA;New York University, Courant Institute of Mathematical Sciences and Department of Physics, 7-3-1 Hongo, 10012, New York, NY, USA;Kanagawa University, Department of Information Systems Creation, 3-27-1 Rokkakubashi, 221-8686, Kanagawa-ku, Yokohama-shi, Kanagawa, Japan;Lawrence Berkeley National Laboratory, High Performance Computing Research Department, 1 Cyclotron Road, Mail Stop 50F1650, 94720, Berkeley, CA, USA

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2007

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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.