Large-scale semidefinite programs in electronic structure calculation

• 成果类型: Article
• 署名作者: Fukuda, Mituhiro; Braams, Bastiaan J.; Nakata, Maho; Overton, Michael L.; Percus, Jerome K.; Yamashita, Makoto; Zhao, Zhengji
• 署名单位: Institute of Science Tokyo; Tokyo Institute of Technology; Emory University; University of Tokyo; New York University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0027-y
• 发表日期: 2007
• 页码: 553-580
• 关键词: reduced-density-matrix; molecular-orbital methods; variational calculation; gaussian expansions; linear inequalities; equation; 1st-order; optimization; APPROXIMATE; energies

摘要

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.