Large-scale semidefinite programs in electronic structure calculation

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...

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Bibliographic Details
Published inMathematical programming Vol. 109; no. 2-3; p. 553
Main Authors Fukuda, Mituhiro, Braams, Bastiaan J, Nakata, Maho, Overton, Michael L, Percus, Jerome K, Yamashita, Makoto, Zhao, Zhengji
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.03.2007
Subjects
Accuracy
Chemistry
Computer science
Eigenvalues
Electrons
Inequality
Mathematical functions
Mathematical programming
Matrix
Methods
Studies
Variables
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-006-0027-y