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First-order semidefinite programming for the two-electron treatment ofmany-electron atoms and molecules

Published online by Cambridge University Press:  16 June 2007

David A. Mazziotti
David A. Mazziotti*
Affiliation:
Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, IL 60637, USA. damazz@uchicago.edu
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Abstract


The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N-electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in the variational calculation of the 2-RDM require a special optimization known as a semidefinite programming. Development of first-order semidefinite programming for the 2-RDM method has reduced the computational costs of the calculation by orders of magnitude [Mazziotti, Phys. Rev. Lett.93 (2004) 213001]. The variational 2-RDM approach is effective at capturing multi-reference correlation effects that are especially important at non-equilibrium molecular geometries. Recent work on 2-RDM methods will be reviewed and illustrated with particular emphasis on the importance of advances in large-scale semidefinite programming.


Keywords

Semidefinite programmingelectron correlationreduced density matricesN-representability conditions.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 2: Special issue on Molecular Modelling , March 2007 , pp. 249 - 259
Copyright
© EDP Sciences, SMAI, 2007

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