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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. [email protected]
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Abstract


The ground-state energy and properties of any many-electron atom ormolecule may be rigorously computed by variationally computing thetwo-electron reduced density matrix rather than the many-electronwavefunction. While early attempts fifty years ago to compute theground-state 2-RDM directly were stymied because the 2-RDM must beconstrained to represent an N-electron wavefunction, recentadvances in theory and optimization have made direct computation ofthe 2-RDM possible. The constraints in the variational calculationof the 2-RDM require a special optimization known as a semidefiniteprogramming. Development of first-order semidefinite programmingfor the 2-RDM method has reduced the computational costs of thecalculation by orders of magnitude [Mazziotti, Phys. Rev. Lett.93 (2004) 213001]. The variational 2-RDM approach is effective atcapturing multi-reference correlation effects that are especiallyimportant at non-equilibrium molecular geometries. Recent work on2-RDM methods will be reviewed and illustrated with particularemphasis on the importance of advances in large-scale semidefiniteprogramming.


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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