First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules
ESAIM: Modélisation mathématique et analyse numérique, Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 249-259.

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.

DOI : 10.1051/m2an:2007021
Classification : 90C22, 81Q05, 52A40
Mots-clés : semidefinite programming, electron correlation, reduced density matrices, $N$-representability conditions
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Mazziotti, David A. First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 249-259. doi : 10.1051/m2an:2007021. http://www.numdam.org/articles/10.1051/m2an:2007021/

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