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 -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.
@article{M2AN_2007__41_2_249_0,
author = {Mazziotti, David A.},
title = {First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {41},
year = {2007},
pages = {249-259},
doi = {10.1051/m2an:2007021},
mrnumber = {2339627},
zbl = {1135.81378},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2007__41_2_249_0}
}
Mazziotti, David A. First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) pp. 249-259. doi : 10.1051/m2an:2007021. http://gdmltest.u-ga.fr/item/M2AN_2007__41_2_249_0/
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