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.
Keywords: semidefinite programming, electron correlation, reduced density matrices, $N$-representability conditions
@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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {249--259},
year = {2007},
publisher = {EDP Sciences},
volume = {41},
number = {2},
doi = {10.1051/m2an:2007021},
mrnumber = {2339627},
zbl = {1135.81378},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2007021/}
}
TY - JOUR AU - Mazziotti, David A. TI - First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 249 EP - 259 VL - 41 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2007021/ DO - 10.1051/m2an:2007021 LA - en ID - M2AN_2007__41_2_249_0 ER -
%0 Journal Article %A Mazziotti, David A. %T First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 249-259 %V 41 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2007021/ %R 10.1051/m2an:2007021 %G en %F 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: Modélisation mathématique et analyse numérique, Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 249-259. doi: 10.1051/m2an:2007021
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