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

David A. Mazziotti

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 2, page 249-259
  • ISSN: 0764-583X

Abstract

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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.


How to cite

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Mazziotti, David A.. "First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules." ESAIM: Mathematical Modelling and Numerical Analysis 41.2 (2007): 249-259. <http://eudml.org/doc/249942>.

@article{Mazziotti2007,
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.
},
author = {Mazziotti, David A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Semidefinite programming; electron correlation; reduced density matrices; N-representability conditions.},
language = {eng},
month = {6},
number = {2},
pages = {249-259},
publisher = {EDP Sciences},
title = {First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules},
url = {http://eudml.org/doc/249942},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Mazziotti, David A.
TI - First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/6//
PB - EDP Sciences
VL - 41
IS - 2
SP - 249
EP - 259
AB - 
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.

LA - eng
KW - Semidefinite programming; electron correlation; reduced density matrices; N-representability conditions.
UR - http://eudml.org/doc/249942
ER -

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