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

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

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

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topMazziotti, 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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