### Abstract

It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large.

Original language | English (US) |
---|---|

Pages (from-to) | 553-580 |

Number of pages | 28 |

Journal | Mathematical Programming |

Volume | 109 |

Issue number | 2-3 |

DOIs | |

State | Published - Mar 2007 |

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### Keywords

- Computational chemistry
- Large-scale optimization
- N-representability
- Parallel computation
- Reduced density matrix
- Semidefinite programming relaxation

### ASJC Scopus subject areas

- Applied Mathematics
- Mathematics(all)
- Safety, Risk, Reliability and Quality
- Management Science and Operations Research
- Software
- Computer Graphics and Computer-Aided Design
- Computer Science(all)

### Cite this

*Mathematical Programming*,

*109*(2-3), 553-580. https://doi.org/10.1007/s10107-006-0027-y

**Large-scale semidefinite programs in electronic structure calculation.** / Fukuda, Mituhiro; Braams, Bastiaan J.; Nakata, Maho; Overton, Michael L.; Percus, Jerome K.; Yamashita, Makoto; Zhao, Zhengji.

Research output: Contribution to journal › Article

*Mathematical Programming*, vol. 109, no. 2-3, pp. 553-580. https://doi.org/10.1007/s10107-006-0027-y

}

TY - JOUR

T1 - Large-scale semidefinite programs in electronic structure calculation

AU - Fukuda, Mituhiro

AU - Braams, Bastiaan J.

AU - Nakata, Maho

AU - Overton, Michael L.

AU - Percus, Jerome K.

AU - Yamashita, Makoto

AU - Zhao, Zhengji

PY - 2007/3

Y1 - 2007/3

N2 - It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large.

AB - It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large.

KW - Computational chemistry

KW - Large-scale optimization

KW - N-representability

KW - Parallel computation

KW - Reduced density matrix

KW - Semidefinite programming relaxation

UR - http://www.scopus.com/inward/record.url?scp=33846664572&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846664572&partnerID=8YFLogxK

U2 - 10.1007/s10107-006-0027-y

DO - 10.1007/s10107-006-0027-y

M3 - Article

VL - 109

SP - 553

EP - 580

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 2-3

ER -