### Abstract

With the aim of developing linear-scaling methods, we discuss perturbative approaches designed to avoid diagonalization of large matrices. Approximate molecular orbitals can be corrected by perturbation theory, in course of which the Laplace transformation technique proposed originally by Almløf facilitates linear scaling. The first order density matrix P corresponding to a one-electron problem can be obtained from an iterative formula which preserves the trace and the idempotency of P so that no purification procedures are needed. For systems where P is sparse, the procedure leads to a linear scaling method. The algorithm is useful in course of geometry optimization or self-consistent procedures, since matrix P of the previous step can be used to initialize the density matrix iteration at the next step. Electron correlation methods based on the Hartree-Fock density matrix, without making reference to molecular orbitals are commented on.

Original language | English |
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Title of host publication | Challenges and Advances in Computational Chemistry and Physics |

Publisher | Springer |

Pages | 83-95 |

Number of pages | 13 |

DOIs | |

Publication status | Published - jan. 1 2011 |

### Publication series

Name | Challenges and Advances in Computational Chemistry and Physics |
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Volume | 13 |

ISSN (Print) | 2542-4491 |

ISSN (Electronic) | 2542-4483 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Chemistry (miscellaneous)
- Physics and Astronomy (miscellaneous)

### Cite this

*Challenges and Advances in Computational Chemistry and Physics*(pp. 83-95). (Challenges and Advances in Computational Chemistry and Physics; Vol. 13). Springer. https://doi.org/10.1007/978-90-481-2853-2_4

**Perturbative approximations to avoid matrix diagonalization.** / Surján, Péter R.; Szabados, A.

Research output: Chapter

*Challenges and Advances in Computational Chemistry and Physics.*Challenges and Advances in Computational Chemistry and Physics, vol. 13, Springer, pp. 83-95. https://doi.org/10.1007/978-90-481-2853-2_4

}

TY - CHAP

T1 - Perturbative approximations to avoid matrix diagonalization

AU - Surján, Péter R.

AU - Szabados, A.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - With the aim of developing linear-scaling methods, we discuss perturbative approaches designed to avoid diagonalization of large matrices. Approximate molecular orbitals can be corrected by perturbation theory, in course of which the Laplace transformation technique proposed originally by Almløf facilitates linear scaling. The first order density matrix P corresponding to a one-electron problem can be obtained from an iterative formula which preserves the trace and the idempotency of P so that no purification procedures are needed. For systems where P is sparse, the procedure leads to a linear scaling method. The algorithm is useful in course of geometry optimization or self-consistent procedures, since matrix P of the previous step can be used to initialize the density matrix iteration at the next step. Electron correlation methods based on the Hartree-Fock density matrix, without making reference to molecular orbitals are commented on.

AB - With the aim of developing linear-scaling methods, we discuss perturbative approaches designed to avoid diagonalization of large matrices. Approximate molecular orbitals can be corrected by perturbation theory, in course of which the Laplace transformation technique proposed originally by Almløf facilitates linear scaling. The first order density matrix P corresponding to a one-electron problem can be obtained from an iterative formula which preserves the trace and the idempotency of P so that no purification procedures are needed. For systems where P is sparse, the procedure leads to a linear scaling method. The algorithm is useful in course of geometry optimization or self-consistent procedures, since matrix P of the previous step can be used to initialize the density matrix iteration at the next step. Electron correlation methods based on the Hartree-Fock density matrix, without making reference to molecular orbitals are commented on.

KW - Density matrix

KW - Idempotency conserving iteration

KW - Laplace-transform

KW - Linear scaling

UR - http://www.scopus.com/inward/record.url?scp=84940282199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940282199&partnerID=8YFLogxK

U2 - 10.1007/978-90-481-2853-2_4

DO - 10.1007/978-90-481-2853-2_4

M3 - Chapter

AN - SCOPUS:84940282199

T3 - Challenges and Advances in Computational Chemistry and Physics

SP - 83

EP - 95

BT - Challenges and Advances in Computational Chemistry and Physics

PB - Springer

ER -