### Abstract

The energy of weakly overlapping group functions can be written as a series according to the powers of the (σ – I) matrix, where σ is the molecular overlap matrix and I is the unit matrix [1,2]. This power series of the energy is studied by investigating the importance of different order terms to obtain accurate energies and to predict equilibrium bond lengths. It is found that the series is truncated advantageously at an even‐order term. Approximate formulas for the first‐ and second‐order terms are proposed in order to reduce computational work. Numerical examples are presented to illustrate the effect of these terms to the energy. The relation of the projection energy to the approximate first‐ and second‐order terms is also discussed. It is found that, by choosing appropriate projection factors, the projection energy corrects the zeroth‐order energy more efficiently than does the first‐order term. The inclusion of the approximate second‐order term represents a slight improvement with respect to the use of the projection energy at the expense of some extra computation. © 1995 John Wiley & Sons, Inc.

Original language | English |
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Pages (from-to) | 485-493 |

Number of pages | 9 |

Journal | International Journal of Quantum Chemistry |

Volume | 53 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

**Approximate energy‐evaluating schemes for a system of weakly overlapping group functions.** / Ferenczy, G.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Approximate energy‐evaluating schemes for a system of weakly overlapping group functions

AU - Ferenczy, G.

PY - 1995

Y1 - 1995

N2 - The energy of weakly overlapping group functions can be written as a series according to the powers of the (σ – I) matrix, where σ is the molecular overlap matrix and I is the unit matrix [1,2]. This power series of the energy is studied by investigating the importance of different order terms to obtain accurate energies and to predict equilibrium bond lengths. It is found that the series is truncated advantageously at an even‐order term. Approximate formulas for the first‐ and second‐order terms are proposed in order to reduce computational work. Numerical examples are presented to illustrate the effect of these terms to the energy. The relation of the projection energy to the approximate first‐ and second‐order terms is also discussed. It is found that, by choosing appropriate projection factors, the projection energy corrects the zeroth‐order energy more efficiently than does the first‐order term. The inclusion of the approximate second‐order term represents a slight improvement with respect to the use of the projection energy at the expense of some extra computation. © 1995 John Wiley & Sons, Inc.

AB - The energy of weakly overlapping group functions can be written as a series according to the powers of the (σ – I) matrix, where σ is the molecular overlap matrix and I is the unit matrix [1,2]. This power series of the energy is studied by investigating the importance of different order terms to obtain accurate energies and to predict equilibrium bond lengths. It is found that the series is truncated advantageously at an even‐order term. Approximate formulas for the first‐ and second‐order terms are proposed in order to reduce computational work. Numerical examples are presented to illustrate the effect of these terms to the energy. The relation of the projection energy to the approximate first‐ and second‐order terms is also discussed. It is found that, by choosing appropriate projection factors, the projection energy corrects the zeroth‐order energy more efficiently than does the first‐order term. The inclusion of the approximate second‐order term represents a slight improvement with respect to the use of the projection energy at the expense of some extra computation. © 1995 John Wiley & Sons, Inc.

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U2 - 10.1002/qua.560530505

DO - 10.1002/qua.560530505

M3 - Article

AN - SCOPUS:84987157246

VL - 53

SP - 485

EP - 493

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 5

ER -