### Abstract

For a homonuclear diatomic molecule with a fixed nuclei, the input information in solving the Schrödinger equation for the ground-state energy at equilibrium is the atomic number Z of the constituent atoms plus the equilibrium bond length R_{e}. As the atomic energy is determined by Z and R_{e} → ∞, the dissociation energy D, conveniently divided by N^{2}, where N = 2Z is the total number of electrons, can be expressed as D N^{2} = d(Z^{2},e), where e is chosen from scaling arguments as e = R_{e}Z^{1/3}. Plots are presented for a variety of homonuclear diatomic molecules, plus some heteronuclear molecules, to show that over a significant range of d the dependence on the variable e is weak. This dependence appears to be reduced further, for the lightest molecules considered, if Z is replaced by the von Weizsäcker inhomogeneity kinetic energy. Some account is also taken of the fact that homonuclear diatomic molecules may not bind beyond some critical atomic number Z_{c}≥ 100.

Original language | English |
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Pages (from-to) | 53-60 |

Number of pages | 8 |

Journal | Journal of Molecular Structure: THEOCHEM |

Volume | 281 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 22 1993 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Computational Theory and Mathematics
- Atomic and Molecular Physics, and Optics

### Cite this

**Molecular dissociation energies characterized by number of electrons and equilibrium bond length.** / Nagy, A.; March, N. H.

Research output: Contribution to journal › Article

*Journal of Molecular Structure: THEOCHEM*, vol. 281, no. 1, pp. 53-60. https://doi.org/10.1016/0166-1280(93)80028-X

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TY - JOUR

T1 - Molecular dissociation energies characterized by number of electrons and equilibrium bond length

AU - Nagy, A.

AU - March, N. H.

PY - 1993/4/22

Y1 - 1993/4/22

N2 - For a homonuclear diatomic molecule with a fixed nuclei, the input information in solving the Schrödinger equation for the ground-state energy at equilibrium is the atomic number Z of the constituent atoms plus the equilibrium bond length Re. As the atomic energy is determined by Z and Re → ∞, the dissociation energy D, conveniently divided by N2, where N = 2Z is the total number of electrons, can be expressed as D N2 = d(Z2,e), where e is chosen from scaling arguments as e = ReZ1/3. Plots are presented for a variety of homonuclear diatomic molecules, plus some heteronuclear molecules, to show that over a significant range of d the dependence on the variable e is weak. This dependence appears to be reduced further, for the lightest molecules considered, if Z is replaced by the von Weizsäcker inhomogeneity kinetic energy. Some account is also taken of the fact that homonuclear diatomic molecules may not bind beyond some critical atomic number Zc≥ 100.

AB - For a homonuclear diatomic molecule with a fixed nuclei, the input information in solving the Schrödinger equation for the ground-state energy at equilibrium is the atomic number Z of the constituent atoms plus the equilibrium bond length Re. As the atomic energy is determined by Z and Re → ∞, the dissociation energy D, conveniently divided by N2, where N = 2Z is the total number of electrons, can be expressed as D N2 = d(Z2,e), where e is chosen from scaling arguments as e = ReZ1/3. Plots are presented for a variety of homonuclear diatomic molecules, plus some heteronuclear molecules, to show that over a significant range of d the dependence on the variable e is weak. This dependence appears to be reduced further, for the lightest molecules considered, if Z is replaced by the von Weizsäcker inhomogeneity kinetic energy. Some account is also taken of the fact that homonuclear diatomic molecules may not bind beyond some critical atomic number Zc≥ 100.

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U2 - 10.1016/0166-1280(93)80028-X

DO - 10.1016/0166-1280(93)80028-X

M3 - Article

VL - 281

SP - 53

EP - 60

JO - Computational and Theoretical Chemistry

JF - Computational and Theoretical Chemistry

SN - 2210-271X

IS - 1

ER -