### Abstract

We use the finite size scaling method to study the critical points, points of non-analyticity, of the ground state energy as a function of the coupling parameters in the Hamiltonian. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given molecular Hamiltonian. To illustrate this approach, we give detailed calculations for systems of one electron and two nuclear centres. Z^{+}e^{-}Z^{+}. Within the Born-Oppenheimer approximation, there is no critical point, but without the approximation the system exhibits a critical point at Z = Z_{c} = 1.228 279 when the nuclear charge, Z, varies. We show also that the dissociation occurs in a first-order phase transition and calculate the various related critical exponents. The possibility of generalizing this approach to larger molecular systems using Gaussian basis sets is discussed.

Original language | English |
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Pages (from-to) | 1485-1493 |

Number of pages | 9 |

Journal | Molecular Physics |

Volume | 98 |

Issue number | 19 |

DOIs | |

Publication status | Published - 10 Oct 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Molecular Physics*,

*98*(19), 1485-1493. https://doi.org/10.1080/002689700419716

**Finite size scaling for critical parameters of simple diatomic molecules.** / Shi, Qicun; Kais, Sabre.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 98, no. 19, pp. 1485-1493. https://doi.org/10.1080/002689700419716

}

TY - JOUR

T1 - Finite size scaling for critical parameters of simple diatomic molecules

AU - Shi, Qicun

AU - Kais, Sabre

PY - 2000/10/10

Y1 - 2000/10/10

N2 - We use the finite size scaling method to study the critical points, points of non-analyticity, of the ground state energy as a function of the coupling parameters in the Hamiltonian. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given molecular Hamiltonian. To illustrate this approach, we give detailed calculations for systems of one electron and two nuclear centres. Z+e-Z+. Within the Born-Oppenheimer approximation, there is no critical point, but without the approximation the system exhibits a critical point at Z = Zc = 1.228 279 when the nuclear charge, Z, varies. We show also that the dissociation occurs in a first-order phase transition and calculate the various related critical exponents. The possibility of generalizing this approach to larger molecular systems using Gaussian basis sets is discussed.

AB - We use the finite size scaling method to study the critical points, points of non-analyticity, of the ground state energy as a function of the coupling parameters in the Hamiltonian. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given molecular Hamiltonian. To illustrate this approach, we give detailed calculations for systems of one electron and two nuclear centres. Z+e-Z+. Within the Born-Oppenheimer approximation, there is no critical point, but without the approximation the system exhibits a critical point at Z = Zc = 1.228 279 when the nuclear charge, Z, varies. We show also that the dissociation occurs in a first-order phase transition and calculate the various related critical exponents. The possibility of generalizing this approach to larger molecular systems using Gaussian basis sets is discussed.

UR - http://www.scopus.com/inward/record.url?scp=0034634010&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034634010&partnerID=8YFLogxK

U2 - 10.1080/002689700419716

DO - 10.1080/002689700419716

M3 - Article

VL - 98

SP - 1485

EP - 1493

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 19

ER -