### Abstract

Perturbation theory is used to perform non-iterative calculations of energy eigenvalues of the coupled ordinary differential equations that result from imposing separability assumptions in terms of normal coordinates on vibrational wavefunctions. Various model Hamiltonians with 2 or 3 coupled normal modes are studied and the increase of computational cost with the number of degrees of freedom is analysed. Quadratic Padé approximants of the perturbation expansions are rapidly convergent, and directly yield complex numbers for resonance eigen-values. For a 3-mode system, results are obtained within partial separability assumptions, with a pair of modes left coupled. Large-order perturbation theory with partial separability is suggested as an alternative to low-order exact perturbation theory.

Original language | English |
---|---|

Pages (from-to) | 477-484 |

Number of pages | 8 |

Journal | Molecular Physics |

Volume | 93 |

Issue number | 3 |

Publication status | Published - 20 Feb 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Molecular Physics*,

*93*(3), 477-484.

**Self-consistent field perturbation theory of molecular vibrations.** / Sergeev, Alexei V.; Goodson, David Z.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 93, no. 3, pp. 477-484.

}

TY - JOUR

T1 - Self-consistent field perturbation theory of molecular vibrations

AU - Sergeev, Alexei V.

AU - Goodson, David Z.

PY - 1998/2/20

Y1 - 1998/2/20

N2 - Perturbation theory is used to perform non-iterative calculations of energy eigenvalues of the coupled ordinary differential equations that result from imposing separability assumptions in terms of normal coordinates on vibrational wavefunctions. Various model Hamiltonians with 2 or 3 coupled normal modes are studied and the increase of computational cost with the number of degrees of freedom is analysed. Quadratic Padé approximants of the perturbation expansions are rapidly convergent, and directly yield complex numbers for resonance eigen-values. For a 3-mode system, results are obtained within partial separability assumptions, with a pair of modes left coupled. Large-order perturbation theory with partial separability is suggested as an alternative to low-order exact perturbation theory.

AB - Perturbation theory is used to perform non-iterative calculations of energy eigenvalues of the coupled ordinary differential equations that result from imposing separability assumptions in terms of normal coordinates on vibrational wavefunctions. Various model Hamiltonians with 2 or 3 coupled normal modes are studied and the increase of computational cost with the number of degrees of freedom is analysed. Quadratic Padé approximants of the perturbation expansions are rapidly convergent, and directly yield complex numbers for resonance eigen-values. For a 3-mode system, results are obtained within partial separability assumptions, with a pair of modes left coupled. Large-order perturbation theory with partial separability is suggested as an alternative to low-order exact perturbation theory.

UR - http://www.scopus.com/inward/record.url?scp=0542424842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0542424842&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0542424842

VL - 93

SP - 477

EP - 484

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 3

ER -