### Abstract

Dimensional pertubation theory is applied to the calculation of complex energies for quasibound, or resonant, eigenstates of central potentials. Energy coefficients for an asymptotic expansion in powers of 1/K, where K= D+2l and D is the Cartesian dimensionality of space, are computed using an iterative matrix-based procedure. For effective potentials which contain a minimum along the real axis in the K→∞ limit, Hermite - Padé summation is employed to obtain complex eigenenergies from real expansion coefficients. For repulsive potentials, we simply allow the radial coordinate to become complex and obtain complex expansion coefficients. Results for ground and excited states are presented for squelched harmonic oscillator (V_{0}r ^{2}e^{-r}) and Lennard-Jones (12-6) potentials. Bound and quasibound rovibrational states for the hydrogen molecule are calculated from an analytic potential. We also describe the calculation of resonances for the hydrogen atom Stark effect by using the separated equations in parabolic coordinates. The methods used here should be readily extendable to systems with multiple degrees of freedom.

Original language | English |
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Pages (from-to) | 7739-7747 |

Number of pages | 9 |

Journal | The Journal of Chemical Physics |

Volume | 99 |

Issue number | 10 |

Publication status | Published - 1 Dec 1993 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*99*(10), 7739-7747.

**Large order dimensional perturbation theory for complex energy eigenvalues.** / Germann, Timothy C.; Kais, Sabre.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 99, no. 10, pp. 7739-7747.

}

TY - JOUR

T1 - Large order dimensional perturbation theory for complex energy eigenvalues

AU - Germann, Timothy C.

AU - Kais, Sabre

PY - 1993/12/1

Y1 - 1993/12/1

N2 - Dimensional pertubation theory is applied to the calculation of complex energies for quasibound, or resonant, eigenstates of central potentials. Energy coefficients for an asymptotic expansion in powers of 1/K, where K= D+2l and D is the Cartesian dimensionality of space, are computed using an iterative matrix-based procedure. For effective potentials which contain a minimum along the real axis in the K→∞ limit, Hermite - Padé summation is employed to obtain complex eigenenergies from real expansion coefficients. For repulsive potentials, we simply allow the radial coordinate to become complex and obtain complex expansion coefficients. Results for ground and excited states are presented for squelched harmonic oscillator (V0r 2e-r) and Lennard-Jones (12-6) potentials. Bound and quasibound rovibrational states for the hydrogen molecule are calculated from an analytic potential. We also describe the calculation of resonances for the hydrogen atom Stark effect by using the separated equations in parabolic coordinates. The methods used here should be readily extendable to systems with multiple degrees of freedom.

AB - Dimensional pertubation theory is applied to the calculation of complex energies for quasibound, or resonant, eigenstates of central potentials. Energy coefficients for an asymptotic expansion in powers of 1/K, where K= D+2l and D is the Cartesian dimensionality of space, are computed using an iterative matrix-based procedure. For effective potentials which contain a minimum along the real axis in the K→∞ limit, Hermite - Padé summation is employed to obtain complex eigenenergies from real expansion coefficients. For repulsive potentials, we simply allow the radial coordinate to become complex and obtain complex expansion coefficients. Results for ground and excited states are presented for squelched harmonic oscillator (V0r 2e-r) and Lennard-Jones (12-6) potentials. Bound and quasibound rovibrational states for the hydrogen molecule are calculated from an analytic potential. We also describe the calculation of resonances for the hydrogen atom Stark effect by using the separated equations in parabolic coordinates. The methods used here should be readily extendable to systems with multiple degrees of freedom.

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M3 - Article

VL - 99

SP - 7739

EP - 7747

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 10

ER -