Large order dimensional perturbation theory for complex energy eigenvalues

Timothy C. Germann, Sabre Kais

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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.

Original languageEnglish
Pages (from-to)7739-7747
Number of pages9
JournalThe Journal of Chemical Physics
Issue number10
Publication statusPublished - 1 Jan 1993


ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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