Use of Gauss-Hermite Quadrature to Approximate the Asymptotic Behavior of Vibronic Resonance Wave Functions
Buenker
Robert J.
Prof. Dr.
Buenker, Robert J.
aut
Li
Yan
Li, Yan
aut
Liebermann
Heinz-Peter
Liebermann, Heinz-Peter
aut
2016-02-11
en
<p> Wave functions obtained employing a standard complex Hamiltonian matrix diagonalization
procedure are square-integrable and therefore cannot accurately describe the asymptotic character
of resonance solutions of the Schrödinger equation. The nature of this approximation is
investigated by means of explicit calculations which are based on diabatic RKR potentials for the
B<sup>1</sup>Σ<sup>+</sup>- D’<sup>1</sup>Σ<sup>+</sup> vibronic resonance states of the CO molecule. It is shown that expanding the basis
of complex harmonic oscillator functions gradually improves the description of the exact
resonance wave functions out to ever larger internuclear distances on the real axis before they
take on artificial bound-state characteristics due to the square-integrable character of the basis
functions. In order to solve the diagonalization problems for as many as 500 such basis
functions, it proves necessary to employ specialized numerical techniques such as Gauss-Hermite
quadrature to evaluate the required Hamiltonian matrix elements..
2015-07-13T10:19:29.422Z
2016-02-11T14:37:07.300Z
published
Pub