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Manuscript Title: A vibrational configuration interaction program for energies and resonance widths.
Authors: S.C. Tucker, T.C. Thompson, J.G. Lauderdale, D.G. Truhlar
Program title: VIBCI
Catalogue identifier: ABDY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 51(1988)233
Programming language: Fortran.
Computer: VAX11/780, OR CRAY-2.
Operating system: VMS 4.3, UNICOS 3.0.1.
RAM: 486K words
Word size: 64
Keywords: Molecular, Vibrational configuration interaction, Golden rule, Stabilization, Feshbach projection operators, Scaling, Harmonic oscillator functions, Resonance width.
Classification: 16.3.

Nature of problem:
The purpose of this program is to calculate energies and widths of vibrational resonances in two-dimensional systems. As detailed previously, we use stabilization to find an approximate resonance function and resonance energy, a Feshbach projection operator formalism to find a representative "continuum" function, and a golden-rule formalism to calculate the width.

Solution method:
The Hamiltonian is expanded in a direct product basis of harmonic oscillator functions. The harmonic oscillator functions contain a non- linear scale factor. We diagonialize the Hamiltonian repeatedly as a function of this scale factor; this enables us to associate one eigenvalue, which is stable with respect to this variation, with the resonance energy. The eigenfunction associated with this root will vary somewhat as a function of scale factor. We let this eigenfunction, in the basis in which it is most localized, represent the resonance function Psi res. We define a Fesbach-type projection operator P, and we diagonialize the matrix Delta = PHP in another series of direct product harmonic oscillator basis sets. Here we consider the basis set in which there is an eigenfunction which has an eigenvalue equal to the resonance energy and we let this eigenfunction represent the continuum function, Chi. This basis will differ by a nonlinear scale factor from that in which the resonance function was defined. Thus, calculating the width from the golden-rule formalism involves the evaluation of the integral <Psi res|H| Chi>, where PSi res and Chi are given as linear combinations of direct product harmonic oscillator functions having different nonlinear scale factors.

The potential must be local, and the number of dimensions is restricted to two. Modifications to include boundary conditions on the "continuum" functions Chi are required to calculate accurate widths for resonances having more than one open channel.

Unusual features:
It contains two calls to MXM, a highly vectorized Cray matrix multiply routine. Run times will be affected by the efficiency of other matrix multiply routines that may be substituted.

Running time:
The total running time for the test run of all three steps (N=90) is 6 seconds on a 1-processor Cray-2, for which most of the calculation runs in vector mode. For large enough N, where N is the number of product basis functions used, running time increases approximately as N**3.