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Manuscript Title: VANVLK: an algebraic manipulation program for canonical Van Vleck perturbation theory.
Authors: E.L. Sibert III
Program title: VANVLK
Catalogue identifier: ABDQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 51(1988)149
Programming language: Fortran.
Computer: VAX-8600.
Keywords: Canonical van vleck Perturbation theory, Vibrational coupling, Molecular, Vibrations.
Classification: 16.3.

Nature of problem:
VANVLK canonically transforms a Hamiltonian, expressed in normal form, to a new representation, where the solutions can be obtained using a significantly smaller basis set than is needed to obtain the solutions of the original representation. The information content is the same. This method allows considerable flexibilty in the choice of the final form of the Hamiltonian, and therefore alleviates the problems with divergences in perturbation expansions. The algebraic manipulation avoids the storage problems associated with matrix based techniques.

Solution method:
Canonical Van Vleck Perturbation theory is implemented in an operator framework, based on harmonic oscillator raising and lowering operators.

Restrictions:
The program is restricted to problems with fewer than ten degrees of freedom. The routine TERMS allocates the space required to carryout the algebraic manipulations. The time requirement is the main restriction.

Unusual features:
The array sizes for VANVLK are set up using TERMS.

Running time:
Case dependent. Transforming a nine degree of freedom problem to an effective block diagonal Hamiltonian through fourth order takes 160 minutes on a VAX-8600.