VIBRATIONAL LEVELS FOR A PAIR OF POTENTIAL CURVES EXHIBITING A SMALL AVOIDED CROSSING.
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Date
1966
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Ohio State University
Abstract
Two potential energy curves of a diatomic molecule having the same symmetry do not intersect, but undergo a so-called avoided crossing. The effect of such an avoided crossing on the vibrational and rotational energy levels for the $B^{2}H$ and $C^{2}H$ states of the NO molecule has been thoroughly characterized experimentally by E. Miescher and co-workers. The problem can be investigated theoretically in two ways: (1) The vibrational energy levels and wave functions for the two potential wells can be calculated assuming no avoided crossing (i.e. no interaction). The ``avoided-crossing matrix elements'' can then be calculated in the ``no-interaction basis set'', and the Hamiltonian matrix can be diagonalized to obtain values for the experimentally observed energy levels. This approach had to be rejected, because it was found that an extremely large basis set of unperturbed vibrational wave functions, including some from the continuum, was needed for each potential well in order to get meaningful results. (2) The second approach involves solving directly, by numerical integration, the pair of coupled, Schr\""{o}dinger-like equations characterizing the vibrational problem associated with two interacting wells. A Computer program has been written which uses Numerov-type integration of the wave equation and which corrects after each iteration in a manner suggested by L. Fox. At the time of writing the abstract the program was not fully operational, but it is hoped that information on the course of the vibrational and rotational energy levels as well as on the form of the vibrational wave functions in the neighborhood of the avoided crossing will be available by the time of the meeting.
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Author Institution: Division of Pure Physics, National Research Council; Department of Chemistry, Carleton University