Energy Transfer in Molecular Collisions

Author: Riley, Merle Eugene

Year: 1968

Degree: Dissertation (Ph.D.)

Advisor: Kuppermann, Aron

Committee Member: Unknown, Unknown

Option: Chemistry

DOI: 10.7907/76fq-q631

Abstract

Two general, numerically exact, quantum mechanical methods have been developed for the calculation of energy transfer in molecular collisions. The methods do not treat electronic transitions because of the exchange symmetry of the electrons. All interactions between the atoms in the system are written as potential energies.

The first method is a matrix generalization of the invariant imbedding procedure, 17, 20 adapted for multi-channel collision processes. The second method is based on a direct integration of the matrix Schrödinger equation, with a re-orthogonalization transform applied during the integration.

Both methods have been applied to a collinear collision model for two diatoms, interacting via a repulsive exponential potential. Two major studies were performed. The first was to determine the energy dependence of the transition probabilities for an H2 on the H2 model system. Transitions are possible between translational energy and vibrational energy, and from vibrational modes of one H2 to the other H2. The second study was to determine the variation of vibrational energy transfer probability with differences in natural frequency of two diatoms similar to N2.

Comparisons were made to previous approximate analytical solutions of this same problem. For translational to vibrational energy transfer, the previous approximations were not adequate. For vibrational to vibrational energy transfer of one vibrational quantum, the approximations were quite good.

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