Study applies the nonequilibrium collision theory of reaction rates to the estimation of rate constants for simple reactions. The complications in the quantum mechanical description of chemical reactions and the care needed in approximating the exact wave function for the collision are shown

Pirkle, J. C., Jr.

English

Quantum mechanical calculations for gas phase bimolecular exchange reactions between hydrogen and bromin

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Quantum mechanical calculations of reactive scattering cross-sections in bimolecular encounters

December 1967	 Brief 67-10527 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Quantum Mechanical Calculations of Reactive Scattering

Cross Sections in Bimolecular Encounters 
Theoretical treatments of gas phase chemical re-
actions can be conveniently classified into two parts. 
The first involves the study of the details of inter-
molecular or intramolecular energy transfer, particle 
exchange, particle emission, or particle capture. 
Secondly, a study must be made of the manner in 
which a usually broad spectrum of the above micro-
scopic processes are reflected in the macroscopic or 
bulk behavior of gas phase reactions. Thus, the first 
task is concerned with the calculation of the proba-
bility of particular events, while the second is con-
cerned with formalizing mathematical relationships 
between these detailed probabilities and observable 
reaction phenomena. 
A study has been made that is involved with the 
application of the nonequilibrium collision theory of 
reaction rates to the estimation of rate constants for 
simple reactions. In the nonequilibrium collision 
theory, the molecular collisions are individually 
studied with regard to initial conditions, particle 
exchange, and energy exchange, the results being de-
fined in terms of cross sections. Then, the kinetic 
theory of gases is used to average over all the effects 
of the individual collisions resulting in reactions to 
obtain the rate constants. 
The following conclusions were reached in this 
study: 
The investigation demonstrated the severe compli-
cations encountered in the quantum mechanical de-
scription of chemical reactions. Even the relatively 
simple derivation of an expression for the reaction 
cross section involved tedious attention to detail. 
Furthermore, the subsequent calculation of the reac-
tion cross section required so much computer time, 
even on a high speed computer, that computations
were limited to a few representative initial conditions. 
It was shown that good agreement between theory 
and experiment can be obtained if sufficient care is 
taken in approximating the exact wave function for 
the collision. Using the perturbed Morse oscillator 
method to describe the distortion of the HBr bond in 
the presence of another bromine atom resulted in 
reaction cross sections which, when used in a sim-
plified collision theory, gave rate constants that com-
pared favorably with experiment. 
Detailed rate constant calculations by the perturbed 
Morse oscillator method reinforce the classical me-
chanical results of Polanyi. That is, "attractive" 
potential energy surfaces lead to higher vibrational 
states for the products, whereas "repulsive" potential 
energy surfaces result in less vibration of the product 
molecule. Since infrared chemiluminescence spec-
troscopy has demonstrated that the product molecules 
in the reaction H + Br  - HBr + Br are formed 
predominantly in the lower vibrational states, it is 
concluded that the potential energy surface for the 
reaction is "repulsive." The exact degree of repul-
siveness has not yet been accurately determined. 
Notes: 
1. This thesis was presented to the faculty of the 
graduate division of the Georgia Institute of Tech-
nology in partial fulfillment of the requirements 
for the degree of doctor of philosophy in the 
School of Chemical Engineering, April 1967. 
2. Inquiries concerning this study may be directed 
to.	
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B67-10527
(continued overleaf) 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19670000526 2020-03-11T21:00:51+00:00Z
Patent status: 
Inquiries about obtaining rights for the commer-
cial use of this invention may be made to NASA, 
Code GP, Washington, D.C. 20546. 
Source: J. C. Pirkie, Jr. 
of Georgia Institute of Technology 
under contract to 
Marshall Space Flight Center 
(MFS-1 3594) 
Brief 67-10527	 Category 03


Quantum mechanical calculations of reactive scattering cross sections in bimolecular encounters

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Quantum mechanical calculations of reactive scattering cross sections in bimolecular encounters

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