A formal quantum theory for the unimolecular rate constant is presented. This theory is an elaboration on an earlier paper by Wilson and Thiele. The theory treats the unimolecular breakdown quantum mechanically, but retains two classical‐like assumptions concerning the collision mechanism and the criteria for reaction. A model calculation suggests that these assumptions can be used if ω≪kT/h. Some arguments are also presented which suggest this same limit of applicability for the general theory.
REFERENCES
1.
(b) N. B. Slater, Theory of Unimolecular Reactions (Cornell University Press, Ithaca, N.Y., 1959).
2.
3.
(d)
R. C.
Baetzold
and D. J.
Wilson
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(1965
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5.
(b) R. D. Levine, in Molecular Relaxation Processes, L. C. Cross, Ed. (Academic Press Ltd., London, 1966);
6.
A. Messiah, Quantum Mechanics (North‐Holland Publ. Co Amsterdam, 1961), Vol. 1, p. 334.
7.
A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover Publications, Inc., New York, 1949), p. 15.
8.
We use the Dirac notation. P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, England, 1958).
9.
W. H. Furry, “Behavior of De Broglie Waves and Wave Packets, in Lectures in Theoretical Physics (Interscience Publishers, Inc., New York, 1963), Vol. V.
10.
The rate constant does not show an Arrhenius temperature dependence. This is an obvious, but for our purposes unimportant, consequence of the model.
11.
12.
In the transition state theory one chooses the boundary in such a way that quick recrossings back into V are eliminated. See, for example,
N. B.
Slater
, J. Chem. Phys.
35
, 445
(1961
).13.
For the quantum result is essentially identical to the classical result. This does not indicate a general agreement since the free particle model is a very special case. It is known that statistically free particles behave alike in both classical and quantum mechanics. See, for example,
M. S.
Bartlett
and J. E.
Moyal
, Proc. Cambridge Phil. Soc.
45
, 545
(1949
).14.
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© 1966 American Institute of Physics.
1966
American Institute of Physics
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