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Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment

Marcus, R. A. (1964) Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment. Journal of Chemical Physics, 41 (9). pp. 2614-2623. ISSN 0021-9606. doi:10.1063/1.1726329.

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In its usual form activated complex theory assumes a quasiequilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced. The new equation for the transmission coefficient contains internal centrifugal terms. The fourth assumption can also be weakened and a rotational interaction included in the formalism. In applications of the rate equation use can be made of the recent finding that in the immediate vicinity of a saddle point or a minimum, a potential energy surface can be imitated in some major topographical respects by a surface permitting separation of variables. The separated wave equation for the reaction coordinate is then curvilinear because of the usual curvature of the path of steepest ascent to the saddle point. Calculations of transmission coefficients and rates can be made and compared with those obtainable from the usual one‐dimensional Cartesian‐like calculations on the one hand and with some based on the numerical integration of the n‐dimensional Schrödinger equation on the other. An application to a common three‐center problem is discussed.

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Marcus, R. A.0000-0001-6547-1469
Additional Information:© 1964 American Institute of Physics. Received 18 June 1964. Online Publication Date: 2 July 2004. This research was supported in part by a fellowship from the Alfred P. Sloan Foundation and by a grant from the U.S. Atomic Energy Commission. A portion of this research was performed under the auspices of the U.S. Atomic Energy Commission, while the author was a Visiting Senior Scientist at Brookhaven National Laboratory.
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Alfred P. Sloan Foundation FellowshipUNSPECIFIED
Atomic Energy CommissionUNSPECIFIED
Issue or Number:9
Record Number:CaltechAUTHORS:20120829-112000188
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Official Citation:Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment R. A. Marcus J. Chem. Phys. 41, 2614 (1964);
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33654
Deposited By: Ruth Sustaita
Deposited On:29 Aug 2012 18:41
Last Modified:09 Nov 2021 21:36

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