Rice theory

In addition, this mechanism was criticized on the basis of the Kassel-Rice theory of vibrationally excited ground states some time earlier by Zimmerman et alS3i)... 

Thermal and charge induced random coil to a-helix transitions of polyll-glutamic acid) (PGA) are measured by optical rotatory dispersion in various solvents. The data of PGA in 0.1 M NaCI are analyzed by the Zimm-Rice theory. The initiation parameter, o, of the Zimm-Rice theory is given by a value of 5 ( 1) x 10 3. Random copolymers of L-glutamic acid and L-alanine containing 10, 30, and 40 molar percents of alanyl residue are analyzed as well. 

These comments complete the discussion of the basic equations of the Marcus- Rice theory and also link them to other familiar concepts. 

Gray-Rice Theory Versus Reactive Island Theory Isomerization in Double-Well Systems Isomerization in a Triple-Well System Isomerization of 3-Phospholene Isomerization of HCN — CNH Isomerization of Cyclobutanone (C4H6O)... 

The original Gray-Rice theory of isomerization was developed from a two-DOF model in which the potential energy surface displays a double well when... 

Figure 20. Schematic surface of section in modeling the Gray-Rice theory of isomerization, showing the separatrix and the phase regions A, B, and C, which are the generalized states of the system.

Zhao and Rice extended the above-sketched Gray-Rice theory to include the effects of intramolecular energy transfer, using analytical approximations for various quantities [15]. Because this extension is in the same spirit as in the case of unimolecular predissociation, the Zhao—Rice approximation presented here is still called the MRRKM theory. Zhao and Rice employed a model double-well potential similar to that used by Gray and Rice, but parameterized to have greater flexibility. Specifically, the three terms in the potential of Eq. (201) are taken to have the following form ... 

D. Gray-Rice Theory Versus Reactive Island Theory... 

Consider first the case where all the three states are taken into account and X2 < Then the isomerization rate from the Gray-Rice theory is characterized... 

To consider the relationship between RIT and the Gray-Rice theory, we reexpress the simplest reaction mechanism of RI T in the form... 

Clearly, Eq. (275) indicates that between state A and state B there are the intermediate states Wab and Wba- Identifying the intermediate states Wab and Wba with the state C in the Gray-Rice theory, one sees that (first-order) RIT and the Gray-Rice theory are based upon the same reaction mechanism. Specifically, for the case of a symmetric double-well potential, RIT yields the rate constant [56]... 

Since the flux Fgr E) in the Gray-Rice theory is defined by the flux crossing the separatrix from the trapped A state to state C = + C, we have... 

This important similarity between the first-order RIT and the Gray-Rice theory was also analyzed by Deleon and Ling [56] with, however, different conclusions. 

The Classical Isomerization Rate Constants of Cyclobutanone from the RRKM Theory, Gray-Rice theory, MRRKM Theory, and Trajectory Calculations (in 10 a.u.)... 

Forst treated the decomposition of azomethane with the quantum harmonic version of the Marcus-Rice theory of unimolecular reactions. He used different models which comprised three dimensional free rotations of the two methyls and of the central nitrogen molecule and adjusted the overall moments of inertia to give the correct total entropy. For planar or tetrahedral methyls calculations gave an increase of six in the number of active rotations in going from the molecule to the complex. With a minimum of assumption it was also possible to reproduce the pressure fall-off curve of the experimental first order rate coefficient for planar and tetrahedral complexes. A further result of the computations is the conclusion that the vibrational frequency pattern of the complex is so much less important than the number of active rotations that both tetrahedral and planar complexes lead to identical fall-off behaviour. 

P. C. Beadle, J. H. Knox, F. Placido, K. C. Waugh, Decomposition of Activated chloroalkyl radicals. Calculations by the Marcus-Rice theory, Trans. Faraday Soc. 65 (1969) 1571. 

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