Unimolecular reaction angular

RRKM theory, developed from RRK theory by Marcus and others [20-23], is the most commonly applied theory for microcanonical rate coefficients, and is essentially the formulation of transition state theory for isolated molecules. An isolated molecule has two important conserved quantities, constants of the motion , namely its energy and its angular momentum. The RRKM rate coefficient for a unimolecular reaction may depend on both of these. For the sake... 

Regardless of the nature of the intramolecular dynamics of the reactant A, there are two constants of the motion in a unimolecular reaction, i.e. the energy E and the total angular momentum j. The latter ensures the rotational quantum number J is fixed during the unimolecular reaction and the quantum RRKM rate constant is specified as lc E, J). 

See, for example, D. L. Bunker, /. Chem. Phys., 40,1946 (1963). Monte Carlo Calculations. IV. Further Studies of Unimolecular Dissociation. D. L. Bunker and M. Pattengill,/. Chem. Phys., 48, 772 (1968). Monte Carlo Calculations. VI. A Re-evaluation erf Ae RRKM Theory of Unimolecular Reaction Rates. W. J. Hase and R. J. Wolf, /. Chem. Phys., 75,3809 (1981). Trajectory Studies of Model HCCH H -P HCC Dissociation. 11. Angular Momenta and Energy Partitioning and the Relation to Non-RRKM Dynamics. D. W. Chandler, W. E. Farneth, and R. N. Zare, J. Chem. Phys., 77, 4447 (1982). A Search for Mode-Selective Chemistry The Unimolecular Dissociation of t-Butyl Hydroperoxide Induced by Vibrational Overtone Excitation. J. A. Syage, P. M. Felker, and A. H. Zewail, /. Chem. Phys., 81, 2233 (1984). Picosecond Dynamics and Photoisomerization of Stilbene in Supersonic Beams. II. Reaction Rates and Potential Energy Surface. D. B. Borchardt and S. H. Bauer, /. Chem. Phys., 85, 4980 (1986). Intramolecular Conversions Over Low Barriers. VII. The Aziridine Inversion—Intrinsically Non-RRKM. A. H. Zewail and R. B. Bernstein,... 

The "statistical formulation (67.Ill) cannot be applied to unimolecular reactions for which the classical activation energy and the reaction heat are equal (E = Q) without introducing some additio-nal assumptions which are necessary for the definition of the transition state. One usually considers the "activated complex (AB) as a rotating "diatomic molecule in which the centrifugal force is balanced by an attractive dipole-induced dipole or dispersion force /HO/. This "diatomic model implies that the angular momentum... 

It is often easier to consider the problem of bimolecular reaction rate theory from the perspective of dissociation of the particles, and then to evaluate the recombination rate from the derived dissociation rate using the equilibrium constant. The principal difference between unimolecular and bimolecular reactions is in the treatment of angular momentum J. In unimolecular reactions the transition state is regarded as fixed by the internal coordinates simply because centrifugal effects are small. In bimolecular reactions this is not the case, as is demonstrated by the behaviour of the effective centrifugal potential... 

At very low bath densities the dissociation rate of a pair of particles can be cast in terms of the rate of accumulation of energy up to a dissociation energy This is well-studied for unimolecular reactions in which the transition state is fixed, but for bimolecular reactions the complexity associated with angular momentum leads to complications Nevertheless, an assumption will be made that a threshold energy Q can be defined such that when E > Q dissociation may take place at a rate k (E), which depends only on the relative density of states of the reactSt and the transition state [3] The steady state dissociation rate is then given by... 

However, dynamics calculations (see Unimolecular Reaction Dynamics) on potential energy surfaces that have been constructed to mimic the ab initio surface tell a different story. Double rotation is predicted by these calculations to be more favorable than single rotation at 400 by a factor of 3-5. The reason is that, in the reaction dynamics calculations, conservation of angular momentum favors a molecule which opens to TM in a disrotatory mode continuing to rotate its methylene groups in this mode, until it recloses to cyclopropane. 

The spontaneous unimolecular reaction obeys two laws conservation of energy and conservation of total angular moment J. The rate of spontaneotis unimolecular reactions is described by the expression... 

The coefficient k( , J) is named the microscopic rate constant of unimolecular reaction. Sometimes this rate constant is named microcanonical because all states with equal e and J values are assumed to the equiprobable. If active molecules A ( e) are formed with some distribution fi[e, J) over the states with the energy e and angular moment J, the averaged rate constant < k(8, J)> is described by the equation... 

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