Generalized transition state theory

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

Garret, B. C. and Truhlar, D. G. Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules, J.Phys.Chem., 83 (1979), 1052-1079... 

D.G. Truhlar, A.D. Isaacson, B.G. Garrett, Generalized Transition State Theory, vol. 4, CRC Press, Boca Raton, FL, 1985. 

Truhlar, D. G., A. D. Isaacson and B. C. Garrett, Generalized transition state theory, in Theory of Chemical Reaction Dynamics, 4, M. Baer, ed., CRC Press, Boca Raton, Florida (1985), 65-137. 

The ability to predict accurate potential surfaces means that we are in a position to investigate the nature of the kinetic barriers, including the activated complexes, of key surface processes. In fact, Born-Oppenheimer potential surfaces can be used not only with the transition-state approach to kinetics but also with the much more general and exact collision theory (e.g., scattering S-matrix ilieory). While methods based on collision and scattering theory have pointed out deficiencies in the traditional transition-state theory (TST), they have also served to uphold many of TST s simple claims. In turn, new generalized transition state theories have been born. For complex systems, the transition-dale approach, while admittedly approximate, has been well established. 

In the following the salient features of the general transition state theory of Sections IIA and IIC, as applied to methyl radical recombination, are summarized, Details, where omitted, are given in Ref. 11c. 

Comparison with experiment in the present Fig. 2 is given for the 1985 results of Macpherson et al.33 whose data appear as open circles. There is agreement with the general transition state theory calculations over the experimentally studied temperature range 296-577 K for curve 1. A feature of the data in Ref. 33 is the accurate determination of the absorption cross section oa for the CH3 absorption at 216.36 nm. This determination was important since most experimental studies of the CH3 recombination rate accurately measure the ratio kx/aa. In many earlier determinations of kx, one source of error appears to lie in the absorption cross section, a case in point being an earlier work of Macpherson et al.34... 

Garrett B. C. and Truhlar D. G. (1979) Generalized Transition State Theory. Quantum Effects for Collinear Reactions of Hydrogen Molecules and Isotopically Substituted Hydrogen Molecules, J. Phys. Chem. 79, 1079-1112. 

If this was the case one could generalize transition state theory to apply also to state specific rates. This is seen by application of detailed balance. If there is a transition state for each state of the products then, for the reversed reaction, each state of the reactants (i.e., the products of the forward reaction) will correlate to its own transition state. 

B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules, J. Phys. Chem. 83 1079 (1979) Errata 84 682 (1980) 87 4553 (1983). 

Once the reaction path and the force-constant matrix at points along the reaction path have been found, one can use improved versions of transition-state theory (TST) called generalized transition-state theory to calculate rate constants more accurate than those given by TST [see references cited in D. G. TVuhlar, R. Steckler, and M. S. Gordon, Chem. Rev., 87, 217 (1987)] and can construct a reaction-path Hamiltonian and use it to study such things as vibrational-energy transfer during the reaction [W. H. Miller et al., J. Chem. Phys., 72,99 (1981) W. H. Miller, J. Phys. Chem., SI, 3811 (1983)]. 

Truhlar DG, Isaaeson AD, Garrett BC (1985) Generahzed transition state theory. In Theory of Chemical Reaction Dyrramics. Baer M (ed), CRC Press, Boea Ratorr, p 65-137 Truhlar DG, Isaaeson AD, Skodje RT, Garrett BC (1982) Incorporation of quantum effects in generalized-transition state theory. J Phys Chem 86 2252-2261... 

The superscript GT denotes the generalized transition state theory, ff is l/ksT, kg is the Boltzmann constant, h is Planck s constant, is the value of s at which is minimum (that is, the location of the canonical variational transition state), <7 is the symmetry factor, and and are partition functions for the generahzed transition state (GTS) and reactants, respectively. To include the tunneUng effect, the calculated rate constant is multi-... 

There have been a number of theoretical investigations on the CH -I- N2 HCN - - N system due, in part, to its importance in the production of NO in the combustion chemistry of hydrocarbons. It is also interesting from the perspective of electronic structure theory because it involves potential energy surfaces of the doublet and quartet states and spin-orbit coupling connecting these states, and because aspects of dynamics by a generalized transition state theory and a nonadiabatic RRKM theory can be used. 

Barriers to rotation around the Cca —N bonds have been determined experimentally for diaminocarbenes (3) and (4) and their protonated and lithiated counterparts the possible involvement of lithium or a proton in the dimerization of these acyclic diaminocarbenes was also reported. A computational study of the dimerization of diaminocarbenes has been performed via rate constant calculations using general transition-state theory calculations. Such a dimerization has been shown to be a rapid equilibrium between the carbenes and the tetra-A-alkyl-substituted enetetramines (5), by characterization of metathesis products when two different tetramines were mixed. The thermodynamic parameters of this Wanzlick equilibrium have been determined for the A-ethyl-substituted compound the enthalpy of dissociation has been evaluated at 13.7kcalmol and the entropy at 30.4calmor K . Complex-ation of diaminocarbenes by alkali metals has been clearly established by a shift of the C NMR signal from the carbene carbon of more than 5 ppm. ... 

Basilevsky, M. V, Chudinov, G. E. (1990). Application of generalized transition state theory for calculation of the rate constant of a chemical reaction with charge transfer in a polar solvent. Chemical Physics, 144,155. 

Schenter GK, Garrett BC, Truhlar DG (2003) Generalized transition state theory in terms of the potential of mean force. J Chem Phys 119(12) 5828-5833... 

Incorporation of Quantum Effects in Generalized-Transition-State Theory. 

This review describes the appHcation of variational transition state theory (VTST) to the calculation of chemical reaction rates. In 1985, two of us, together with Alan D. Isaacson, wrote a book chapter on this subject entitled Generalized Transition State Theory for the multi-volume series entitled Theory of Chemical Reaction Dynamics Since that time, VTST has undergone... 

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