Transition state theories

Poliak E 1987 Transition state theory for photoisomerization rates of f/ a/rs-stilbene in the gas and liquid phases J. Chem. Phys. 86 3944 

Poliak E 1993 Variational transition state theory for dissipative systems Acf/Vafed Barrier Crossinged G Fleming and P Hanggi (New Jersey World Scientific) p 5 

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877 

This is connnonly known as the transition state theory approximation to the rate constant. Note that all one needs to do to evaluate (A3.11.187) is to detennine the partition function of the reagents and transition state, which is a problem in statistical mechanics rather than dynamics. This makes transition state theory a very usefiil approach for many applications. However, what is left out are two potentially important effects, tiiimelling and barrier recrossing, bodi of which lead to CRTs that differ from the sum of step frmctions assumed in (A3.11.1831. 

Miller W H 1974 Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants J. Chem. Phys. 61 1823-34 

Makarov D E and Topaler M 1995 Quantum transition-state theory below the crossover temperature Phys. Rev. E 52 178 

Bennett C H 1977 Molecular dynamics and transition state theory the simulation of infrequent events Algorithms for Chemical Computation (ACS Symposium Series No 46) ed R E Christofferson (Washington, DC American Chemical Society) 

Poliak E and Liao J-L 1998 A new quantum transition state theory J. Chem. Phys. 108 2733 

Gershinsky G and Poliak E 1995 Variational transition state theory application to a symmetric exchange in water J. Chem. Phys. 103 8501 

Shao J, Liao J-L and Poliak E 1998 Quantum transition state theory—perturbation expansion J. Chem. Phys. 108 9711 Liao J-L and Poliak E 1999 A test of quantum transition state theory for a system with two degrees of freedom J. 

A3.4.7 STATISTICAL THEORIES BEYOND CANONICAL TRANSITION STATE THEORY 

Truhlar D G and Garrett B C 1980 Variational transition-state theory Acc. Chem. Res. 13 440-8 

Laidier K J and King M C 1983 The deveiopment of transition state theory J. Phys. Chem. 87 2657-64 

Poliak E, Tucker S C and Berne B J 1990 Variational transition state theory for reaction rates in dissipative systems Phys. Rev. Lett. 65 1399 

Miller W H, Hernandez R, Moore C B and Polik W F A 1990 Transition state theory-based statistical distribution of unimolecular decay rates with application to unimolecular decomposition of formaldehyde J. Chem. Phys. 93 5657-66 

Song K and Chesnavich W J 1989 Multiple transition states in chemical reactions variational transition state theory studies of the HO2 and HeH2 systems J. Chem. Rhys. 91 4664-78 

Finally, the generalization of the partition function q m transition state theory (equation (A3.4.96)) is given by 

Miller W H 1975 Semiclassical limit of quantum mechanical transition state theory for nonseparable systems J. Chem. Phys. 62 1899 

Hu X and Hase W L 1989 Properties of canonical variational transition state theory for association reactions without potential energy barriers J. Rhys. Chem. 93 6029-38 

The quasi-equilibrium assumption in the above canonical fonn of the transition state theory usually gives an upper bound to the real rate constant. This is sometimes corrected for by multiplying (A3.4.98) and (A3.4.99) with a transmission coefifiwient 0 < k < 1. 

Truhiar D G, Garrett B C and Kiippenstein S J 1996 Current status of transition state theory J. Rhys. Chem. A 100 12,771-800 

Voth G A 1990 Analytic expression for the transmission coefficient in quantum mechanical transition state theory Chem. Phys. Lett. 170 289 

These equations lead to fomis for the thermal rate constants that are perfectly similar to transition state theory, although the computations of the partition functions are different in detail. As described in figrne A3.4.7 various levels of the theory can be derived by successive approximations in this general state-selected fomr of the transition state theory in the framework of the statistical adiabatic chaimel model. We refer to the literature cited in the diagram for details. 

As LEED studies have shown, the stmcture of a chemisorbed phase can change with 6. In terms of transition state theory, we can write A = (I/tq) and a common observation is that while E may change with a phase change, AS will tend to change also, and similarly. The result, again known as a compensation effect, is that the product remains relatively constant 

It may be iisefiil to mention here one currently widely applied approximation for barrierless reactions, which is now frequently called microcanonical and canonical variational transition state theory (equivalent to the minimum density of states and maximum free energy transition state theory in figure A3,4,7. This type of theory can be understood by considering the partition fiinctions Q r ) as fiinctions of r similar to equation (A3,4.108) but with F (r ) instead of V Obviously 2(r J > Q so that the best possible choice for a 

In deriving the RRKM rate constant in section A3.12.3.1. it is assumed that the rate at which reactant molecules cross the transition state, in the direction of products, is the same rate at which the reactants fonn products. Thus, if any of the trajectories which cross the transition state in the product direction return to the reactant phase space, i.e. recross the transition state, the actual unimolecular rate constant will be smaller than that predicted by RRKM theory. This one-way crossing of the transition state, witii no recrossmg, is a fiindamental assumption of transition state theory [21]. Because it is incorporated in RRKM theory, this theory is also known as microcanonical transition state theory. 

The first two of these we can readily approach with the knowledge gained from the studies of trappmg and sticking of rare-gas atoms, but the long timescales involved in the third process may perhaps more usefiilly be addressed by kinetics and transition state theory [35]. 

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]. 

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