Canonical variational transition state theory

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... 

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... 

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 rate of hydrogen transfer can be calculated using the direct dynamics approach of Truhlar and co-workers which combines canonical variational transition state theory (CVT) [82, 83] with semi-classical multidimensional tunnelling corrections [84], The rate constant is calculated using [83] ... 

Canonical variational transition state theory, with transitional modes treated as harmonic oscillators refs. S... 

Of course, one is not really interested in classical mechanical calculations. Thus in normal practice the partition functions used in TST, as discussed in Chapter 4, are evaluated using quantum partition functions for harmonic frequencies (extension to anharmonicity is straightforward). On the other hand rotations and translations are handled classically both in TST and in VTST, which is a standard approximation except at very low temperatures. Later, by introducing canonical partition functions one can direct the discussion towards canonical variational transition state theory (CVTST) where the statistical mechanics involves ensembles defined in terms of temperature and volume. There is also a form of variational transition state theory based on microcanonical ensembles referred to by the symbol p,. Discussion of VTST based on microcanonical ensembles pVTST is beyond the scope of the discussion here. It is only mentioned that in pVTST the dividing surface is... 

TST = conventional Transition State Theory, ICVT = Improved Canonical Variational Transition state theory, ICVT/SCT = ICVT/Small Curvature Tunneling, ICVT/p,OMT = ICVT/Microcanonical Optimized Multidimensional Tunneling. 

Chemical kinetic rate methods including conventional transition state theory (TST), canonical variational transition state theory (CVTST) and Rice-Ramsper-ger-Kassel-Marcus in conjunction with master equation (RRKM/ME) and separate statistical ensemble (SSE) have been successfully applied to the hydrocarbon oxidation. Transition state theory has been developed and employed in many disciplines of chemistry [41 4]. In the atmospheric chemistry field, conventional transition state theory is employed to calculate the high-pressure-limit unimole-cular or bimolecular rate constants if a well-defined transition state (i.e., a tight... 

The RBU model can be used to study the effect of exciting the vibrational modes treated within the model. For the reactions X (X=C1, 0 and H) + CH4 HX + CH3 we find that exciting a vibrational inode results in a lower threshold to reaction. It was also found that exciting the reactive C-H stretch enhances the reactivity more than exciting the CH4 umbrella mode. Vibrational enhancements for the umbrella and C-H stretch vibrations have also been found in other studies of the dynamics[75, 80] and in canonical variational transition state theory (C T) calculations [84]. Enhancement of the Cl + CH4 reaction due to vibrational excitation of the H-CH3 stretch has also been confirmed b experimental measurements by Zare and coworkers[85]. 

The microcanonical and canonical variational transition-state theories are based on the assumption that trajectories cross the transition state (TS) only once in forming products(s) or reactants(s) [70,71]. The correction to the transition-state theory rate constant is determined by initializing trajectories at the TS and sampling their coordinates and momenta from the appropriate statistical distribution [72-76]. The value for is the number of trajectories that form product(s) divided by the number of crossings of the TS in the reactant(s) -> produces), direction. Transition state theories assume this ratio is unity. 

ICVTST improved canonical variational transition-state theory... 

Canonical variational transition-state theory (CVT) gives the rate constant at temperature T as [125]... 

The partition functions and numbers of accessible states can all be calculated from the reaction path data, (j) and F(s), assuming harmonic vibrations and separation of vibration and rigid-body rotation. The vibrational partition function may be improved in accuracy by accounting for anharmonicity in some modes. This has been done simply in a separable mode approximation (e.g., Morse stretches and quartic terms in the bending potentials) [129-131]. There are now a number of examples of applications of various forms of canonical variational transition-state theory using ab initio reaction path calculations [15,106,108,112,131-142]. 

Biradicals as Intermediates. Canonical Variational Transition-State Theory Results for Trimethylene. 

A more sophisticated reaction path approach is to replace in eq. (40) by 8jjq(sJj This is the essence of the approach taken by Garrett and Truhlar and generalized by Miller et al. and Skodje and Truhlar for polyatomic reactions. Truhlar and coworkers have proposed one-dimensional paths which deviate from the reaction path in order to compute accurate tunneling probabilities from which transmission coefficients (see below) are then used to correct their version of variational transition state theory, the so-called improved canonical variational [transition state] theory (ICVT) (also see below). 

In canonical variational transition state theory the partition function Qy(T) is computed along the reaction path s and minimized with respect to s.)... 

When the canonical variational transition state is strongly dependent on temperature, a more consistent theory is provided by improved canonical variational transition state theory (ICVTST or, for short. 

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