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** Classical transition state theory **

** Quantum transitional state theory **

The above discussion, as most of this chapter, is based on a classical picture of the chemical reactions. Quantum mechanical transition state theory is far less obvious even a transition state cannot be well defined. A particularly simple case that can be formulated within TST is described next. [Pg.497]

We present an overview of variational transition state theory from the perspective of the dynamical formulation of the theory. This formulation provides a firm classical mechanical foundation for a quantitative theory of reaction rate constants, and it provides a sturdy framework for the consistent inclusion of corrections for quantum mechanical effects and the effects of condensed phases. A central construct of the theory is the dividing surface separating reaction and product regions of phase space. We focus on the robust nature of the method offered by the flexibility of the dividing surface, which allows the accurate treatment of a variety of systems from activated and barrierless reactions in the gas phase, reactions in rigid environments, and reactions in liquids and enzymes. [Pg.67]

A well defined theory of chemical reactions is required before analyzing solvent effects on this special type of solute. The transition state theory has had an enormous influence in the development of modern chemistry [32-37]. Quantum mechanical theories that go beyond the classical statistical mechanics theory of absolute rate have been developed by several authors [36,38,39], However, there are still compelling motivations to formulate an alternate approach to the quantum theory that goes beyond a theory of reaction rates. In this paper, a particular theory of chemical reactions is elaborated. In this theoretical scheme, solvent effects at the thermodynamic and quantum mechanical level can be treated with a fair degree of generality. The theory can be related to modern versions of the Marcus theory of electron transfer [19,40,41] but there is no [Pg.284]

Although the methods discussed above to incorporate electronic structure theory to model the PES and NQEs to determine the rate process are based on very different theories, a common strategy is to estimate approximately the quantum mechanical rate constant by introducing a quantum correction factor to bridge with the classical transition state theory [Pg.552]

Table 6.3 A comparison of different theoretical approaches to the evaluation of the thermal rate constant for the F + H2 —> HF + H reaction at T = 300 K. TST is transition-state theory (Example 6.2), QCT is the quasi-classical trajectory method [Chem. Phys. Lett. 254, 341 (1996)], and QM is (exact) quantum mechanics [J. Phys. Chem. 102, 341 (1998)]. |

One conclusion that can be reached from the early work on effective potentials [1,21-23], the work of Cao and Voth [3-8], as well as the centroid density-based formulation of quantum transition-state theory [42-44,49] is that the path centroid is a particularly useful variable in statistical mechanics about which to develop approximate, but quite accurate, quantum mechanical expressions and to probe the quantum-classical correspondence principle. It is in this spirit that a general centroid density-based formulation of quantum Boltzmann statistical mechanics is presented in the present section. This topic is the subject of Paper I, and the emphasis in this section is on analytic theory as opposed to computational approaches (cf. Sections III and IV). [Pg.141]

There are two corrections to equation (12) that one might want to make. The first has to do with dynamical factors [19,20] i.e., trajectories leave Ra, crossing the surface 5/3, but then immediately return to Ra. Such a trajectory contributes to the transition probability Wfia, but is not really a reaction. We can correct for this as in variational transition-state theory (VTST) by shifting Sajj along the surface normals. [8,9] The second correction is for some quantum effects. Equation (14) indicates one way to include them. We can simply replace the classical partition functions by their quantum mechanical counterparts. This does not correct for tunneling and interference effects, however. [Pg.744]

** Classical transition state theory **

** Quantum transitional state theory **

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