Reaction path variational method

In order to use variational transition state theory or reaction path Hamiltonian methods (see Transition State Theory) to calculate rate constants, one needs vibrational frequencies perpendicular to the reaction path. These are obtained by projecting out motion along the tangent, D. The projector, P, and the projected Hessian, H, are given by... 

S is the path length between the points a and b. The Euler equation to this variation problem yields the condition for the reaction path, equation (B3.5.14). A similar method has been proposed by Stacho and Ban [92]. 

Two main methods of approach are used in discussing the variation of E . These have been associated with different parts of the reaction path the isolated molecule method is usually assumed to refer to the initial stages of the reaction, and the localization method is generally associated with a transition state in the region of the maximum of the energy curve. Each method has its own reactivity indices these are defined in detail in later Sections, but at this point it is useful to list them, along with certain additional indices relating to models introduced more recently, and to indicate their applicability. 

Nondynamical electron correlation effects are generally important for reaction path calculations, when chemical bonds are broken and new bonds are formed. The multiconfiguration self-consistent field (MCSCF) method provides the appropriate description of these effects [25], In the last decade, the complete active space self-consistent field (CASSCF) method [26] has become the most widely employed MCSCF method. In the CASSCF method, a full configuration interaction (Cl) calculation is performed within a limited orbital space, the so-called active space. Thus all near degeneracy (nondynamical electron correlation) effects and orbital relaxation effects within the active space are treated at the variational level. A full-valence active space CASSCF calculation is expected to yield a qualitatively reliable description of excited-state PE surfaces. For larger systems, however, a full-valence active space CASSCF calculation quickly becomes intractable. 

Jaume et al. (1984) studied the contribution of solvent relaxation to the reaction coordinate of the F (H20) + CH3F(H20)SN2 reaction. Potential energy calculations were performed using the ab initio MO method with the 3-21G basis set. The authors found large variation of the solvation parameters along the reaction path and concluded that solvent coordinates are an important part of the reaction coordinate. They showed that the solvent acts not only as a medium for the reaction but also as a rectant. Thus, the solvent does not adjust its position to the changing chemical system but rather takes part in it. 

Chapter 2, Michael L. McKee and Michael Page address an important issue for bench chemists how to go from reactant to product. They describe how to compute reaction pathways. The chapter begins with an introduction of how to locate stationary points on a potential energy surface. Then they describe methods of computing minimum energy reactions pathways and explain the reaction path Hamiltonian and variational transition state theory. 

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