Large-curvature path

Physically the cutting-corner trajectory implies that the particle crosses the barrier suddenly on the time scale of the slow -vibration period. In the literature this approximation is usually called sudden , frozen bath and fast flip approximation, or large curvature case. In the opposite case of small curvature (also called adiabatic and slow flip approximation), coj/coo < sin tp, which is relevant for transfer of fairly heavy masses, the MEP may be taken to a good accuracy to be the reaction path. 

Hydrogen transfer between Cl and CHj corresponds to a heavy-light-heavy mass combination and this reaction has a small skew angle of about 17° and regions of large curvature along the reaction path. The reaction is endoergic by... 

Large curvature indicates the reaction path is undergoing a tight turn, and small curvature corresponds to a shallow turn. 

D. K. Bondi, J. N. L. Connor, B. C. Garrett, and D. G. Truhlar, Test of variational transition state theory with a large-curvature tunneling approximation against accurate quantal reaction probabilities and rate coefficients for three collinear reactions with large reaction-path curvature Cl + HC1, Cl + DC1, and Cl + MuCl, 7. Chem. Phys. 78 5981 (1983). 

A refinement by Schlegel improves the ability of this approach to follow a curved reaction path, as shown in Fig. 12. The point X/. i is chosen so that the reaction path between x and x +1 is an arc of a circle and so that the gradients git and g 4.i are tangent to this path. Like the Muller and Brown method, this algorithm requires an N — l)-dimensional optimization on a hypersphere, but about the point xf. j = Xj — isgj / gj rather than Xj. For similar step sizes, this algorithm follows an IRC with large curvature more closely than the Muller and Brown method. 

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