Reaction path curvature

Figure 5-3. Active site and calculated PES properties for the reactions studied, with the transferring hydrogen labelled as Hp (a) hydride transfer in LADH, (b) proton transfer in MADH and (c) hydrogen atom transfer in SLO-1. (i) potential energy, (ii) vibrationally adiabatic potential energy, (iii) RTE at 300K and (iv) total reaction path curvature. Reproduced with permission from reference [81]. Copyright Elsevier 2002...

Schenter, G. K., McRae, R. P. and Garrett, B. C. Dynamic solvent effects on activated chemical reactions. I. Classical effects of reaction-path curvature, J.Chem.Phys., 97 (1992), 9116-9137... 

Sn-2 reactivity is dramatically reduced at the primary C(6) position of galacto-configured pyranoses, relative to their gluco isomers. The low reactivity is widely attributed to dipole-dipole interactions in the transition structure, but ab initio calculations on model compounds suggest that the energy attributable to such interactions is not sufficient to explain the reactivity difference,9 whereas rotameric populations and reaction path curvature are.10... 

The B3LYP/6-31+G(d,p) level of theory has been used to calculate the rotamer populations, the energy barriers, and the reaction path curvature for the SN2 identity... 

The integration limits Si and 2 are the reaction coordinate classical turning points /u-eff is the reduced mass, which introduces the reaction path curvature and V (s) is the adiabatic ground-state potential. 

The in-1 vibrational frequencies, C0 (s), are obtained from normal-mode analyses at points along the reaction path via diagonalization of a projected force constant matrix that removes the translational, rotational, and reaction coordinate motions. The B coefficients are defined in terms of the normal mode coefficients, with those in the denominator of the last term determining the reaction path curvature, while those in the numerator are related to the non-adiabatic coupling of different vibrational states. A generalization to non-zero total angular momentum is available [59]. 

Several approximate models for computing resonance energies and widths have been compared, with numerical Illustrations for blmolecular reactive resonances for which an adiabatic separation in reaction-path coordinates Is reasonable. For systems In which the reaction-path curvature Is not too great, the adiabatic model... 

As a first approximation we will assume that the reaction-path curvature can be neglected, but we will eliminate this approximation after Eq. (27.22) because the curvature of the reaction path is very important for tunneling. 

We first consider the case where the reaction probabilities are computed for the adiabatic model with the reaction-path curvature neglected, the so-called vibrationally adiabatic zero-curvature approximation [36]. We approximate the quantum mechanical ground-state probabilities P (E) for the one-dimensional scattering problem by a uniform semiclassical expression [48], which for E < is given by... 

Figure 27.8 Potential energy contours for two harmonic vibrational modes, which are orthogonal to the reaction coordinate, for the Cl + CH, reaction at s = -0.49 Oo on the reaction coordinate. The straight line is the direction u, of the reaction-path curvature vector and the symbols are turning points for zero-point harmonic motion along g, (square), gj (triangle), and u, (circle).

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