Hammond coefficient

The existence of a detectable change in p or Py (Hammond coefficient) depends on the sharpness of the curvature of the reaction coordinate at the saddle point broad curvature gives a large change in... 

The Hammond and Cordes-Thornton coefficients can be utilised to characterise transition states in terms of structure reactivity surfaces as follows. The Hammond coefficient is defined so that it is positive when an increase in energy of the products (relative to reactants) accompanies an increase in the first derivative. This describes the generalisation (Hammond effect) that endergonic reactions tend to have product-like transition structures. A positive Hammond coefficient is expected for a fundamental process where structural change affects the energy of one end of a reaction coordinate, as a consequence of the maximum (negative curvature) at the saddle-point in the direction along the reaction coordinate. 

Figure 13 Curvature in a free energy relationship due to a positive Hammond coefficient for the proton transfer from >ff,-dimethyl (9-fluorenyl)sulfonium tetrafluoroborate. The dashed line is fit of the data to a linear Bronsted equation...

Non-additivity of substituent effects has been proposed as a criterion for the operation of the RSR so the linearity argues against its applicability in this system. In a description of transition states by structure-reactivity coefficients (Jencks and Jencks, 1977), two alternative types of behaviour were discussed. In Hammond -type reactions the more endothermic reactions have later transition states, whereas anti-Hammond behaviour is characterized by an adjustment of the transition-state structure to take advantage of favourable substituent effects. These results illustrate that different systems can display quite different behaviour in linear free energy correlations. Thus, in alkene protonations, such correlations cover vast ranges in reactivity with only modest changes in sensitivities, while in solvolytic reactions the selectivity p varies depending on the electron supply at the electron-deficient centre (Johnson, 1978). 

Equations (12-14) can be solved to obtain the curvatures a, b and c in terms of Hammond and Cordes-Thornton coefficients (Equations 15-17). 

We pause to remark that the Bronsted coefficient a has often been used to describe TS structure via the Hammond postulate [15] or the Evans-Polanyi relation [45], where a is viewed as a measure of the relative TS structure along the reaction coordinate, usually a bond order or bond length. The important point is that, although adiabatic PT has a quite different, environmental, coordinate as the reaction coordinate, Eq. (10.12) is consistent with that general picture, with a proper recognition that quantum averages are involved. 

Very similar results are found for reactions of quinuclidines with phos-phorylated pyridine, which follow a Brpnsted slope of Pnuc = —0.1. The less reactive phosphorylated 4-morpholinopyridine follows a slope of (3nuc = -0.01 (12). The changes in (3nuc for these phosphorylated pyridines and phosphate esters with a poorer leaving group (lg) represent Hammond effects that are described by the cross-interaction coefficient, pxy, of equation 3. This cross coefficient is larger than the direct coefficient that describes... 

In order to apply Eqs. (6.3) or (6.4) to the sediment zone subject to bioturbation or physical disturbance, a number of researchers have suggested that the effects of biogenic or physical reworking on pore-water distributions be lumped into an effective or apparent transport coefficient (Hammond eta/., 1975 Vanderborght eta/., 1977 Goldhaber eta/., 1977). D is arbitrarily adjusted until the observed pore-water profile is fit to the appropriate solution, say, to Eq. (6.4). This approach has been found to work reasonably well in sediments where biogenic or physical disturbance is limited to the upper few centimeters (Vanderborght et al., 1977 Aller,... 

Question by M. B. Hammond, North American Aviation Was any attempt made to increase the inside tube heat transfer coefficient until liquid air formed Does this work only with LN2 sink temperatures or can it be used for surfaces nearer, say, to 32°F ... 

For dissociation reactions in which the reverse, recombination step is slow, dissociation is virtually complete once the pair has separated to the contact distance. Under these conditions the magnitude of the interaction in the dissociated pair, in particular the screening of this interaction by ions, would not affect the dissociation rate. In terms of the Hammond postulate [22] and its extensions [23] an exothermic dissociation process would have its transition state close to the bound state, so that the equilibrium and recombination rate coefficients would change in parallel. In such a case one expects no salt effect on the dissociation reaction, in agreement with the classical picture of Bronsted and Bjerrum for kinetic salt effects [7]. 

Nakanishi, K. (1978). Prediction of diffusion coefficient of nonelectrolytes in dilute solution based on generalized Hammond-Stokes plot. Ind Eng. Chem. Fundam., 17,253-256. Quayle, O. R. (1953). The parachors of organic cottqmunds. An interpretation and catalogue. Chem. Rev., 53,439-589. 

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