Reactions of carbocations with water and azide ion: calculation of rate constants from equilibrium constants and distortion energies using No Barrier Theory

Rate constants for the reaction of water or azide ion with various substituted benzylic carbocations can be calculated from the equilibrium constants for cation formation and distortion energies by means of the No Barrier Theory. Rate constants for the water reactions span 10 orders of magnitude. Most but not all of the azide reactions are diffusion controlled. The rate constants, and in particular those less than diffusion controlled, were successfully calculated. The set of equilibrium constants available from the literature was supplemented using alkyl chloride hydrolysis equilibrium constants and relative cation formation equilibrium constants derived from DFT/continuum calculations. The model used for these reactions allows for the entropic cost of bringing solutes together, the desolvational cost of losing hydrogen bonding solvation by water and the cost of moving the aryl ring through the solvent as the central atom changes from sp(2) to sp(3) hybridization and from planar to pyramidal geometry. Copyright (C) 2004 John Wiley Sons, Inc.