Classical proton transfer reaction

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

The approach presented above is referred to as the empirical valence bond (EVB) method (Ref. 6). This approach exploits the simple physical picture of the VB model which allows for a convenient representation of the diagonal matrix elements by classical force fields and convenient incorporation of realistic solvent models in the solute Hamiltonian. A key point about the EVB method is its unique calibration using well-defined experimental information. That is, after evaluating the free-energy surface with the initial parameter a , we can use conveniently the fact that the free energy of the proton transfer reaction is given by... 

This model has obvious shortcomings. For example, the interaction with the solvent in the initial state is straightforward since the proton is in the ionic form, whereas in the final state, the proton is the nonionic adsorbed H atom and its interaction with the solvent should be negligible. No consideration of this fact was made in the potential of the final state Uf m Eq. (43). However, this treatment incorporates the basic feature of the proton transfer reaction interaction with the solvent, tunneling as well as classical transition of the proton, and the effect of the electric field on the potential energy surfaces of the system. 

We have examined the proton transfer reaction AH-B A -H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. The intermolecular and the complex-solvent potentials have a Lennard-Jones and a Coulomb component as described in detail in the original papers. There have been other quantum studies of this system. Azzouz and Borgis performed two calculations one based on centroid theory and another on the Landau-Zener theory. The two methods gave similar results. Hammes-Schiffer and Tully used a mixed quantum-classical method and predicted a rate that is one order of magnitude larger and a kinetic isotope effect that is one order of magnitude smaller than the Azzouz-Borgis results. 

Enthalpies of activation, transition-state geometries, and primary semi-classical (without tunneling) kinetic isotope effects (KIEs) have been calculated for 11 bimolecu-lar identity proton-transfer reactions, four intramolecular proton transfers, four nonidentity proton-transfer reactions, 11 identity hydride transfers, and two 1,2-intramole-cular hydride shifts at the HF/6-311+G, MP2/6-311+G, and B3LYP/6-311+-1-G levels.134 It has been found that the KIEs are systematically smaller for hydride transfers than for proton transfers. The differences between proton and hydride transfers have been rationalized by modeling the central C H- C- unit of a proton-transfer transition state as a four-electron, three-centre (4-e 3-c) system and the same unit of a hydride-transfer transition state as a 2-e 3-c system. 

A. Warshel. Dynamics of reactions in polar-solvents - semi-classical trajectory studies of electron-transfer and proton-transfer reactions. J. Phys. Chem., 86(12) 2218-2224, 1982. 

Recent gas-phase studies of proton-transfer reactions with stepwise solvation of the reactants i.e. incremental addition of solvent molecules to form supermolecular clusters) have demonstrated that the acid/base behaviour of isolated solvent molecules can be dramatically different from their performance as bulk liquids. Water, the classical amphiprotic solvent, shall serve as an example. 

In an analysis of the influence of charged substituents on the pK values of carboxylic acids, Bjerrum (1923) suggested that, for symmetrical proton transfer reactions such as Equation (4), pK differences can be accounted for in terms of purely electrostatic field effects (and statistical effects, whenever they are warranted). If the proton and charged substituent are treated as point charges separated by a distance r in a solvent continuum whose dielectric constant D is that of the bulk solvent, the work required to transfer the proton from r to infinity in the electrostatic field of the charged substituent can be calculated from classical electrostatic theory. The pK difference between the unsubstituted and substituted acids (ApK) is then given by... 

The experimental techniques for studying fast reactions provided a means of studying fundamental processes in solution that were previously considered to be instantaneous. These include electron and proton transfer reactions. Proton transfer is the elementary step involved in acid-base reactions, which are so important in classical analytical chemistry. On the other hand, electron transfer is the elementary step involved in redox reactions. The theory of electron transfer is especially well developed and is discussed in detail below. 

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