Proton Transfer Reactions and the EVB Model

Exercise 2.4. Repeat Exercise 1.6 with the LD solvent model instead of the external charge. 

VB Potential Surface for Proton Transfer Reactions in Solutions 

A very useful example of treating solvent effects is provided by considering the proton transfer reaction 

This reaction can be described by the three resonance structures 

The electrons involved in the actual reaction (which are designated here by dots and referred to here as the active electrons) can be treated according to the general prescription of the four-electron three-orbital problem with the VB wave functions (Ref. 5) 

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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... 

A method that has certain connections with QM/MM techniques even if it does not usually involve simultaneous evaluation of QM and MM operators during a particular calculation is the empirical valence bond method (EVB Warshel and Weiss 1980). At the heart of the EVB method is the notion diat arbitrarily complex reactions may be modeled as the influence of a surrounding environment on a fundamental process that may be represented by some combination of valence bond resonance structures. For example, tlie proton transfer from one water molecule to another may, at any point along the reaction path, be envisaged as involving some admixture of tlie two VB wave functions corresponding formally to... 

One of the first attempts to introduce the solvent effect in a VB analysis for the comprehension of a chemical reaction in solution has been given by Warshel and Weiss [10]. These authors introduced the Empirical Valence Bond method (EVB) for the modeling of proton transfer processes in enzymatic reactions in aqueous environment. 

Despite all the problems inherent to QM/CM approaches, some extremely interesting and perceptive work has been described in the literature recently in which all sorts of approaches have been used, improvements introduced and results obtained ([351, 372] and references therein). The study of enzyme catalysed reaction mechanisms, the calculation of relative binding free energies of substrates and inhibitor, and the determination of proton transfer processes in enzymatic reactions, are all good examples of enzyme-ligand interactions studies. Even though Warshel s EVB method [349] probably remains the most practical QM/CM approach for the study of enzyme catalysis, very useful work has been reported on enzyme catalysed reactions ([381] for an excellent review-[238, 319, 382-384]). This is a consequence of the accuracy of QM to treat the active site and inhibitor/substrate and the viability of classical mechanics to model the bulk of the enzyme not directly involved in the chemical reaction. 

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