EVB method

For this reason, there has been much work on empirical potentials suitable for use on a wide range of systems. These take a sensible functional form with parameters fitted to reproduce available data. Many different potentials, known as molecular mechanics (MM) potentials, have been developed for ground-state organic and biochemical systems [58-60], They have the advantages of simplicity, and are transferable between systems, but do suffer firom inaccuracies and rigidity—no reactions are possible. Schemes have been developed to correct for these deficiencies. The empirical valence bond (EVB) method of Warshel [61,62], and the molecular mechanics-valence bond (MMVB) of Bemardi et al. [63,64] try to extend MM to include excited-state effects and reactions. The MMVB Hamiltonian is parameterized against CASSCF calculations, and is thus particularly suited to photochemistry. 

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... 

The empirical valence bond (EVB) method of Warshel [19] has features of both the structurally and thermodynamically coupled QM/MM method. In the EVB method the different states of the process studied are described in terms of relevant covalent and ionic resonance structures. The potential energy surface of the QM system is calibrated to reproduce the known experimental... 

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... 

Valence bond (VB) theories or empirical valence bond (EVB) methods have been developed in order to solve this problem with bond potential functions that (i) allow the change of the valence bond network over time and (ii) are simple enough to be used efficiently in an otherwise classical MD simulation code. In an EVB scheme, the chemical bond in a dissociating molecule is described as the superposition of two states a less-polar bonded state and an ionic dissociated state. One of the descriptions is given by Walbran and Kornyshev in modeling of the water dissociation process.4,5 As... 

The EVB method is a semiempirical method based on the construction of the wavefunction by solving a secular problem in which the Hamiltonian matrix elements are written in terms of empirical parameters. In order to obtain these parameters, the reaction is first studied in the gas phase with the most convenient method, ab initio when possible, and... 

Later, in 1990, Kim and Heynes [11] investigated the role of solvent polarization in fast electron transfer processes and pointed out that, when the solvent is instantaneously equilibrated to the quantum charge distribution of the solute, the Hamiltonian itself is a functional of the wave-function, giving a non-linear Schrodinger equation. The resulting solvent contribution to the Hamiltonian matrix on the diabatic basis thus cannot be simply described as in the former EVB method. 

The decarboxylation reaction coordinate was then explored using the EVB methods described above, assuming, based on the results of solution simulations, that a stepwise decarboxylation-then-proton transfer mechanism (mechanism... 

We have employed the EVB method to study the energetics of nucleophile activation by proton transfer to a dianionic substrate in both LMPTP and human PTPIB. The two valence bond states O, and O2 used in the calculations are shown in Figure 3. These states represent the reactants and products for the reaction where a proton is transferred from the cysteine residue to the phenyl phosphate dianion. Starting coordinates for the protein simulations were the structure of bovine liver LMPTP in complex with sulfate and human PTPIB (C215S mutant) in complex with phosphotyrosine (PDB entries IPHR [5] and IPTV [9] respectively). 

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. 

VB functions have been championed by Warshel and his co-workers for use in studying reactions in enzymes and in solution. The method, which they term the empirical VB (EVB) method, supposes that the wave-function for a particular problem, i/>,can be written as a linear combination of the wavefunctions of resonant forms, v i, which are postulated to be important in the process. For example, for a bond breaking reaction, AB — A+ + B, which produces ionic products, the contributing resonant forms could be the covalent, AB, and ionic, A B+,states that dissociate to atoms and ions respectively. The total wavefunction is ... 

As stated above, reliable studies of enzyme catalysis require accurate results for the difference between the activation barriers in enzyme and in solution. The early realization of this point led to a search for a method that could be calibrated using experimental and theoretical information of reactions in solution. It also becomes apparent that in studies of chemical reactions, it is more physical to calibrate surfaces that reflect bond properties (i.e., valence bond-based (VB-based) surfaces) than to calibrate surfaces that reflect atomic properties (e.g., molecular orbital-based surfaces). Furthermore, it appears to be very advantageous to force the potential surfaces to reproduce the experimental results of the broken fragments at infinite separation in solution. This can be easily accomplished with the VB picture. The resulting EVB method has been discussed extensively elsewhere,21 22 but its main features will be outlined below, because it provides the most direct microscopic connection to concepts of physical organic chemistry. 

The seemingly simple appearance of the EVB method may have led to the initial impression that this is an oversimplified qualitative model, rather than a powerful quantitative approach. However, the model has been eventually widely adopted as a general model for studies of reactions in large molecules and in condensed phase (e.g., Refs. 29-32). Several very closely related versions have been put forward with basically the same ingredients as in the EVB method (see Ref. 33). 

The EVB method proposed by Warshel [6] is an elegant and computationally very efficient method of describing the entire BO surface, thus allowing treatment of chemical reactions such as proton transfer in hydrogen bonds. It can also be used in vibrational analysis. In conjunction with the environment described at the molecular mechanics level it was the first QM/MM method. Vibrational analyses of hydrogen bonded systems and of enzymatic catalysis have a lot in common. 

Warshel and coworkers have employed the empirical valence-bond (EVB) method [49] to simulate FERs for PT [50] and other reactions [51]. The PT step between two water molecules in the mechanism of the reaction catalysed by carbonic anhy-drase was described as an effective two-state problem involving reactant-like (H0H)(0H2) and product-like (HO )(HOH2+) VB structures [50a], Diabatic energy curves for these two VB structures were calibrated to reproduce the experimental free energy change for autodissociation in water, and the mixing of the... 

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