Empirical valence bond calculation

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. 

Warshel is to utilize a formula identical to (11.22) in this chapter to compute the free energy change. They employed an empirical valence bond (EVB, below) approach to approximately model electronic effects, and the calculations included the full experimental structure of carbonic anhydrase. An H/D isotope effect of 3.9 1.0 was obtained in the calculation, which compared favorably with the experimental value of 3.8. This benchmark calculation gives optimism that quantum effects on free energies can be realistically modeled for complex biochemical systems. 

The empirical valence bond (EVB) approach introduced by Warshel and co-workers is an effective way to incorporate environmental effects on breaking and making of chemical bonds in solution. It is based on parame-terizations of empirical interactions between reactant states, product states, and, where appropriate, a number of intermediate states. The interaction parameters, corresponding to off-diagonal matrix elements of the classical Hamiltonian, are calibrated by ab initio potential energy surfaces in solu-fion and relevant experimental data. This procedure significantly reduces the computational expenses of molecular level calculations in comparison to direct ab initio calculations. The EVB approach thus provides a powerful avenue for studying chemical reactions and proton transfer events in complex media, with a multitude of applications in catalysis, biochemistry, and PEMs. 

Molecular dynamics free-energy perturbation simulations utilizing the empirical valence bond model have been used to study the catalytic action of -cyclodextrin in ester hydrolysis. Reaction routes for nucleophilic attack on m-f-butylphenyl acetate (225) by the secondary alkoxide ions 0(2) and 0(3) of cyclodextrin giving the R and S stereoisomers of ester tetrahedral intermediate were examined. Only the reaction path leading to the S isomer at 0(2) shows an activation barrier that is lower (by about 3kcal mol ) than the barrier for the corresponding reference reaction in water. The calculated rate acceleration was in excellent agreement with experimental data. ... 

In 1976 Warshel and Levitt introduced the idea of a hybrid QM/MM method [23] that treated a small part of a system (e.g., the solute) using a quantum mechanical representation, while the rest of the system, which did not need such a detailed description (e.g., the solvent) was represented by an empirical force field. These hybrid methods, in particular the empirical valence bond approach, were then used to study a wide variety of reactions in solution. The combined QM/MM methods use the MM method with the potential calculated ab initio [24]. 

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... 

Marelius J, Kolmodin K, Feierberg I, Aqvist J (1998) Q a molecular dynamics program for free energy calculations and empirical valence bond simulations in biomolecular systems. J Mol Graph Model 16(4-6) 213-225, 261... 

The empirical valence bond model has shown good predicting power if one defines the bond multiplicity to be two for compounds such as CePd or BaPd and three for compounds such as LaRh, Ylr, or RhTh. The limitations of the model could also be shown (40) when applied to assumed quadruple bond formation, as in RuV or ThRu or to double bond formation as in CePt or ThPt. The case of ThRu (41) shows that quadruple bonding is approached where suitable valence states are available, but not fully achieved, apparently because of the directional requirements of the bonding in a diatomic molecule. The examples of CePt and ThPt (40) show the calculated values that have been based on an assumed double bond to be too low. Platinum has no suitable valence state for triple bond formation, but apparently forms triple bonds with other... 

A comparison of experimental values for intermetallic diatomic molecules with gold with the corresponding value calculated by the Pauling model and by the atomic cell model has been given in Table 6 of Reference ( ). Table 7 of Reference ( ) shows a comparison between experimental dissociation energies with values calculated by the atomic cell model and the empirical valence bond model. Table 9 of Reference ( ) takes Mledema s refinements (43) of the atomic cell model into account In these comparisons. 

Warshel and collaborators (Warshel and Sussman, 1986 Warshel et al., 1988) developed the empirical valence bond method for obtaining free-energy differences and activation free energies. The effects of Gly-to-Ala mutations in trypsin were accurately simulated. This method was earlier applied to calculation of the potential surface for general acid catalysis of a disaccharide in solution and bound to lysozyme (Warshel and Weiss, 1980). 

Molecular dynamics simulations of enzyme reactions have been performed successfully with semiempirical QM/MM methods [54,57,64,72] (see section 6). The sampling provided by such QM/MM molecular dynamics simulations may be used to calculate activation free energies (and to address dynamical effects on the reaction). Thus, semiempirical QM/MM simulations have an important role to play. It has been suggested that a mapping procedure can be used to calculate ab initio QM/MM reaction free energies from empirical valence bond simulations [39,176]. This approach shows promise, but calculation of energies within the QM system (as opposed to its interaction with its surroundings) from such a simulation remains problematic. 

The interiors of proteins are more densely packed than liquids [181], and so the participation of the atoms of the protein surrounding the reactive system in an enzyme-catalysed reaction is likely to be at least as important as for a reaction in solution. There is experimental evidence which indicates that protein dynamics may modulate barriers to reaction in enzymes [10,11]. Ultimately, therefore, the effects of the dynamics of the bulk protein and solvent should be included in calculations on enzyme-catalysed reactions. Dynamic effects in enzyme reactions have been studied in empirical valence bond simulations Neria and Karplus [180] calculated a transmission coefficient of 0.4 for proton transfer in triosephosphate isomerase, a value fairly close to unity, and representing a small dynamical correction. Warshel has argued, based on EVB simulations of reactions in enzymes and in solution, that dynamical effects are similar in both, and therefore that they do not contribute to catalysis [39]. 

Sawaryn and Sokalski (1979) considered the MEP of a few amino-acid residues around the active site and suggested that the Zn24 and OH" ions stabilise the transition state of the reaction. Unfortunately, the mechanism studied involves an attack of water rather than hydroxyl on C02 and the calculation did not treat correctly the protein dielectrics. The crucial role of the Zn2f cation and its local environment was determined quantitatively by the Empirical Valence Bond/Free Energy Perturbation study ofAqvist and Warshel (1992) and Aqvist et al. (1993). This study demonstrated... 

The computer simulations reported in this chapter are based on the empirical valence bond (EVB) model that will be only briefly described here as it has been extensively discussed elsewhere [1,2], The enzymic reaction of TIM is used as our main example to illustrate both the origin of catalytic effects on PT and methodological aspects of the computational strategy. A more detailed account of the TIM calculations discussed in the next section has recently been reported by Aqvist Fothergill [3]. 

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