The empirical valence bond method

The diagonal elements of the EVB hamiltonian correspond to the diabatic energies of the valence bond states and are given by a regular force field expression 

One advantage with the EVB approach is that and Hy can be calibrated using experimental information on reaction free energies and activation barriers (AG ) for relevant reference reactions in solution. The resulting parameters (typically Aa and H J) are then used without change in simulations of the enzyme reaction. The obtained result is then the effect on the free energy profile when the reaction is transferred from one environment (water solution) to another (solvated enzyme). 

The free energy is evaluated by driving the system between different VB states using an FEP mapping potential of the form  

The actual ground-state free energy is then obtained from the expression  

AG(i ) in Equation 5 denotes the mapping free energy for a particular value of the mapping vector that contributes the sampling of the reaction coordinate value X. The generalized multidimensional reaction coordinate is as usual taken as the energy gap Ae.. between relevant diabatic VB states [18-20]. 

---

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. 

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). 

These problems were attacked through simulation by Keirstead, Wilson, and Hynes. 232 jhg techniques they used are similar to those used in the simulation of electron-transfer reactions by Zichi et al. and are related to the empirical valence bond method of WarsheP discussed previously. The technique involved constructing an overall Hamiltonian from the Hamiltonians for the covalent, H ov> and ionic, electronic states of the t-butyl chloride... 

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. 

This chapter presents the implementaiton and applicable of a QM-MM method for studying enzyme-catalyzed reactions. The application of QM-MM methods to study solution-phase reactions has been reviewed elsewhere [44]. Similiarly, empirical valence bond methods, which have been successfully applied to studying enzymatic reactions by Warshel and coworkers [19,45], are not covered in this chapter. 

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... 

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]. 

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

The Knudsen effusion method In conjunction with mass spectrometrlc analysis has been used to determine the bond energies and appearance potentials of diatomic metals and small metallic clusters. The experimental bond energies are reported and Interpreted In terms of various empirical models of bonding, such as the Pauling model of a polar single bond, the empirical valence bond model for certain multiply-bonded dlatomlcs, the atomic cell model, and bond additivity concepts. The stability of positive Ions of metal molecules Is also discussed. 

In the empirical valence bond (EVB) model [304, 349, 370] a fairly small number of VB functions is used to fit a VB model of a chemical reaction path the parameterisation of these functions is carried out to reproduce experimental or ab initio MO data. The simple EVB Hamiltonian thus calibrated for a model reaction in solution can subsequently be used in the description of the enzyme-ligand complex. One of the most ingenious attributes of the EVB model is that the reduction of the number of VB resonance structures included in the model does not introduce serious errors, as would happen in an ab initio VB formulation, due to the parameterisation of the VB framework which ensures the reproduction of the experimental or other information used. This computationally efficient approach has been extensively used with remarkable success [305, 306, 371, 379] A similar method presented by Kim and Hymes [380] considers a non-equilibrium coupling between the solute and the solvent, the latter being treated as a dielectric continuum. 

Empirical Valence Bond Methods. - To examine some important questions relating to enzyme action (e.g. to analyse the causes of catalysis, i.e. why an enzymic reaction proceeds faster than the equivalent, uncatalysed reaction in solution), it is necessary to use a method that not only captures the essential details of the chemical reaction, but also includes the explicit effects of the enzyme and solvent enviroment. One notable method in this area is the empirical valence bond (EVB) model.143 In the empirical valence bond approach, resonance structures (for example ionic and covalent resonance forms)... 

QM/MM (AM1/CHARMM) or empirical valence bond methods, respectively164 168), for forcing the conformation of chorismate in solution into the more restricted conformation found in the enzyme. This equates to a catalytic benefit of only around 40-55% of the total AA G between enzyme and solvent. The good agreement between these findings, which applied completely different theoretical methods, is striking and suggests that this is a reliable result. 

Formulating chemical reactivity in solutions and in enzymes in a computationally convenient way the empirical valence bond and other QM/MM methods 203... 

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... 

---