Valence bond potential surfaces

D. L. Miller and R. E. Wyatt, Comparison of diatomics-in-molecules and simple valence-bond potential surfaces for FH25 Chem. Phys. Lett. 38 410 (1976). 

Additional globally defined surfaces in the literature include the pairwise potential of Berard and Thomarrson,28 the semiempirical valence bond potential of Wilkins, and the modified Stockmayer potential of Coltrin et al ... 

A.J.C. Varandas and V.M.F. Morais, Semi-Empirical Valence Bond Potential Energy Surfaces for Homonuclear Alkali Trimers , Mol. Phys. 47, 1241 (1982). T.C. Thompson, G. Izmirlian Jr., S.J. Lemon, D.G. Truhlar, and C.A. Mead, Consistent Analytic Representation of the Two Lowest Potential Energy Surfaces for Lis, Nas, and Ks , J- Chem. Phys. 82, 5597 (1985). 

N. C. Blais and D. G. Truhlar, Monte Carlo trajectories Dynamics of the reaction F 4- D2 on a semiempirical valence-bond potential energy surface, J. Chem. Phys. 58 1090 (1973). 

We shall present results for several kinds of potential energy surfaces. Many of the surfaces are obtained by the London-Eyring-Polanyi-Sato (LEPS) method, involving a single adjustable (Sato) parameter, or by the extended LEPS method, in which different Sato parameters are used for different atomic pairs. These methods are reviewed elsewhere.For other calculations we used rotated Morse curves (RMC),semiempirical valence bond (VB) surfaces, and rotated-Morse-bond-energy-bond-order (RMBEBO) surfaces. 

The main features of the chemical bonding formed by electron pairs were captured in the early days of quantum mechanics by Heitler and London. Their model, which came to be known, as the valence bond (VB) model in its later versions, will serve as our basic tool for developing potential surfaces for molecules undergoing chemical reactions. Here we will review the basic concepts of VB theory and give examples of potential surfaces for bond-breaking processes. 

Here (in contrast to the approach taken in Chapter 2) we do not assume that the energy of each valence bond structure is correlated with its solvation-free energy. Instead we use the actual ground-state potential surface to calculate the ground-state free energy. To see how this is actually done let s consider as a test case an SN2 type reaction which can be written as... 

Figure 4-2. Computed potential energy surface from (A) ab initio valence-bond self-consistent field (VB-SCF) and (B) the effective Hamiltonian molecular-orbital and valence-bond (EH-MOVB) methods for the S 2 reaction between HS- and CH3CI...

Song L, Gao J (2008) On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory. J Phys Chem A ASAP... 

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... 

FIGURE 22.3 The bond order of the C-C bond, the total and the free valence of the C atoms as a function of the C-C distance (obtained in a relaxed potential surface scan using the UHF method). 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

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. 

The electrostatic potential surface for trimethylamine results from a single non-bonded valence molecular orbital (the HOMO), while the electrostatic potential surfaces for dimethyl ether and methyl fluoride result from a combination of two and three high-lying non-bonded molecular orbitals, respectively, i.e. 

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

One other effect that deals with the structure of the interface and how it affects electrochemical reaction rates can be mentioned. As explained in Cliapter 6, some ions (usually anions) chemisorb on the electrode, bending back their solvation sheaths so that the ion itself comes into contact with the electrode surface and forms valence bonds with it. Such effects are potential dependent, and since the adsorption will tend to block the electrode surface, it will change the dependence of log i on Aty assumed earlier [Eq. (7.7)]. Such effects are particularly important in organoelectrochemistiy (see Cliapter 11) where the reactants themselves may adsorb in contact with the electrode as a function of potential and complicate the theory of the dependence of the rate of reaction (or current density, i) on potential... 

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