Valence-bond representation forces

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... 

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]. 

INS experiments evidence decoupling of the proton bending modes from carbonate entities [Fillaux 1988 Kashida 1994], Simulations of the spectral profile with valence-bond force-field models based on infrared and Raman spectra [Nakamoto 1965], yield spectacular differences between observation and calculations. Discrepancies arise from the force-field representation itself and cannot be eliminated by straightforward adjustment of the force constants. The model protons, bound to oxygen atoms by strong forces, ride displacements at low frequency of carbonate entities, mainly below 200 cm-1. Calculated intensities for these lattice modes are overestimated by at least one order of magnitude. 

The following simplified treatment is presented to illustrate some roughly quantitative aspects of the theory. The value of 0 is taken to be constant, with AO = 120°. The interaction constant p is taken as 0.36 yaV22ipiARi, in which pt is the fraction of ions i in the crystal and ARt is the change in radius. The quantity v v, the cube of the average valence for the metal or alloy, is an approximate representation of the force constant k of the bonds, which enters linearly in the expression for V. The coefficient z has the value +1 for M+ and —1 for M. The number 0.36 has been introduced to give agreement with the observed... 

The focus in the reaction dynamics studies was on the N02 elimination channel, but they also studied the HONO elimination reactions [70]. They based the potential energy surface on experimental data but performed some minimal basis set ab initio calculations to determine geometries, force fields, torsional potentials, and some information about the reaction paths. The representations of the global potential energy surfaces were based on valence force fields for equilibrium structures with arbitrary switching functions operating on the potential parameters to effect smooth and (assumed) proper behavior along the reaction paths. Based on the available experiments [71-73], they assumed that the primary decomposition reaction is simple N-N bond rupture to eliminate N02. 

Intimately connected to the choice of bending parameters is the choice between a general valence force (GVFF) expression (including a stretch-bend interaction) or a UBFF representation. The necessity for the inclusion of either a stretch-bend or a Urey-Bradley term to account for the abnormally long bonds in e.g. norbomane was pointed out by several authors 17,22,31), Several representations have been proposed normal non-bonded interactions 24) the classical UB expression 21) and whittled atoms 7,31,56) (smaller radii in the direction of the geminal atoms), but a further theoretical analysis of the UB potentials seems mandatory. 

The quantum mechanical and bond valence theories can thus be seen as complementary descriptions, both being exact representations of the Coulomb force, one expressed through the electric potential, the other through electric field. The quantum model gives the energy of a molecule or crystal and describes its excited states. It also gives the distribution of the electron density, but it does not give the... 

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