A valence bond perspective of the reaction force formalism

The reaction force formalism represents a convenient approach to analyze the course of a reaction step. From this analysis, the reaction path can be separated in a number of regions that are associated to either structural changes or electronic reorganization. This empirical observation is rationalized in this work on the basis of a simple two-state valence bond correlation diagram. We demonstrate that the ratio between the integrated reaction force and the region of interest (w_ii/ w_i for the forward reaction and w_iii/ w_iv for the backward reaction) increases with the ratio between the quantum mechanical resonance energy and the energy required to reach the crossing point at the transition state, we call to this ratio the strength of the resonance. This observation means that the size of the transition region (region ii and iii), that includes the transition state, depends on the strength of the resonance, and the structural zones (region i and iv), that are regions associated with the pure valence bond state curves (no resonance). We propose a simple analytical relationship for w_ii/ w_i and w_iii/ w_iv based on three parameters: (i) the quantum mechanical resonance energy, (ii) the energy of the reaction and (iii) the overlap between the VB structures at the transition state. The previous conclusions were supported by a reaction force analysis of a S _N2 reactions, X ^-+ CH ₃- Y → X - CH ₃+ Y ^-(X = F , Cl , Br). The valence bond parameters for these reactions are estimated from empirical considerations. A very good agreement is found between the computed reaction force ratios and the predicted one.