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A valence bond perspective of the reaction force formalism

  • Luis RinconEmail author
  • F. Javier Torres
  • Jose R. Mora
  • Cesar H. Zambrano
  • Vladimir Rodriguez
Regular Article
  • 47 Downloads
Part of the following topical collections:
  1. Chemical Concepts from Theory and Computation

Abstract

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 (\(w_{\text{ii}}/w_{\text{i}}\) for the forward reaction and \(w_{\text{iii}}/w_{\text{iv}}\) 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 \(w_{\text{ii}}/w_{\text{i}}\) and \(w_{\text{iii}}/w_{\text{iv}}\) 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 \({\text{S}}_{N}2\) reactions, \({\text{X}}^{-} + {\text{CH}}_{3}{-}{\text{Y}} \rightarrow {{\text{X}}{-}{\text{CH}}}_{3} + {\text{Y}}^{-} ({\text{X}} = {\text{F}}, {\text{Cl}}, {\text{Br}})\). 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.

Keywords

Reaction force Valence bond correlation diagrams Valence bond resonance energy \({\text{S}}_{N}2\) mechanism 

Notes

Acknowledgements

This work has been performed by employing the resources of the USFQ’s High Performance Computing system (HPC-USFQ). The authors would like to thank to the 2019 USFQ’s collaboration grants and Poli-grants program for financial support.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Grupo de Química Computacional y Teórica, Departamento de Ingeniería QuímicaUniversidad San Francisco de QuitoQuitoEcuador
  2. 2.Instituto de Simulación ComputacionalUniversidad San Francisco de QuitoQuitoEcuador
  3. 3.Departamento de MatemáticasUniversidad San Francisco de QuitoQuitoEcuador

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