A quantum toy-model for inelastic scattering and catalysis based on Bäcklund transformations

Abstract

This work presents a scalar self-consistent quantum model for molecular simulation. This model employs Bäcklund transformations to eliminate the wave function from Klein-Gordon and Schrödinger-type equations. The nonlinear PDE obtained after coupling the quantum model with the Gauss law of electromagnetism contains only the interaction potential. The analytical solutions obtained reproduce some relevant effects related to the evolution of the electronic clouds induced by nonlinear scattering. One of the most relevant results obtained from this new formulation is to confirm and fully justify the fact that Cl2 molecules do not react directly with aromatic rings. This result cannot be reproduced by classical models for molecular simulation. On the other hand, quantum chemistry only furnishes indicia that such electrophilic reactions may not occur, but does not shows explicitly how the electronic clouds evolve along the chemical process.