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.
Cite this paper
Zabadal, J. , Staudt, E. , Ribeiro, V. , Petersen, C. Z. and Schramm, M. (2022). A Quantum Toy-Model for Inelastic Scattering and Catalysis Based on Bäcklund Transformations. Open Access Library Journal, 9, e8659. doi: http://dx.doi.org/10.4236/oalib.1108659.
Nakagawa, K. (2020) Study of LCAO-MO Calculation by Using Completely Numerical Basis Functions. IOP Conference Series: Materials Science and Engineering, 835, Article ID: 012013. https://doi.org/10.1088/1757-899X/835/1/012013
Schwan, L.O. (1976) LCAO-MO-Matrix Method for Many Electron Systems and Their Application to Defects in Ionic Crystals! Le Journal de Physique Colloques, 37, C7-174-C7-176. https://doi.org/10.1051/jphyscol:1976739
Dewar, M.J.S. and Kelemen, J. (1971) LCAO MO Theory Illustrated by Its Application to H2. Journal of Chemical Education, 48, 494.
https://doi.org/10.1021/ed048p494
Chung, L.W., Sameera, W.M.C., Ramozzi, R., Page, A.J., Hatanaka, M., Petrova, G.P., Harris, T.V., Li, X., Ke, Z., Liu, F., Li, H.-B., Ding, L. and Morokuma, K. (2015) The Oniom Method and Its Applications. Chemical Reviews, 115, 5678-5796.
https://doi.org/10.1021/cr5004419
Feng, Y. and Mazzucato, A.L. (2022) Global Existence for the Two-Dimensional Kuramoto-Sivashinsky Equation with Advection. Communications in Partial Differential Equations, 47, 279-306. https://doi.org/10.1080/03605302.2021.1975131
van den Berg, J.B. and Queirolo, E. (2022) Rigorous Validation of a Hopf Bifurcation in the Kuramoto-Sivashinsky PDE. Communications in Nonlinear Science and Numerical Simulation, 108, Article ID: 106133.
https://doi.org/10.1016/j.cnsns.2021.106133
Zabadal, J.R., Borges, V., Ribeiro, V. and Santos, M. (2015) Analytical Solutions for Dirac and Klein-Gordon Equations Using Backlund Transformations. INAC 2015: International Nuclear Atlantic Conference Brazilian Nuclear Program State Policy for a Sustainable World, 47, 1-12.
Lanczos, C. (2021) Dirac’s Wave Mechanical Theory of the Electron and Its Field Theoretical Interpretation, Independent Scientific Research Institute Version ISRI-04-13.3, 1-20.
