Interactively Applying the Variational Method to the Dihydrogen Molecule: Exploring Bonding and Antibonding

摘要

In this work we are going to present how an interactive platform can be used as a powerful tool to allow students to better explore a foundational problem in quantum chemistry: the application of the variational method to the dihydrogen molecule using simple Gaussian trial functions. The theoretical approach for the hydrogen atom is quite straightforward, however, the level of complexity increases considerably for the dihydrogen molecule. Although, as shown in this work, it is possible to obtain an analytical expression for the dihydrogen molecule variational integral by "pen-and-paper", this expression cannot be completely appreciated without the proper tools. In this work the "dry" analytical equations were implemented into an interactive platform that allows the students to visualize results (like probability densities and meaningful graphs), play with parameters, and thus gain a deeper understanding of the problem itself. Having an interactive environment is also important as a way of minimizing complex equations, testing analytical results with numerical calculations, among other things,that otherwise would be unachievable by "pen and paper" only. Additionally, in this work the bonding and antibonding behaviors of the dihydrogen molecule were investigated and evaluated in detail. As a final outcome, this article shows that important properties regarding, the dihydrogen molecule (like equilibrium bond length an favorability of formation) can be explained and approximated with the variational method.