Abstract:

We have designed and implemented in our classes a series of new numerical exercises aiming to motivate our second year students of Chemistry to learn how to work with a “difficult part” of Quantum Chemistry: variational methods. Our particular implementation has been conceived to encourage individual work with computer facilities that are usually available to undergraduate students. As a consequence, we have observed a significant improvement in the general computing abilities shown by the students. Moreover, learning results on this issue (traditionally reported by students as too theoretical, abstract, or particularly hard to be understood) are significantly better and a smaller, but non-negligible, improvement has been also achieved in the qualifications of the Quantum Chemistry course we teach.

It is well known that molecular orbital theory and valence bond are the two principal models of molecular structure usually employed to rationalise the formation of chemical bonds. Usually they are taught within a physical chemistry course. In our particular case, they are studied in the second year. Whereas the study of these models is ubiquitous, there is only a small number of published numerical examples to illustrate it. This serious shortcoming encouraged us to develop new exercises that could expand the limited group of problems available in the textbooks to enlighten the study of the molecular orbital theory. At the same time, we were interested in challenging our students with practical questions that could catch their attention and they could bring as home work. Finally, we thought it would be desirable that our propositions should be solved making use of worksheets or other software facilities the students could be familiar to or they should become massive users when getting their degree.

The three exercises here proposed exemplify important features of the theory, such as: approximated values approach to the exact solution when the number of variational parameters (basis functions) increases, the effects of including polarization and diffuse functions within the basis functions. For the sake of simplicity and to take advantage of the existence of an exact solution, all the cases are enunciated for the hydrogen molecule-ion in the context of the Born-Oppenheimer approximation, and ask for the electronic energy of the ground state. Also, in all cases, we make use of the usual expressions of overlap, Coulomb, and resonance integrals for 1s hydrogen orbitals. Nevertheless, some additional integrals have to be computed making use of worksheets where numerical integrations methods, like Gauss-Laguerre quadrature, are implemented.

Keywords:

Molecular orbital theory, valence bond theory, chemistry degree, exercises in quantum chemistry.