Abstract:

Due to the fact that Chemistry is mostly an experimental science, degree students in this discipline are intrinsically well-prepared to understand the theory behind different experiments. However, when moving to a more abstract branch of this science, as the Quantum Chemistry, they are usually lost, as experimental references are, generally, outside the scope of a chemistry laboratory. For this reason it is of importance to provide students with exercises that connect different concepts in an easy manner.

One of the cornerstones of a Quantum Chemistry subject, in general associated to the 2nd or 3rd year of the degree in Chemistry, is the mono-determinal Hartree-Fock method. We have found that students usually have difficulties when extending their knowledge acquired from one-determinal wave functions to open shell systems, where the single Slater determinant vision fails. The way to deal with such situations is often avoided in the lectures of Physical Chemistry, which in our concern is a terrible mistake. In order to correct this, we have proposed, to our students, different exercises. We have found that a well structurated exercise of a simple case comprising good leading questions was followed by an improvement in the results of our students. Here, as done in our lessons, we present a complete exercise for a two-unpaired-electron system divided into two parts: one analyzing the reason of why the one-determinant approximation is not good for the description of the system and which wave function could be suitable approximation, and the other applying the variational principle and allowing the student to find that the variational method is able to discriminate between spin-states when the spin is not considered in the Hamiltonian. A extended version of the exercise (involving a system of three electrons) is also presented and recommended as an optional exercise.

We found that these exercises strengthened several concepts that are known by the students (Slater determinants, Hartree-Fock method, variational method or Hund’s rule) and introduce new ones (spin-adapted configurations, the role of the spin matrix or the Configuration Interaction method) in a simple and effective way.

Keywords:

Spin adapted configurations, pure spin states, Hund’s rule, S2 matrix, configuration interaction, variational method.