Hartree-Fock course for the Han-sur-Lesse Winterschool of 2021

Requirements

For going through these exercises, please install the Anaconda suite. Next, install PyQInt and PyTessel.

Exercises

Exercise 01: Integrals for the H atom

This exercise teaches you about contracted Gaussian functions and the various different integrals that can be constructed. We start simple by exploring a single H atom which has a single electron.

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Exercise 02: Integrals for the He atom

We expand upon the previous exercise and start to look into a He atom. He contains two electrons and as such, a two-electron integral occurs corresponding to the repulsion between these two electrons. In this exercise, you will learn how to evaluate a two-electron integral and calculate the total electronic energy for the He atom.

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Exercise 03: Integrals for the H2 molecule

In this exercise, we are going to evaluate the integrals for the H2 molecule. Because the H2 molecule has two CGFs (one for each H atom), we are going to obtain matrices rather than scalar values for the integrals. Instead of a single value for the overlap and kinetic integrals, we will obtain 2x2 matrices. For the nuclear attraction integral, we in fact obtain two such 2x2 matrices (one for each H atom). Finally, there will be 16 two-electron integrals which will contain a total of 4 unique values.

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Exercise 04: Building the transformation matrix

To perform the SCF algorithm, we need to produce a unitary transformation matrix that orthogonalizes the basis functions in the basis set. We will use the canonical procedure for this which is demonstrated in this exercise.

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Exercise 05