Finite element density functional description of linear molecules

Sammanfattning: This report describes a project performed at Linnaeus University with the task of solving the Schrodinger equation for electrons in homonuclear diatomic molecules, using the finite element method in Python. The Schrodinger equation is solved for the hydrogen atom, nitrogen atom, hydrogen molecule and nitrogen molecule using a finite element method. The results of the hydrogen atom showed a high accuracy compared to the analytical solution, given that the domain had high enough resolution. The solutions of the hydrogen molecule, nitrogen atom and nitrogen molecule showed reasonable accuracy although the resolution appeared sufficient. This foundation of Python code can be further built upon to explore more molecules and more properties, such as total energies and vibrational energies.