Trying to tame the Hartree-Fock method

Hi everyone! My name is Edi, I just finished my Master’s degree in condensed matter physics and I was lucky enough to get accepted to project 2108. I was born in Romania, but I did my studies in Budapest, Hungary at ELTE University. Above you can see a view of the city from the Gellért Hill. On the right, in the distance you might recognize the iconic Parliament building.

During my studies I had the opportunity to get involved in 2D materials research, I was always interested in the crossing point of physics and chemistry, where chemistry can help us design materials with specific physical properties. This can also go the other way round, when we use physics to determine the structure and properties of different molecules. The latter is the case of project 2108: Efficient Fock matrix construction in localized Hartree-Fock method. I know, I know, the name is quite intimidating, but the principle is quite simple: take a guess for the electron density of a molecule, do some simple algebra like matrix-multiplications and matrix diagonalization and in some magical way you obtain a guess for the ground state energy of the molecule.

In reality this is quite complicated due to the electron-electron interaction part of the energy: simply put it’s basically impossible to guess how multiple electrons will arrange themselves, when each of the interacts with the other. In this aspect, our situation is similar to the 3 body problem. We have to first guess the electron density of the system, and verify if it is energetically favorable, if not, we modify it and we rinse and repeat. Fortunately, we don’t have to actually understand all the steps in the algorithm ( which is an implementation of the Hartree-Fock method ) in the project, instead we are looking at how different numerical algorithms can help speed up the calculations, and how we can use the architecture of the supercomputer in Zilina, Slovakia to get the fastest results. In short, the task in not the easiest, since we must have a basic understanding of the algorithm we are modifying, but we can doing without having an in-depth knowledge of the physics. We have already come quite a long way, we managed to create a new working code, but we still have ahead all kinds of testing and optimizing steps. I plan to write about this in more detail in the next post.

And for closure, I will add a photo of myself below. I hope you are doing well with your projects, and I wait to see what we manage to achieve during SoHPC 2021. Have a nice summer!