Geometric Machine Learning in Quantum Chemistry

Quantum chemistry allows predicting the properties of molecular systems with great precision by invoking, and solving numerically, the laws of quantum mechanics. Unfortunately, it is held back by the computational effort which scales badly with the size of the system under study. Machine Learning is about to revolutionize the field of electronic structure theory by greatly reducing this computational effort. Principled machine learning approaches respect the roto-translational symmetries of the problem. This is the dominion of geometric machine learning.

Spherical harmonics give all irreducible representations of SO(3). Figure from [e3nn.org](https://e3nn.org/). — Spherical harmonics give all irreducible representations of SO(3). Figure from e3nn.org.

The aim of the lecture is to enable you to approach and understand the latest literature in this burgeoning field. Its first half is an introduction to elements of electronic structure theory, the quantum mechanics of many-electron systems. The second half introduces geometric machine learning in SO(3) and its applications to quantum chemistry.

Style

The lecture is a slow-paced blackboard lecture. There are no lecture notes and you are expected to take your own notes (not just take a picture at the end of class). In the final part of the semester, you will read some of the latest works in the field, and we will discuss those in an inverted classroom setting.

Exercises are mostly computational (running experiments with pySCF and other packages, plus some python coding) and partly pen-and-paper.

Part 1: Quantum Chemistry

Introduction, Born-Oppenheimer approximation
Multi electron wave functions, Hartree product, Slater determinants
Hartree-Fock approximation
Basis functions and numerical evaluation of integrals
Density functional theory
Exchange and correlation holes and functionals

Part 2: Geometric Machine Learning

Graph convolutional neural networks, attention, message passing neural networks
Irreducible representations of SO(3) and spherical harmonics
Tensor field equivariant neural networks

Part 3: Synthesis

KineticNet (Inverted classroom)
M-OFDFT (Inverted classroom)

Prerequisites

One lecture in quantum mechanics (required), basic notions of machine learning (recommended).

Formalities

Time and Place: To allow students to reach Neuenheimer Feld in time for the next lecture, we start at 9h00 (not 9h15). The lecture is on Thursdays in the “Kleine Hörsaal” (second floor) of Philosophenweg 12.

The lecture accounts for 6CP and can be elected as part of the Computational Physics specialization.

Registration is not required. Simply come to the first lecture on April 18th.

Literature

Frank Jensen, Introduction to Computational Chemistry (3rd edition)