• Water freezing in nano-confined systems

We all know that bulk water freezes at 0 degree Celsius. However, when we confine water in a tube or tunnel with a diameter of few nanometres its freezing temperature can drop by tens of degrees. Moreover, the freezing temperature can differ in different parts of the tube or tunnel, such as in the graphene wrinkle shown in the picture. There are several topics that can be studied for such systems. For example, we can use computer simulations to understand how the flexibility and surface of the tube or tunnel affect the freezing temperature. As it's very difficult to freeze water in computer simulations, even below zero Celsius, another topic could be to to test if the freezing can be induced by fixing some of the water molecules in the structure of ice.

• Using neural networks to predict interactions between molecules

Simulations of complex systems are often performed using simplified models of molecules capturing electrostatic interactions, attractive dispersion forces, and repulsive short range interactions. While they are computationally cheap, the models are often too simple to describe the fine details of the interactions. Recent years have seen a growing interest into models based on neural networks or other machine learned potentials. They offer higher accuracy at computational cost lower than high-level methods based on quantum mechanics. The goal of this project will be to test some of these approaches for modelling interactions in molecular solids.

• Solving the CO₂ puzzle

Carbon dioxide is a very important molecule. It is therefore necessary to be able to accurately describe its interactions with different materials. The most widely used methods for computer simulations of materials surprisingly fail in accurately describing the interactions even in the simplest system involving carbon dioxide, its crystal phase (the dry ice). In this project we will analyze the interactions between the molecules in the CO₂ crystal to find out what is the cause of this problem.

• Interactive homeworks for quantum mechanics

To goal of this project is to create interactive Jupyter notebooks with homeworks given in the lecture course Introduction to quantum mechanics taught in the summer term of the second year of BSc. Some of the homeworks are on this page. Examples of such notebooks can be found for example here (files ending with ipynb) or here for a bit advanced topics.

• Precision of ab-initio calculations (funded by ERC)

One often finds differences when comparing published binding energies of molecular solids. And the differences can be large, in fact, terribly large. They can be even found for results published with the same computational package! One of the goals of this project is to understand the limits of precision of widely used programmes and identify settings that allow trustworthy results to be obtained. This will allow the candidate to make reliable predictions of important properties of molecular solids, such as of the transition pressures between high pressure phases of matter.