QUANTUM CHEMISTRY ON A CLIFFORD TORUS

Work package:
What is the best way to model a solid? A solid is usually modeled either as an infinite periodic system or as a small finite fragment. However, infinite periodic systems are not compatible with the long- range Coulomb potential that governs the interactions between the particles, while finite fragments severely suffer from border effects. Is there not a better approach to model solids? We have recently proposed an alternative approach to model periodic systems, such as solids, using a Clifford topology [1,2]. This periodicity is similar to the periodicity of the PacMan universe. When PacMan exits on one side of the screen, it reappears immedi- ately on the opposite side. We have successfully applied this approach to Wigner crystals, i.e., crystals containing only electrons [3,4]. We now want to extend our approach to crystalline solids. To achieve this, we have to describe both electrons and nuclei as well as their interactions within the Clifford topology. We will use accurate many-body quantum theories such as coupled-cluster theory to describe the electron-electron interactions. During the internship the student will develop equations to perform quantum-chemistry calculations in the Clifford topology and implement these equations in a computer code that will perform calculations on solids. This Master project is part of a more vast project financed by the ANR. It is desirable that the candidate for this internship likes to discuss and exchange ideas. It is also an advantage if the candidate has some programming skills.