Webrelaunch 2020

How molecules get in shape

  • Speaker: Dr. Ioannis Anapolitanos
  • Place: Kollegiengebäude Mathematik, Englerstraße 2, Seminarraum 1.067
  • Time: 24.5.2022, 17:30
  • Invited by: Prof. Dr. Dirk Hundertmark

Abstract

Chemical properties of a molecule are determined by its shape. For example, the energy needed to initiate chemical reactions depends highly on the shape and structure of the involved molecules. It has also been known for a long time that the biological properties of protein molecules are determined by their structure.
This naturally leads to several deep questions: How to determine the structure of molecules, is there a way to optimize the energy needed for chemical reactions, and so on.

I will explain how to mathematically formulate this type of question for a specific group of chemical reactions, which are called isomerizations. This involves a single molecule, which changes its shape. Often, the initial and final shape of a molecule are given and one is seeking a path in the configuration space of the molecule, which describes how it changes its shape. The calculation of such reaction paths is very standard in quantum chemistry. While in quantum chemistry it is tentatively assumed that an optimal reaction path exists, this is far from obvious from a mathematical point of view. In fact, it is still an open problem!

I will discuss recent results which provide a first step in this direction. In particular, I will describe some fundamental properties of molecules, concerning their structure and the forces between them. While our personal experience of the world involves mostly classical terms, the properties of molecules and matter at a microscopic scale necessarily involve quantum mechanics. However, for the purpose of this talk, I will not assume any previous knowledge of quantum mechanics. The talk is based on two recent papers, one with Mathieu Lewin, which was recently published, the other one being work in progress with Marco Olivieri and Sylvain Zalczer.