The investigation of molecular structures is a hot research forefront at the triple point of Materials Science, Chemistry, and Physics. Driven by their fascinating electronic and mechanical properties, research on low-dimensional materials is exponentially growing. New findings are emerging at an always increasing pace, ranging from fundamental concepts to applications.

We focus on the variational modeling of molecular geometries within the frame of Molecular Mechanics: effective configurations are identified as minimizers of classical configurational potentials. In contrast to the wealth of experimental evidence and numerical simulations currently available, rigorous mathematical results on local and global crystalline geometries are scarce and the study of the emergence of different scales within molecular structures is still in its infancy.

The project aims at obtaining new mathematical understanding of molecular geometries and scale effects. Ranging from the nano to the macroscale, we address crystallization for molecular compounds, the description of local molecular features including defects and rigidity, the occurrence of global geometric characteristics such as flatness in 3d and stratification, and eventually the passage from discrete to continuum theories.

Compared with simulations, the theoretical approach bears the advantage of being system-size independent, a crucial asset for investigating effects across scales. Grounded on variational methods for atomistic models, the methodology will integrate techniques from discrete mathematics and stochastics as well.

This project is embedded within the activities of the Research Group of Manuel Friedrich at Friedrich-Alexander-Universität Erlangen-Nürnberg (previously based at the Westfälische Wilhelms-Universität Münster), and of the Research Group on Applied Mathematics and Modeling of Ulisse Stefanelli at the University of Vienna.