Topological analysis of density fields: an evaluation of segmentation methods for quantum chemistry applications

Topological and geometric segmentation methods provide powerful concepts for analysis and visualization of density fields. Thereby highly accurate geometric segmentation is required for a reliable quantitative analysis, which cannot always be guaranteed. There is a large discrepancy between the promising theory and the available computational approaches. We compared and evaluated various segmentation methods with the aim to identify and quantify the extent of these discrepancies. Thereby, we focus the analysis of electron density fields, a scalar quantity that can be experimentally measured or theoretically computed. We consider methods originating from the domain of quantum chemistry and computational topology. We apply the methods to the charge density of a set of crystals and molecules. As a result, we conclude that an accurate geometry determination can be crucial for correctly segmenting and analyzing electron density fields.

Figure Caption: Different segmentation in comparison for the molecule PNA.

Reference: Topological analysis of density fields: an evaluation of segmentation methods. Alexei Abrikosov, Talha Bin Masood, Martin Falk, and Ingrid Hotz. Computers & Graphics 98, 231 (2021).