Topological analysis of density fields: An evaluation of segmentation methods

Alexei I Abrikosov,Talha Bin Masood,Martin Falk,Ingrid Hotz

doi:10.1016/j.cag.2021.05.015

Alexei I Abrikosov, Talha Bin Masood + Show 2 more

Open Access

https://doi.org/10.1016/j.cag.2021.05.015

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Journal: Computers & Graphics	Publication Date: Jun 16, 2021
Citations: 2	License type: cc-by

Affiliation: Linköping University

Abstract

Topological and geometric segmentation methods provide powerful concepts for detailed field analysis and visualization. However, when it comes to a quantitative analysis that requires highly accurate geometric segmentation, there is a large discrepancy between the promising theory and the available computational approaches. In this paper, we compare and evaluate various segmentation methods with the aim to identify and quantify the extent of these discrepancies. Thereby, we focus on an application from quantum chemistry: the analysis of electron density fields. It is a scalar quantity that can be experimentally measured or theoretically computed. In the evaluation 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. Therefore, we segment the volumes into atomic regions and derive and compare quantitative measures such as total charge and dipole moments from these regions. As a result, we conclude that an accurate geometry determination can be crucial for correctly segmenting and analyzing a scalar field, here demonstrated on the electron density field.

Highlights

Segmentation is a fundamental step in many visualization pipelines
During the analysis of electronic charge density fields, we observed large differences in the segmentation results using different implementations of the same topological concepts which can have a severe impact on the visualization and the analysis results
The goal of our work is to evaluate commonly used algorithms and models for the segmentation of the electronic charge density field which are used to compute atomic charges and dipole moments as well as their use for visualization

Summary

Introduction

Segmentation is a fundamental step in many visualization pipelines. When it comes to scalar density fields a common class of approaches build on topological concepts. During the analysis of electronic charge density fields, we observed large differences in the segmentation results using different implementations of the same topological concepts which can have a severe impact on the visualization and the analysis results. A common way to compute the density field ρ(r) is by utilizing one of the many density functional theory (DFT) packages with the most popular being VASP [18] and GAUSSIAN [20] These packages generate a discrete 3D grid to represent the charge density distribution as a scalar field in some arbitrary total volume Vtot. Because it lacks the description of core electrons there are cavities around the atoms (Fig. 1(a,b)) This leads to a more complex topological structure of the density field and makes the direct determination of the correct maximum, associated with the atomic position, impossible without utilizing additional algorithms. The description of the electronic charge density field is less accurate and leads to errors when computing charges; a fact statement that will be evident in the results section

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Results

Conclusion