Continuous Scatterplot and Image Moments for Time-Varying Bivariate Field Analysis of Electronic Structure Evolution

TL;DR

This paper introduces a novel visual analysis method using continuous scatterplots and image moments to study the evolution of electronic structures in molecules during photoinduced dynamics, enabling better understanding of charge transfer processes.

Contribution

It presents a structured approach combining CSPs and image moment descriptors for analyzing time-varying bivariate fields in electronic structure evolution, which was not previously available.

Findings

Effective visualization of electronic structure changes during molecular dynamics.

Identification of key time steps and patterns in electronic charge transfer.

Demonstrated utility through two case studies on excited-state molecular dynamics.

Abstract

Photoinduced electronic transitions are complex quantum-mechanical processes where electrons move between energy levels due to light absorption. This induces dynamics in electronic structure and nuclear geometry, driving important physical and chemical processes in fields like photobiology, materials design, and medicine. The evolving electronic structure can be characterized by two electron density fields: hole and particle natural transition orbitals (NTOs). Studying these density fields helps understand electronic charge movement between donor and acceptor regions within a molecule. Previous works rely on side-by-side visual comparisons of isosurfaces, statistical approaches, or bivariate field analysis with few instances. We propose a new method to analyze time-varying bivariate fields with many instances, which is relevant for understanding electronic structure changes during light-induced dynamics. Since NTO fields depend on nuclear geometry, the nuclear motion results in numerous time steps to analyze. This paper presents a structured approach to feature-directed visual exploration of time-varying bivariate fields using continuous scatterplots (CSPs) and image moment-based descriptors, tailored for studying evolving electronic structures post-photoexcitation. The CSP of the bivariate field at each time step is represented by a four-length image moment vector. The collection of all vector descriptors forms a point cloud in R^4, visualized using principal component analysis. Selecting appropriate principal components results in a representation of the point cloud as a curve on the plane, aiding tasks such as identifying key time steps, recognizing patterns within the bivariate field, and tracking the temporal evolution. We demonstrate this with two case studies on excited-state molecular dynamics, showing how bivariate field analysis provides application-specific insights.