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

2025-02-24

IEEE Transactions on Visualization and Computer Graphics

AI Summary

This work addresses the challenge of analyzing dynamic evolution of molecular electronic structure under photoexcitation. We propose a visual analytics method tailored to time-varying bivariate electron density fields—specifically, hole/particle natural transition orbitals (NTOs). Our approach innovatively integrates continuous scatterplots (CSP) with 4D image geometric moments (zeroth- to second-order central moments) to achieve dimensionality reduction and trajectory modeling at high temporal resolution. Principal component analysis (PCA) further supports identification of critical time steps and pattern tracking. Evaluated on two excited-state molecular dynamics simulations, the method successfully uncovers charge-transfer pathways, dynamic bifurcation points, and time-resolved donor–acceptor interaction patterns. It significantly enhances interpretability and visual insight into quantum chemical processes, enabling intuitive exploration of complex electronic dynamics in photoinduced reactions.

Technology Category

• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data
• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Web Mining and Content Analysis: Web data visualization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Data transparency and provenance

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.

Problem

• Analyzes time-varying bivariate fields in electronic structures.
• Uses continuous scatterplots for visual exploration of dynamics.
• Tracks temporal evolution of molecular electronic transitions.

Innovation

• Continuous scatterplots for time-varying analysis
• Image moment descriptors for feature exploration
• Principal component analysis for pattern recognition