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.

翻译：光诱导电子跃迁是复杂的量子力学过程，其中电子因光吸收而在能级间移动。这会引发电子结构和核几何构型的动力学变化，驱动光生物学、材料设计和医学等领域的重要物理与化学过程。演化中的电子结构可通过两个电子密度场表征：空穴与粒子自然跃迁轨道（NTOs）。研究这些密度场有助于理解分子内供体与受体区域间的电子电荷迁移。以往研究依赖于等值面的并列视觉比较、统计方法或仅含少数实例的双变量场分析。本文提出一种分析含大量实例的时变双变量场的新方法，这对理解光诱导动力学过程中的电子结构变化具有重要意义。由于NTO场依赖于核几何构型，核运动导致需要分析大量时间步长。本文提出一种结构化方法，利用连续散点图（CSPs）和基于图像矩的描述符，针对光激发后演化电子结构的研究，实现时变双变量场的特征导向可视化探索。每个时间步长下双变量场的CSP由一个四维图像矩向量表示。所有向量描述符的集合构成R^4空间中的点云，并通过主成分分析进行可视化。选取合适的主成分可将点云表示为平面上的曲线，从而辅助完成关键时间步识别、双变量场内模式识别及时间演化追踪等任务。我们通过两个激发态分子动力学的案例研究进行演示，展现双变量场分析如何提供针对特定应用的深入见解。