标题： 连续散点图和图像矩用于电子结构演化的时变双变量场分析 显示英文标题

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

摘要： 光诱导的电子跃迁是复杂的量子力学过程，其中电子由于吸收光而从一个能级跃迁到另一个能级。 这会引起电子结构和核几何的动态变化，推动光生物学、材料设计和医学等领域中的重要物理和化学过程。 演化的电子结构可以通过两个电子密度场来表征：空穴和粒子自然跃迁轨道（NTOs）。 研究这些密度场有助于理解分子内给体和受体区域之间的电子电荷运动。 以往的研究依赖于等值面的并排视觉比较、统计方法或少量实例的双变量场分析。 我们提出了一种新方法，用于分析具有许多实例的时间变化的双变量场，这对于理解光诱导动力学期间的电子结构变化具有重要意义。 由于NTO场依赖于核几何结构，核运动导致需要分析大量的时间步长。 本文提出了一种结构化的方法，利用连续散点图（CSPs）和基于图像矩的描述符进行时间变化的双变量场的特征导向可视化探索，专门用于研究光激发后的演化电子结构。 每个时间步长的双变量场的CSP由一个四长度的图像矩向量表示。 所有向量描述符的集合形成一个R^4中的点云，并使用主成分分析进行可视化。 选择适当的主成分可以将点云表示为平面上的曲线，有助于识别关键时间步长、识别双变量场内的模式以及跟踪时间演变。 我们通过两个激发态分子动力学的案例研究展示了这一点，说明双变量场分析如何提供特定应用的见解。 显示英文摘要

摘要： 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.