The study of electronic transitions within a molecule connected to the absorption or emission of light is a common task in the process of the design of new materials. The transitions are complex quantum mechanical processes and a detailed analysis requires a breakdown of these processes into components that can be interpreted via characteristic chemical properties. We approach these tasks by providing a detailed analysis of the electron density field. This entails methods to quantify and visualize electron localization and transfer from molecular subgroups combining spatial and abstract representations. The core of our method uses geometric segmentation of the electronic density field coupled with a graph‐theoretic formulation of charge transfer between molecular subgroups. The design of the methods has been guided by the goal of providing a generic and objective analysis following fundamental concepts. We illustrate the proposed approach using several case studies involving the study of electronic transitions in different molecular systems.

Figure 1: Studying electronic transitions in a copper complex Cu-PHE-PHEOME. (a) Continuous scatter plot (CSP) of the hole and particle NTO (φ h , φ p ) and query line segments (green and red). (b) Fiber surfaces corresponding to the query line segments displayed on a ball-and-stick model of the molecule. (c) A Voronoi diagram-based segmentation of the molecule into its subgroups. (d,e,f) Peeled CSP corresponding to the subgroups (Cu, PHE, PHEOME; inset -Voronoi regions) help study their behavior.

Electronic transitions in molecules due to the absorption or emission of light is a complex quantum mechanical process. Their study plays an important role in the design of novel materials. A common yet challenging task in the study is to determine the nature of electronic transitions, namely which subgroups of the molecule are involved in the transition by donating or accepting electrons, followed by an investigation of the variation in the donor-acceptor behavior for different transitions or conformations of the molecules. In this paper, we present a novel approach for the analysis of a bivariate field and show its applicability to the study of electronic transitions. This approach is based on two novel operators, the continuous scatterplot (CSP) lens operator and the CSP peel operator, that enable effective visual analysis of bivariate fields. Both operators can be applied independently or together to facilitate analysis. The operators motivate the design of control polygon inputs to extract fiber surfaces of interest in the spatial domain. The CSPs are annotated with a quantitative measure to further support the visual analysis. We study different molecular systems and demonstrate how the CSP peel and CSP lens operators help identify and study donor and acceptor characteristics in molecular systems.

We present a pipeline for the interactive visual analysis and exploration of molecular electronic transition ensembles. Each ensemble member is specified by a molecular configuration, the charge transfer between two molecular states, and a set of physical properties. The pipeline is targeted towards theoretical chemists, supporting them in comparing and characterizing electronic transitions by combining automatic and interactive visual analysis. A quantitative feature vector characterizing the electron charge transfer serves as the basis for hierarchical clustering as well as for the visual representations. The interface for the visual exploration consists of four components. A dendrogram provides an overview of the ensemble. It is augmented with a level of detail glyph for each cluster. A scatterplot using dimensionality reduction provides a second visualization, highlighting ensemble outliers. Parallel coordinates show the correlation with physical parameters. A spatial representation of selected ensemble members supports an in‐depth inspection of transitions in a form that is familiar to chemists. All views are linked and can be used to filter and select ensemble members. The usefulness of the pipeline is shown in three different case studies.

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