Electron Density Transport During Chemical Reactions

Statistical analyses are emerging as powerful new tools to characterize changes in electronic structure during reactions or upon molecular excitation. Of particular need are tools that have the potential to be implemented in high-throughput studies of reactions in complex environments. This requires not only computational efficiency, but also minimal pre- or post-processing from the output of a quantum mechanical calculation. Toward that end, this work explores two techniques: Optimal transport (OT) theory and multiresolution dynamic mode decomposition (MrDMD). OT creates a transport plan for a given mass of electron density from one discretized electron density distribution to another. MrDMD uses an adapted form of singular value decomposition to identify slow and fast fluctuation modes by recursively subdividing the data. The Bergman cyclization reaction is used as a model reaction that demonstrates the chemical intuitiveness of the OT plan. Additional chemical insights are extracted through various partitioning schemes (shown in this work) of the transport plan. MrDMD is shown to reconstruct the density evolution during the reaction with minimal error. The different modes of electron density fluctuations, identified by MrDMD, show varying ability to distinguish between the σ bond formation and diradical formation events along the reaction coordinate.