Earth Mover's Charge Transfer Distance: A General and Robust Approach for Describing Excited State Locality

A novel approach for assessing the extent of electron displacement in optical transitions is proposed by implementing the Earth Mover's Distance (EMD) method, which quantifies the spatial dissimilarity between ground and excited state electron density distributions. In contrast to previous descriptors, this index provides a representative and intuitively understandable distance under a robust and computationally efficient scheme for all possible forms of locality, even in the most difficult to dissect topological cases. The theoretical differences among the existing indices and our method are first illustrated with the help of a simplified model system, followed by a benchmarking of several partial atomic charge models using experimentally relevant push-pull compounds with diverse symmetries. These same molecules are finally employed to further demonstrate the principal advantages of the EMD index and its capabilities in rationalizing charge transfer phenomena.