have been developed for analyzing chemical reactions. Below we briefly mention some of these tools, which we would loosely classify into atomic-population-based, bond-order/energy-based, and topology-based ones. The readers are referred to reviews for many other available tools. Atomic charge populations are the intuitive coarsegrained representation of the electronic density. But they are not uniquely defined, practically leading to numerous procedures for computing these charges. These procedures include the decomposition of the one-particle density matrix (actually its product with the overlap matrix, leading to Mulliken and Löwdin charges ), the partitioning of the electronic density (such as the Bader Atom-in-Molecule charges and the Hirshfeld and related charges ), the fitting of electrostatic potentials (such as Merz-Kollman ESP charges and CHELPG charges ), and the natural bond orbital analysis. Besides examining the atomic charge differences between stationary structures, one can also analyze the Fukui functions, which are often approximated as the electron density difference between a neutral molecule and its anion/cation. The corresponding "atomic charges" are widely used to identify electrophilic and nucleophilic sites of reactants.