Advances in Charge Displacement Analysis

We define new general density-based descriptors for the quantification of charge transfer and polarization effects associated with the interaction between two fragments and the formation of a chemical bond. Our aim is to provide a simple yet accurate picture of a chemical interaction by condensing the information on the charge rearrangement accompanying it into a few chemically meaningful parameters. These charge displacement (CD) parameters quantify the total charge displaced upon bond formation and decompose it into a charge transfer component between the fragments and charge rearrangements taking place within the fragments. We then show how the new parameters can be easily calculated using the well-known CD function, which describes the charge flow along a chosen axis accompanying the formation of a bond. The approach presented here can be useful in a wide variety of contexts, ranging from weak interactions to electronic excitations to coordination chemistry. In particular, we discuss here how the scheme can be used for the characterization of the donation and back-donation components of metal−ligand bonds, in combination with the natural orbitals for chemical valence (NOCV) theory. In doing so, we discuss the interesting relationship between the proposed parameters and the corresponding NOCV eigenvalues, commonly used as a measure of the electron charge displacement associated with a given bonding contribution. As a prototype case study, we investigate the bond between a N-heterocyclic carbene and different metallic fragments. Finally, we show that our approach can be used in combination with the energy decomposition of the extended transition state method, providing an estimate of both charge transfer and polarization contributions to the interaction energy.