Ambiguities in Decomposing Molecular Polarizability into Atomic Charge Flow and Induced Dipole Contributions

Abstract

The molecular dipole polarizability can be decomposed into components corresponding to the charge flow between atoms and changes in atomic dipole moments. Such decompositions are recognized to depend on how atoms are defined within a molecule, as, for example, by Hirshfeld, iterative Stockholder, or quantum topology partitioning of the electron density. For some of these, however, there are significant differences between the numerical results obtained by analytical response methods and finite field calculations. We show that this difference is due to analytical response methods accounting for (only) the change in electron density by a perturbation, while finite field methods may also include a component corresponding to a perturbation-dependent change in the definition of an atom within a molecule. For some atom-in-molecule definitions, such as the iterative Hirshfeld, iterative Stockholder, and quantum topology methods, the latter effect significantly increases the charge flow component. The decomposition of molecular polarizability into atomic charge flow and induced dipole components thus depends on whether the atom-in-molecule definition is taken to be perturbation-dependent.

Four-Dimensional Scaling of Dipole Polarizability: From Single-Particle Models to Atoms and Molecules

“…Of these, assigning polarizabilities to atomic centers is the oldest and the most widely used approach. , This, however, suffers from two shortcomings, namely, the ambiguity of defining atomic polarizabilities and the fact that long-range delocalization and charge transfer effects are not directly amenable to atomic coarse-graining. These problems have been addressed either by including bond-dependent contributions, or by evaluating charge flow effects. , …”