Origin-Independent Decomposition of the Static Polarizability

Real-space analysis tools afford additive and transferable contributions of atoms to molecular properties. In the case of the molecular (hyper)polarizabilities, the atomic contributions that have been derived so far include a charge-transfer term that is origin-dependent. In this letter, we present the first genuinely origin-independent energy-based (OIEB) methodology for the decomposition of the static (hyper)polarizabilities that benefits from real-space molecular energy decomposition schemes, focusing on the static polarizability and showing that extension to static hyperpolarizabilities is straightforward. The numerical realization of the OIEB method shows the expected origin independence, atomic additivity, and transferability of atomic and functional group polarizability tensors. Furthermore, the OIEB atomic (fragment) polarizability tensors are symmetric by definition.