Real Space Partitioning of the First Hyperpolarizability

Two approximate partitioning schemes for the principal component of the first static hyperpolarizability are introduced within the framework of the quantum theory of atoms in molecules (QTAIM). The first approach employs a two-state model, while the second utilizes finite difference techniques. Both methods decompose the principal hyperpolarizability component into contributions arising from atom polarizations and charge transfer. We decompose the hyperpolarizability of 14 D-π-A systems. Our results highlight the dominant role of the charge transfer component. Moreover, a strong correlation is observed between the strength of the donor and acceptor groups and the activation of the π-fragment, which amplifies the principal hyperpolarizability component. Notably, the acceptor fragments across different compounds exhibit partially transferable hyperpolarizability values. These findings shed light on the intricate relationship between functional group characteristics and the nonlinear optical properties of molecules, offering strategic insights into the rational design of advanced materials tailored for optical applications.