N. H. List, R. Zaleśny, N. A. Murugan, J. Kongsted, W. Bartkowiak, H. Ågren
We establish the relationships between the metric of charge transfer excitation (Δr) for the bright ππ* state and the two-photon absorption probability as well as the first hyperpolarizability for two families of push–pull π-conjugated systems. As previously demonstrated by Guido et al. (J. Chem. Theory Comput. 2013, 9, 3118–3126), Δr is a measure for the average hole–electron distance upon excitation and can be used to discriminate between short- and long-range electronic excitations. We indicate two new benefits from using this metric for the analyses of nonlinear optical properties of push–pull systems. First, the two-photon absorption probability and the first hyperpolarizability are found to be interrelated through Δr; if β ∼ (Δr)k, then roughly, δTPA ∼ (Δr)k+1. Second, a simple power relation between Δr and the molecular hyperpolarizabilities of push–pull systems offers the possibility of estimating properties for longer molecular chains without performing calculations of high-order response functions explicitly. We further demonstrate how to link the hyperpolarizabilities with the chain length of the push–pull π-conjugated systems through the metric of charge transfer.