N. H. List, R. Zaleśny, N. A. Murugan, J. Kongsted, W. Bartkowiak, H. Ågren

*J. Chem. Theory Comput. ***2015**, 11, 4182

**Abstract**

We establish the relationships between the metric of charge transfer excitation (Δ*r*) 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), Δ*r* 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 Δ*r*; if β ∼ (Δ*r*)^{k}, then roughly, δ^{TPA} ∼ (Δ*r*)^{k+1}. Second, a simple power relation between Δ*r* 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.