Relation between Nonlinear Optical Properties of Push-Pull Molecules and Metric of Charge Transfer Excitations

We establish the relationships between the metric of charge transfer excitation (Delta r) for the bright pi pi* state and the two-photon absorption probability as well as the first hyperpolarizability for two families of push pull pi-conjugated systems. As previously demonstrated by Guido et al. (J. Chem. Theory Comput. 2013, 9, 3118-3126), Delta 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 Delta r; if, beta similar to (Delta r)(k), then roughly, delta(TPA) similar to (Delta r)(k+1). Second, a simple power relation between Delta 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 pi-conjugated systems through the metric of charge transfer.