Origin, scaling, and saturation of second order polarizabilities in donor/acceptor polyenes

Two-dimensional plots representing the changes in charge and bond-order distributions induced by the optical field are used to investigate the size-scaling of polarizabilities of donor/acceptor substituted elongated polyenes. The second order polarizability (β) is shown to originate from localized regions at the donor/acceptor ends and therefore saturates to a constant value, independent on polyene size n, for large n. In contrast, the linear (α) and cubic (γ) polarizabilities have contributions from the entire chain and grow linearly with n. These real-space plots reveal directly the relevant electronic coherence sizes that control the optical response and should be most valuable in the design of new optical materials.