Density analysis of imaginary part of γ related to two-photon absorption

We have developed a method for elucidating the spatial contributions of electrons to dynamic second hyperpolarizability, γ(−ω;ω,ω,−ω), using an analytical expression of the γ density. The merit of this method is that the dynamic γ density, whose imaginary part is related to the two-photon absorption (TPA) cross-section, can be calculated easily for each virtual excitation process. This method can also be applied to other dynamic response properties. We present, as an example, an interpretation of the spatial contributions of π-electrons to Im γ for trans-stilbene and its donor-disubstituted derivative, i.e., 4,4′-diamino-trans-stilbene.