Fundamental limits on two-photon absorption cross sections

We apply sum rules to calculate the maximum limit of the resonant two-photon absorption cross section. Comparison of the theory with experimental data from the literature shows that no molecule ever measured exceeds this limit. Molecules with more π electrons have larger two-photon cross sections; but, the two-photon cross sections fall further below the fundamental limit as the number of electrons increases—implying that the additional electrons are not participating efficiently. The sum rules can aid in developing structure property relationships by providing metrics that lead to a deeper understanding of the available data.