  We apply scaling and the theory of the fundamental limits of the second-order
molecular susceptibility to identify material classes with ultralarge
nonlinear-optical response. Size effects are removed by normalizing all
nonlinearities to get intrinsic values so that the scaling behavior of a series
of molecular homologues can be determined. Several new figures of merit are
proposed that quantify the desirable properties for molecules that can be
designed by adding a sequence of repeat units, and used in the assessment of
the data. Three molecular classes are found. They are characterized by
sub-scaling, nominal scaling, or super-scaling. Super-scaling homologues most
efficiently take advantage of increased size. We apply our approach to data
currently available in the literature to identify the best super-scaling
molecular paradigms with the aim of identifying desirable traits of new
materials.
