  The scaling of the fundamental limits of the second hyperpolarizability is
used to define the intrinsic second hyperpolarizability, which aids in
identifying material classes with ultralarge nonlinear-optical response per
unit of molecular size. The intrinsic nonlinear response is a size-independent
metric that we apply to comparing classes of molecular homologues, which are
made by adding repeat units to extend their lengths. Several new figures of
merit are proposed that quantify not only the intrinsic nonlinear response, but
also how the second hyperpolarizability increases with size within a molecular
class. Scaling types can be classified into sub-scaling, nominal scaling that
follows the theory of limits, and super-scaling behavior. Super-scaling
homologues that have large intrinsic nonlinearity are the most promising
because they efficiently take advantage of increased size. We apply our
approach to data in the literature to identify the best super-scaling molecular
paradigms and articulate the important underlying parameters.
