  We use numerical optimization to study the properties of (1) the class of
one-dimensional potential energy functions and (2) systems of point charges in
two-dimensions that yield the largest hyperpolarizabilities, which we find to
be within 30% of the fundamental limit. We investigate the character of the
potential energy functions and resulting wavefunctions and find that a broad
range of potentials yield the same intrinsic hyperpolarizability ceiling of
0.709.
