  Using the sum-rules, the sum-over-states expression for the diagonal term of
first hyperpolarizability can be expressed as the sum of three-state
interaction terms. We study the behavior of a generic three-state term to show
that is possible to tune the contribution of resonant terms by tuning the
spectrum of the molecule. When extrapolated to the off-resonance regime, the
three-state interaction terms are shown to behave in a similar manner as the
three-level model used to derive the fundamental limits. We finally show that
most results derived using the three-level ansatz are general, and apply to
molecules where more than three levels contribute to the second-order nonlinear
response or/and far from optimization.
