Quantum sum rules impose limits on the hyperpolarizability, beta. A survey of the largest second-order molecular susceptibilities finds what appears to be a universal gap between the experimental results and the fundamental limits. In this work, we use theory, linear spectroscopy, Raman spectroscopy, and measured values of beta (using hyper-Rayleigh scattering and Stark Spectroscopy) to show that this gap is due to an unfavorable arrangement of excited state energies. The question of whether this result is a universal property of a quantum system or a matter of present paradigms for making molecules is discussed. (C) 2004 American Institute of Physics.