The hyperpolarizability has been extensively studied to identify universal properties when it is near the fundamental limit. Here, we employ the Monte Carlo method to study the fundamental limit of the second hyperpolarizability. As was found for the hyperpolarizability, the largest values of the second hyperpolarizability approaches the calculated fundamental limit. The character of transition moments and energies of the energy eigenstates are investigated near the second hyperpolarizability's upper bounds using the missing state analysis, which assesses the role of each pair of states in their contribution. In agreement with the three-level ansatz, our results indicate that only three states (ground and two excited states) dominate when the second hyperpolarizability is near the limit.
Sum rules have been used to show that there is an upper limit to molecular susceptibilities. Such calculations have been applied to the diagonal part of the second-order susceptibility tensor as measured with electric-field-induced second-harmonic generation, and to a variety of third-order measurements. The results show that the off-resonant susceptibilities of all molecules measured fall within the calculated limits. In this contribution, we show that the most susceptibilities measured with hyper Rayleigh scattering (HRS) fall below the two-dimensional theoretical limit, and discuss the issue of why some molecules appear to break this limit.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.