A few posts back, I discussed Monte Carlo studies that shed light on many unexplained observations. For those of you interested in seeing a preprint, it can be found on the physics archives at: http://lanl.arxiv.org/PS_cache/arxiv/pdf/1101/1101.1041v1.pdf. The manuscript is now under review at the Journal of the Optical Society of America B.
I am still excited by our observations because of the breadth of understanding that has resulted. While this paper may not be appreciated by a large number of people, it is certainly on my list of top 5 papers that I have published over my career. Ironically, while my most highly-cited papers report solid science that has been useful to many other researchers, I prefer to judge my work on the degree to which it opens my mind; and, the awe/wonder that it elicits. Ideas that paint the universe with the broadest of brushes are king. This recent work is an intellectual creation that, like a brilliant child, has grown beyond its creators. I marvel at all that it continues to teach us as well as its ability to inspire new lines of research.
The abstract and conclusion says it all:
ABSTRACT: Studies aimed at understanding the global properties of the hyperpolarizabilities have focused on identifying universal properties when the hyperpolarizabilities are at the fundamental limit. These studies have taken two complimentary approaches: (1) Monte Carlo techniques that statistically probe the full parameter space of the Schrodinger Equation using the sum rules as a constraint; and, (2) numerical optimization studies of the first and second hyperpolarizability where models of the scalar and vector potentials are parameterized and the optimized parameters determined, from which universal properties are investigated. Here, we employ an energy spectrum constraint on the Monte Carlo method to bridge the divide between these two approaches. The results suggest an explanation for the origin of the factor of 20-30 gap between the best molecules and the fundamental limits and establishes the basis for the three-level ansatz.
Classifying Monte Carlo simulations using an energy spectrum function resolves several long-standing questions. First, our work shows the centrality of energy spacing in determining the intrinsic nonlinear response. While a broad range of transition moments are observed in atoms and molecules, the energy spacing - as characterized by the energy parameter, E, varies little between systems. Indeed, the importance of the energy parameter in attaining larger hyperpolarizabilities has been demonstrated in several experimental studies.[6, 37]
Monte Carlo calculation using the energy classification scheme have bridged the divide between Monte Carlo simulations and potential energy optimization studies. The power of the Monte-Carlo technique lies in the fact that all possible Hilbert spaces are probed, leading to very broad and fundamental relationships. Using energy classifications allows the parameter space to be reduced to subsets that describe atoms and molecules. Future refinements may lead to more specific design guidelines for making improved molecules for a variety of applications. The potential for discovering new fundamental science with this approach is of equal importance.