Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and thomas-kuhn sum rules

Successfully predicting the frequency dispersion of electronic hyperpolarizabilities is an unresolved challenge in materials science and electronic structure theory. We show that the generalized Thomas-Kuhn sum rules, combined with linear absorption data and measured hyperpolarizability at one or two frequencies, may be used to predict the entire frequency-dependent electronic hyperpolarizability spectrum. This treatment includes two- and three-level contributions that arise from the lowest two or three excited electronic state manifolds, enabling us to describe the unusual observed frequency dispersion of the dynamic hyperpolarizability in high oscillator strength M-PZn chromophores, where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are connected via an ethyne unit that aligns the high oscillator strength transition dipoles of these components in a head-to-tail arrangement. We show that some of these structures can possess very similar linear absorption spectra yet manifest dramatically different frequency dependent hyperpolarizabilities, because of three-level contributions that result from excited state-to excited state transition dipoles among charge polarized states. Importantly, this approach provides a quantitative scheme to use linear optical absorption spectra and very limited individual hyperpolarizability measurements to predict the entire frequency-dependent nonlinear optical response. Copyright © 2010 American Chemical Society.

Natural hybridization between genera that diverged from each other approximately 60 million years ago.

A fern from the French Pyrenees-×Cystocarpium roskamianum-is a recently formed intergeneric hybrid between parental lineages that diverged from each other approximately 60 million years ago (mya; 95% highest posterior density: 40.2-76.2 mya). This is an extraordinarily deep hybridization event, roughly akin to an elephant hybridizing with a manatee or a human with a lemur. In the context of other reported deep hybrids, this finding suggests that populations of ferns, and other plants with abiotically mediated fertilization, may evolve reproductive incompatibilities more slowly, perhaps because they lack many of the premating isolation mechanisms that characterize most other groups of organisms. This conclusion implies that major features of Earth's biodiversity-such as the relatively small number of species of ferns compared to those of angiosperms-may be, in part, an indirect by-product of this slower "speciation clock" rather than a direct consequence of adaptive innovations by the more diverse lineages.