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.

Magnetic resonance water proton relaxation in protein solutions and tissue: T(1rho) dispersion characterization.

BACKGROUND: Image contrast in clinical MRI is often determined by differences in tissue water proton relaxation behavior. However, many aspects of water proton relaxation in complex biological media, such as protein solutions and tissue are not well understood, perhaps due to the limited empirical data. PRINCIPAL FINDINGS: Water proton T(1), T(2), and T(1rho) of protein solutions and tissue were measured systematically under multiple conditions. Crosslinking or aggregation of protein decreased T(2) and T(1rho), but did not change high-field T(1). T(1rho) dispersion profiles were similar for crosslinked protein solutions, myocardial tissue, and cartilage, and exhibited power law behavior with T(1rho)(0) values that closely approximated T(2). The T(1rho) dispersion of mobile protein solutions was flat above 5 kHz, but showed a steep curve below 5 kHz that was sensitive to changes in pH. The T(1rho) dispersion of crosslinked BSA and cartilage in DMSO solvent closely resembled that of water solvent above 5 kHz but showed decreased dispersion below 5 kHz. CONCLUSIONS: Proton exchange is a minor pathway for tissue T(1) and T(1rho) relaxation above 5 kHz. Potential models for relaxation are discussed, however the same molecular mechanism appears to be responsible across 5 decades of frequencies from T(1rho) to T(1).