General treatment of paramagnetic relaxation enhancement associated with translational diffusion.
A theory of nuclear spin relaxation in isotropic liquids for nuclear spins interacting with electron spins, residing in other molecules (the outer-sphere relaxation), is presented. The approach, valid outside of the Redfield limit for electron spin relaxation, is an extension of the Swedish slow motion theory [Benetis et al., Mol. Phys. 48, 329 (1983); Nilsson and Kowalewski, J. Magn. Reson. 146, 345 (2000)] for inner-sphere relaxation. It is demonstrated that the outer-sphere relaxation rate can be expressed as an integral of a product of a translational diffusion correlation function and a function analogous to the inner-sphere spectral density. A numerical implementation of the theory is described and applied to a large number of realistic parameter sets for S = 7/2 and S = 1, which may correspond to Gd(III) and Ni(II) systems. It is shown that the outer-sphere contribution is relevant and should be included into the analysis of nuclear magnetic relaxation dispersion relaxation profiles, especially for slow relative translational diffusion and fast molecular tumbling.
Quantitative cw Overhauser effect dynamic nuclear polarization for the analysis of local water dynamics.
Liquid state Overhauser effect Dynamic Nuclear Polarization (ODNP) has experienced a recent resurgence of interest. The ODNP technique described here relies on the double resonance of electron spin resonance (ESR) at the most common, i.e. X-band (∼10GHz), frequency and ¹H nuclear magnetic resonance (NMR) at ∼15 MHz. It requires only a standard continuous wave (cw) ESR spectrometer with an NMR probe inserted or built into an X-band cavity. We focus on reviewing a new and powerful manifestation of ODNP as a high frequency NMR relaxometry tool that probes dipolar cross relaxation between the electron spins and the ¹H nuclear spins at X-band frequencies. This technique selectively measures the translational mobility of water within a volume extending 0.5-1.5 nm outward from a nitroxide radical spin probe that is attached to a targeted site of a macromolecule. It allows one to study the dynamics of water that hydrates or permeates the surface or interior of proteins, polymers, and lipid membrane vesicles. We begin by reviewing the recent advances that have helped develop ODNP into a tool for mapping the dynamic landscape of hydration water with sub-nanometer locality. In order to bind this work coherently together and to place it in the context of the extensive body of research in the field of NMR relaxometry, we then rephrase the analytical model and extend the description of the ODNP-derived NMR signal enhancements. This extended model highlights several aspects of ODNP data analysis, including the importance of considering all possible effects of microwave sample heating, the need to consider the error associated with various relaxation rates, and the unique ability of ODNP to probe the electron-¹H cross-relaxation process, which is uniquely sensitive to fast (tens of ps) dynamical processes. By implementing the relevant corrections in a stepwise fashion, this paper draws a consensus result from previous ODNP procedures and then shows how such data can be further corrected to yield clear and reproducible saturation of the NMR hyperpolarization process. Finally, drawing on these results, we broadly survey the previous ODNP dynamics literature. We find that the vast number of published, empirical hydration dynamics data can be reproducibly classified into regimes of surface, interfacial, vs. buried water dynamics.
Hybrid ligand-field theory/quantum chemical calculation of the fine structure and ZFS in lanthanide(III) complexes
Ligand field effects in lanthanide ions compounds have consequences for optical and magnetic spectroscopy. In the analysis of electron paramagnetic resonance spectra of Gd3+ complexes, a major role is played by the zero field splitting (ZFS), which is a high order consequence of the ligand field and the spin–orbit coupling. We present a general parameterized method and a computer program for the study of the excited states of lanthanide complexes. We apply it for the first principles determination of the ZFS of the [Gd(H2O)8]3+ aqua ion and the corresponding EPR peak-to-peak width in solution. We calculate the influence of the various contributions to the effective Hamiltonian on the splitting of the ground state multiplet.