(a) Diagram of the variation in magnetic field strength as a function of time, ( interval , interval , and interval ). The grid beneath and lined up with the intervals shows the spin topologies associated with each interval. (b) Schematic representation of the equatorial ligands in the octahedral complex. The central metal is labeled , whereas and are the hydrogen atoms derived from parahydrogen. Ligand is the substrate, and ligand a second ligand, which may or may not be the same as the substrate.
Mixing field dependence of the longitudinal magnetization created for model complexes with spin topology in which the bound model substrate comprises a single spin.
Mixing field dependence of the spin states created for model complexes with , , and ABCD spin topologies. The relative amplitudes for the zero quantum coherences (black closed squares: ABCD; open squares: ; and gray closed squares: ) and longitudinal two-spin order (black closed circles: ABCD; open circles: ; and gray closed circles: ) are plotted as functions of the mixing field over the ranges of (a) 0–25 mT and (b) 25–250 mT. The relative amplitudes for the longitudinal magnetization (black closed squares: ABCD; open squares: ; and gray closed squares: ) and (black closed circles: ABCD; open circles: ; and gray closed circles: ) are plotted as functions of the mixing field over the ranges of (c) 0–25 mT and (d) 25–250 mT.
The relative amplitudes of the longitudinal magnetization and associated with the isochronous substrate model plotted as a function of the mixing field. The plot shows the relative amplitudes after evolution of the free substrate nuclear spins in the mixing field, (open squares) and (open circles), and after transfer into the measurement field, and (closed circles).
The relative amplitudes of the zero quantum coherence for the Anisochronous model plotted as a function of the mixing field after evolution at the mixing field (closed squares) and transfer to the measurement field (closed circles). For comparison, the amplitude of the same coherence for the complex at the point of dissociation is also included (open squares). The results are shown over the ranges of (a) 0–20 mT and (b) 20–250 mT. In (a), only one plot is apparent because the data sets for both the mixing field and complex produce exactly the same curve.
The relative amplitudes of the longitudinal magnetization and for the Anisochronous model plotted as functions of the mixing field strength: at the mixing field (open squares, and closed squares, ) and after transfer to the measurement field (open circles, and closed circles, ). For comparison the same terms are included for the complex (open diamonds, and closed diamonds, ). The results are shown for the ranges of (a) 0–20 mT and (b) 20–250 mT.
Schematic representation of the spin evolution for the four-spin complex at (a) zero field and (b) non-zero field. Dashed lines indicate initial scalar coupling evolution; dotted lines indicate chemical shift evolution. The solid lines connect states that equilibrate to form a dynamic steady state over time. (a) At zero field, the initial singlet state of parahydrogen evolves under scalar coupling into three-spin zero quantum coherences involving both parahydrogen nuclei and one of the substrate nuclei, i.e., spin triplets and . These three-spin coherences evolve further into two- and four-spin zero quantum coherences involving all four spins, , and into all two-spin zero quantum coherences involving spin pairs with at least one parahydrogen nucleus, , , , , and . These two-spin coherences and the four-spin coherences evolve into a mixture of all possible three-spin zero quantum coherences . The complete set of two-, three-, and four-spin zero quantum coherences continues to interconvert until the complex dissociates or a steady state is reached. (b) At non-zero field, the coherences evolve in a similar manner with scalar couplings interchanging two-, three-, and four-spin zero quantum coherences. In addition, the chemical shift evolution converts a particular coherence into its conjugate for a given number of spins, i.e., two-spin . Furthermore, the concerted effects of both scalar coupling and chemical shift also produce longitudinal magnetization, , , , and , and longitudinal three-spin order, , , , and . All longitudinal terms are referred to as LO.
Chemical shifts, , and scalar coupling parameters, , used in the models. The spins originating from parahydrogen are labeled and and those from the substrate are labeled and .
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