*para*hydrogen-induced polarization

^{1}, Simon B. Duckett

^{1,a),b)}, Richard A. Green

^{1}, David C. Williamson

^{1,a),c)}and Gary G. R. Green

^{2}

### Abstract

When *para*hydrogen adds to a metal template containing a substrate of interest, the substrate and *para*hydrogen become coupled, and polarization is shared between the two without the incorporation of the *para*hydrogen into the substrate. A mechanism for this polarization transfer is presented in which the transfer is propagated through the scalar couplings. At zero field, polarization is transferred between two-, three-, and four-spin zero quantum states, but no single spin magnetization is created. The interplay between the chemical shift evolution and the evolution under scalar coupling at non-zero field generates additional longitudinal spin order and now includes single spin longitudinal -magnetization. The additional chemical shift interaction introduces a field dependency to the nuclear spin states of the polarized substrate. The net effect of the polarization field strength on the resultant nuclear spin states is shown to be predictable but complex.

We wish to thank the University of York, the BBSRC, the EPSRC, and the MRC for their financial support in this work. We are also grateful to Bruker Biospin and to Oxford Instruments for financial and other support that they have provided.

I. INTRODUCTION

II. METHOD

A. Spin topologies

III. THEORY

A. Evolution of the four-spin complex in the mixing field (period )

B. Evolution of the two-spin free substrate spin system in the mixing field (period )

C. Evolution of the two-spin free substrate spin system during the dynamic field period (period )

D. Time averaging

IV. RESULTS AND DISCUSSION

A. Generation of free substrate with polarization transfer at zero field

B. Evolution of the four-spin complex at non-zero field

C. Evolution of the free substrate in the Isochronous model

D. Evolution of the free substrate in the Anisochronous model

V. CONCLUSION

### Key Topics

- Polarization
- 56.0
- Chemical shifts
- 53.0
- Topology
- 29.0
- Nuclear spin
- 13.0
- Classical spin models
- 11.0

## Figures

(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 *para*hydrogen. Ligand is the substrate, and ligand a second ligand, which may or may not be the same as the substrate.

(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 *para*hydrogen. 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 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.

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 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 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.

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 *para*hydrogen evolves under scalar coupling into three-spin zero quantum coherences involving both *para*hydrogen 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 *para*hydrogen 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.

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 *para*hydrogen evolves under scalar coupling into three-spin zero quantum coherences involving both *para*hydrogen 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 *para*hydrogen 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.

## Tables

Chemical shifts, , and scalar coupling parameters, , used in the models. The spins originating from *para*hydrogen are labeled and and those from the substrate are labeled and .

Chemical shifts, , and scalar coupling parameters, , used in the models. The spins originating from *para*hydrogen are labeled and and those from the substrate are labeled and .

Article metrics loading...

Full text loading...

Commenting has been disabled for this content