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Multiplets at zero magnetic field: The geometry of zero-field NMR

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10.1063/1.4803144

### Abstract

For liquid samples at Earth's field or below, nuclear-spin motion within scalar-coupled networks yields multiplets as a spectroscopic signature. In weak fields, the structure of the multiplets depends on the magnitude of the Zeeman interaction relative to the scalar couplings; in Earth's field, for example, heteronuclear couplings are truncated by fast precession at distinct Larmor frequencies. At zero field, weak scalar couplings are truncated by the relatively fast evolution associated with strong scalar couplings, and the truncated interactions can be described geometrically. When the spin system contains a strongly coupled subsystem A, an average over the fast evolution occurring within the subsystem projects each strongly coupled spin onto F A , the summed angular momentum of the spins in A. Weakly coupled spins effectively interact with F A , and the coupling constants for the truncated interactions are found by evaluating projections. We provide a formal description of zero-field spin systems with truncated scalar couplings while also emphasizing visualization based on a geometric model. The theoretical results are in good agreement with experimental spectra that exhibit second-order shifts and splittings.

© 2013 AIP Publishing LLC

Received 06 February 2013
Accepted 15 April 2013
Published online 10 May 2013

Acknowledgments: Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Contract No. DE-AC02-05CH11231 [theoretical work, salaries for T. Theis, J. Blanchard, A. Pines], and by the National Science Foundation under Award No. CHE-095765 [zero-field experiments and instrumentation, salaries for M. Butler, M. Ledbetter, D. Budker, A. Pines]. J. Blanchard is supported by a National Science Foundation Graduate Research Fellowship under Grant No. DGE-1106400. We thank Professor Marcis Auzinsh for comments on the manuscript.

Article outline:

I. INTRODUCTION

II. GEOMETRIC MODEL

III. FORMAL GEOMETRIC DESCRIPTION OF A THREE-SPIN SYSTEM

A. Energy levels

B. Spin dipole

C. Spectrum

IV. (XA_{n})B_{m} SYSTEMS

A. Energy levels

B. Spectrum

V. STRONGLY COUPLED AND WEAKLY COUPLED SUBSYSTEMS

VI. CONCLUSION

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/content/aip/journal/jcp/138/18/10.1063/1.4803144

2013-05-10

2014-04-21

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