Mark C. Butler

Zero-field NMR enhanced by parahydrogen in reversible exchange.

We have recently demonstrated that sensitive and chemically specific NMR spectra can be recorded in the absence of a magnetic field using hydrogenative parahydrogen induced polarization (PHIP) (1-3) and detection with an optical atomic magnetometer. Here, we show that non-hydrogenative parahydrogen-induced polarization (4-6) (NH-PHIP) can also dramatically enhance the sensitivity of zero-field NMR. We demonstrate the detection of pyridine, at concentrations as low as 6 mM in a sample volume of 250 μL, with sufficient sensitivity to resolve all identifying spectral features, as supported by numerical simulations. Because the NH-PHIP mechanism is nonreactive, operates in situ, and eliminates the need for a prepolarizing magnet, its combination with optical atomic magnetometry will greatly broaden the analytical capabilities of zero-field and low-field NMR.

High-Resolution Zero-Field NMR J‑Spectroscopy of Aromatic Compounds

We report the acquisition and interpretation of nuclear magnetic resonance (NMR) J-spectra at zero magnetic field for a series of benzene derivatives, demonstrating the analytical capabilities of zero-field NMR. The zeroth-order spectral patterns do not overlap, which allows for straightforward determination of the spin interactions of substituent functional groups. Higher-order effects cause additional line splittings, revealing additional molecular information. We demonstrate resonance linewidths as narrow as 11 mHz, permitting resolution of minute frequency differences and precise determination of long-range J-couplings. The measurement of J-couplings with the high precision offered by zero-field NMR may allow further refinements in the determination of molecular structure and conformation.

Ab initio simulation of proton spin diffusion.

The many-body nature of the ubiquitous spin diffusion phenomenon makes it difficult to predict accurately from first principles. We show how the use of reduced Liouville spaces makes it possible to reproduce experimental proton spin diffusion measurements directly from crystalline geometry for powdered solids under magic-angle spinning.

Numerical simulation of free evolution in solid-state nuclear magnetic resonance using low-order correlations in Liouville space

The design of simulations of free evolution in dipolar-coupled nuclear-spin systems using low-order correlations in Liouville space (LCL) is discussed, and a computational scheme relying on the Suzuki-Trotter algorithm and involving minimal memory requirements is described. The unusual nature of the approximation introduced by Liouville-space reduction in a spinning solid is highlighted by considering the accuracy of LCL simulations at different spinning frequencies, the quasiequilibria achieved by spin systems in LCL simulations, and the growth of high-order coherences in the exact dynamics. In particular, it is shown that accurate LCL simulations of proton spin diffusion occur in a regime where the reduced space excludes the coherences that make the dominant contribution to ∥σ∥(2), the norm-squared of the density matrix.

Room-temperature operation of a radiofrequency diamond magnetometer near the shot-noise limit

1 and T � 1 2 , where T1 and T2 are the longitudinal and transverse relaxation times of the electron spin during optical irradiation. We measured a maximum detection bandwidth of � 1.6 MHz with optical excitation intensity of � 2.3 MW/cm 2 , limited by the available optical power. The sensitivity of the NV ensemble for continuous-wave magnetometry in the presence of photon shot noise is analyzed. Two detection schemes are compared, one involving modulation of the fluorescence by an oscillating magnetic field while the microwave frequency is held constant, and the other involving double modulation of the fluorescence when the microwave frequency is modulated during the detection. For the first of these methods, we measure a sensitivity of 4.6 6 0.3 nT/Hz, unprecedented in a detector with this active volume of � 10lm 3 and close to the photonshot-noise limit of our experiment. The measured bandwidth and sensitivity of our device should allow detection of micro-scale NMR signals with microfluidic devices. V C 2012 American Institute

A first-principles description of proton-driven spin diffusion

Herein we design a reduced Liouville space for the simulation of proton-driven spin diffusion. Using this approach, the experimentally observed carbon-13 polarisation transfer in a powder sample undergoing magic-angle spinning is quantitatively described, directly from crystal geometry and without any adjustable parameters.

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

For liquid samples at Earths 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 Earths 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 FA, the summed angular momentum of the spins in A. Weakly coupled spins effectively interact with FA, 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.

Parahydrogen-induced polarization at zero magnetic field

We use symmetry arguments and simple model systems to describe the conversion of the singlet state of parahydrogen into an oscillating sample magnetization at zero magnetic field. During an initial period of free evolution governed by the scalar-coupling Hamiltonian HJ, the singlet state is converted into scalar spin order involving spins throughout the molecule. A short dc pulse along the z axis rotates the transverse spin components of nuclear species I and S through different angles, converting a portion of the scalar order into vector order. The development of vector order can be described analytically by means of single-transition operators, and it is found to be maximal when the transverse components of I are rotated by an angle of ±π∕2 relative to those of S. A period of free evolution follows the pulse, during which the vector order evolves as a set of oscillating coherences. The imaginary parts of the coherences represent spin order that is not directly detectable, while the real parts can be identified with oscillations in the z component of the molecular spin dipole. The dipole oscillations are due to a periodic exchange between Iz and Sz, which have different gyromagnetic ratios. The frequency components of the resulting spectrum are imaginary, since the pulse cannot directly induce magnetization in the sample; it is only during the evolution under HJ that the vector order present at the end of the pulse evolves into detectable magnetization.

Optically detected nuclear quadrupolar interaction ofN14in nitrogen-vacancy centers in diamond

We report sensitive detection of the nuclear quadrupolar interaction of the 14N nuclear spin of the nitrogen-vacancy (NV) center using the electron spin echo envelope modulation technique. We applied a weak transverse magnetic field to the spin system so that certain forbidden transitions became weakly allowed due to second-order effects involving the nonsecular terms of the hyperfine interaction. The weak transitions cause modulation of the electron spin-echo signal, and a theoretical analysis suggests that the modulation frequency is primarily determined by the nuclear quadrupolar frequency; numerical simulations confirm the analytical results and show excellent quantitative agreement with experiments. This is an experimentally simple method of detecting quadrupolar interactions, and it can be used to study spin systems with an energy structure similar to that of the nitrogen vacancy center.