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The Journal of Chemical Physics

Intermolecular multiple-quantum coherence transfer echoes and multiple echoes in nuclear magnetic resonance

Rainer Kimmich, Ioan Ardelean

Published Feb 22, 1999• 32 citations
Publisher

Abstract

In recent years evidence was presented that two radio frequency pulses in combination with suitably matched field gradient pulses produce cross peaks in two-dimensional NMR spectroscopy that reveal all the features of multiple-quantum/single-quantum coherence transfer signals. This experiment was termed CRAZED by Warren et al. Quite amazingly, identical signals were predicted on a purely classical basis. Thus the intriguing question arises whether this means that a classical analog to multiple-quantum coherences exists. In this study we show that this is clearly not the case. Coherence pathways of a purely single-quantum basis are excited anyway and lead independently to superimposed identical signals in parallel. Moreover, the observation of CRAZED signals per se neither disproves the adequacy of the high-temperature approximation, which was questioned in this context, nor proves a strong influence of intermolecular multiple-quantum coherences. However, the indispensable prerequisite for the description of the manifold CRAZED phenomena is that long-range dipolar interactions are taken into account either explicitly or in the continuous-limit form.

DOI
10.1063/1.478261

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In recent years evidence was presented that two radio frequency pulses in combination with suitably matched field gradient pulses produce cross peaks in two-dimensional NMR spectroscopy that reveal all the features of multiple-quantum/single-quantum coherence transfer signals. This experiment was termed CRAZED by Warren et al. Quite amazingly, identical signals were predicted on a purely classical basis. Thus the intriguing question arises whether this means that a classical analog to multiple-quantum coherences exists. In this study we show that this is clearly not the case. Coherence pathways of a purely single-quantum basis are excited anyway and lead independently to superimposed identical signals in parallel. Moreover, the observation of CRAZED signals per se neither disproves the adequacy of the high-temperature approximation, which was questioned in this context, nor proves a strong influence of intermolecular multiple-quantum coherences. However, the indispensable prerequisite for the description of the manifold CRAZED phenomena is that long-range dipolar interactions are taken into account either explicitly or in the continuous-limit form.
Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.
Multiple quantum experiments on nuclear magnetic resonance on spins of 19 F in calcium fluorapatite have been performed. It has been shown that more than 97% of the observed signal refers to the multiple quantum coherences of the zeroth and plus/minus second orders. The dependences of the intensities of these coherences on the time of the preparation period of the multiple quantum NMR experiment have been obtained. The dipole relaxation of multiple quantum coherences on the evolution period of the multiple quantum nuclear magnetic resonance experiment has been studied. A probe providing short radio-frequency pulses with the duration up to 0.3 μs has been developed for experiments. The experimental results show that the studied system can be used for the transmission of quantum information and the study of the decoherence process in strongly correlated multispin clusters.
The 19F^{19}\text{F}19F spins in a crystal of fluorapatite have often been used to experimentally approximate a one-dimensional spin system. Under suitable multipulse control, the nuclear-spin dynamics may be modeled to first approximation by a double-quantum one-dimensional Hamiltonian, which is analytically solvable for nearest-neighbor couplings. Here, we use solid-state nuclear magnetic resonance techniques to investigate the multiple quantum coherence dynamics of fluorapatite, with an emphasis on understanding the region of validity for such a simplified picture. Using experimental, numerical, and analytical methods, we explore the effects of long-range intrachain couplings, cross-chain couplings, as well as couplings to a spin environment, all of which tend to damp the oscillations of the multiple quantum coherence signal at sufficiently long times. Our analysis characterizes the extent to which fluorapatite can faithfully simulate a one-dimensional quantum wire.
A large body of conspicuous publications in recent years asserts that the high temperature approximation (HTA), a mostly tested and most widely used assumption in NMR spectroscopy and MRI technology, is invalid for concentrated samples in high magnetic fields such as for a proton COSY spectrum of water. A by product of the alleged collapse of HTA, which is equally surprising, is the existence of intermolecular multi quantum coherences (MQC) in low viscosity liquids such as water. In this work, both HTA and intermolecular MQCs in liquids will be critically examined in light of our theoretical analysis and experimental results. Our conclusions are: (1) There are no macroscopic quantum systems in conventional NMR samples such as water at room temperature. (2) At room temperature, high temperature approximation is still one of the most trustworthy approximations applicable to NMR and (3) The MQCs observed in proton COSY spectrum in, e.g., water, have nothing to do with quantum mechanical intermolecular spin interactions.
We study multiple-spin coherence transfers in linear Ising spin chains with nearest-neighbor couplings. These constitute a model for efficient information transfers in future quantum computing devices and for many multidimensional experiments for the assignment of complex spectra in nuclear magnetic resonance spectroscopy. We complement prior analytic techniques for multiple-spin coherence transfers with a systematic numerical study where we obtain strong evidence that a certain analytically motivated family of restricted controls is sufficient for time optimality. In the case of a linear three-spin system, additional evidence suggests that prior analytic pulse sequences using this family of restricted controls are time optimal even for arbitrary local controls. In addition, we compare the pulse sequences for linear Ising spin chains to pulse sequences for more realistic spin systems with additional long-range couplings between nonadjacent spins. We experimentally implement the derived pulse sequences in three- and four-spin systems and demonstrate that they are applicable in realistic settings under relaxation and experimental imperfections---in particular---by deriving broadband pulse sequences which are robust with respect to frequency offsets.
Recently, two-dimensional NMR experiments have been performed, which were likely to show that a coupling between otherwise uncoupled or equivalent spins was observable, yielding signals originating from multiple-spin multiple-quantum operators in the density matrix. According to the authors, such surprising results could be interpreted as a consequence of the radiation damping phenomenon. For this purpose, a fully quantum-mechanical frame was used, thus treating the radiation field in a quantized manner. Our analysis, based on the same theoretical grounds, as well as on new experimental arguments, lead us to diverging conclusions.