Multiple Quantum Coherence NMR Research Articles

Lindblad Relaxation of Multiple Quantum NMR Coherence in Two-Spin Systems

Lindblad Relaxation of Multiple Quantum NMR Coherence in Two-Spin Systems

AI-designed RF pulses enable fast pulsing heteronuclear multiple quantum coherence NMR experiment at high and ultra-high magnetic fields.

We present a new AI-optimized 2D heteronuclear multiple quantum coherence (RAPID-HMQC) pulse sequence for NMR spectroscopy. RAPID-HMQC is a longitudinal 1H relaxation-optimized experiment with new AI-designed band-selective pulses to accelerate the analysis of organic compounds, metabolites, biopolymers, and real-time monitoring of dynamic processes at high- and ultra-high magnetic fields.

Many-Spin Entanglement in Multiple Quantum NMR with a Dipolar Ordered Initial State

Multiple quantum (MQ) NMR with a dipolar ordered initial state opens new possibilities for the exploration of many-spin entanglement. In this paper, we investigate many-spin entanglement in a gas of spin-carrying molecules (atoms) in nanocavities in the conditions of MQ NMR with a dipolar ordered initial state. The second moment of the distribution of the intensities of MQ NMR coherences, which provides a lower bound on the quantum Fisher information, is used for an estimate of the number of the entangled spins. Many-spin entanglement is investigated at different temperatures and different numbers of spins.

Optimization of pulses with low bandwidth for improved excitation of multiple-quantum coherences in NMR of quadrupolar nuclei.

We discuss the commonly encountered problem when optimizing nuclear magnetic resonance (NMR) pulses using optimal control that the otherwise very precise NMR theory does not provide as excellent agreement with experiments. We hypothesize that this disagreement is due to phase transients in the pulse due to abrupt phase and amplitude changes resulting in a large bandwidth. We apply the gradient optimization using parametrization algorithm that gives high fidelity pulses with a low bandwidth compared to the typical gradient ascent pulse engineering pulses. Our results obtain a better agreement between experiments and simulations supporting our hypothesis and solution to the problem.

Orientational dependencies of dynamics and relaxation of multiple quantum NMR coherences in one-dimensional systems.

Dynamics and relaxation, or decoherence, of multiple quantum (MQ) coherences are investigated experimentally and theoretically for different orientations of a single crystal of fluorapatite with respect to the external magnetic field. Dynamics of MQ coherences is studied as a function of the preparation period of the MQ NMR experiment. Their relaxation, or decoherence, during the evolution period is also investigated. Universal curves for dynamics and relaxation are obtained and describe the experimental data for different orientations of the investigated sample. Those curves prove the dipolar nature of the observed relaxation process. The contribution of the heteronuclear interactions to the dipolar relaxation is also investigated. The source of discrepancies between experimental data and theoretical results in the experiments with a large angle between the nuclear spin chains and the external magnetic field are discussed.

Contributions of different parts of dipole-dipole interactions to relaxation of multiple quantum NMR coherences in a single crystal of calcium fluorapatite

Contributions of different parts of dipole-dipole interactions to relaxation of multiple quantum NMR coherences in a single crystal of calcium fluorapatite

Using Diamagnetic Yttrium and Lanthanum Complexes to Explore Ligand Reduction and C–H Bond Activation in a Tris(aryloxide)mesitylene Ligand System

[Y(N(SiMe3)2)3] reacts with (Ad,MeArOH)3mes to form the Y3+ complex [((Ad,MeArO)3mes)Y], 1-Y. This complex reacts with potassium metal in the presence of 2.2.2-cryptand to give a cocrystallized mixture of [K(2.2.2-cryptand)][((Ad,MeArO)3mes)Y], 2-Y, and [K(2.2.2-cryptand)][((Ad,MeArO)3mes)YH], 3-Y. The electron paramagnetic resonance spectrum of this crystalline mixture exhibits an isotropic signal at 77 K ( giso = 2.000, Wiso = 1.8 mT), suggesting that 2-Y is best described as a Y3+ complex of the tris(aryloxide)mesitylene radical ((Ad,MeArO)3mes)4-. Evidence of the hydride ligand in 3-Y was obtained by 89Y-1H heteronuclear multiple quantum coherence NMR spectroscopy, and a coupling constant of JYH = 93 Hz was observed. A single crystal of 3-Y was also obtained in pure form and structurally characterized for comparison with the crystal data on the mixed component 2-Ln/3-Ln crystals. The origin of the hydride in 3-Ln is unknown, but further studies of the reduction of 1-La, previously found to form 2-La, revealed a possible source. Ligand-based C-H bond activation and loss of hydrogen can occur under reducing conditions to form a tetraanionic ligand derived from ((Ad,MeArO)3mes)3-, as observed in [K(2.2.2-cryptand)][((Ad,MeArO)3(C6Me3(CH2)2CH)La], 4-La.

The Second Moments of the Line Shapes of Multiple Quantum NMR Coherences in One-Dimensional Systems

The second moments of the line shapes of the zeroth- and second-order multiple quantum NMR coherences determined by the dipole–dipole interactions of nuclear spins in crystals have been calculated. The second moments determined by the zz part of the dipole–dipole interaction have been derived both by a direct calculation and based on the exact solution (in terms of the zz model) for the decay of the multiple quantum coherence intensities on the evolution period of a multi-quantum NMR experiment. The decay of the multiple quantum NMR coherence intensities in a single crystal of calcium fluorapatite is well described by the Gaussian curves with the calculated second moments.

Probing the 1H spin distribution in hybrid organic-inorganic gels by multiple-quantum NMR spectroscopy

Multiple-quantum (MQ) NMR was used to characterize the organic phase distribution in a series of hybrid organic-inorganic gels namely methyltrimethoxysilane aerogel and QM resins (trimethylsiloxysilicate polymers) with different composition. The Gaussian model of distribution of MQ coherence intensities was used to determine the effective 1H spin cluster size (N). The growth of the effective cluster size with the time of excitation of MQ NMR coherences τ indicates the uniform distribution of organic moieties in the studied gels, but the growth rate is significantly slower than that of adamantane which was used for comparison as an example of the systems with uniform distribution of 1H spins. The growth rate was described by the exponents α in the scaling law of the form N~τα. The obtained values of α were 3.07 for adamantane, 1.27 for aerogel and 1.8 for QM resins. This difference was attributed to the surface distribution of the 1H spins in the studied gels. The growth rate of spin clusters in aerogel is slower in comparison with QM resins with different content of 1H spins which show similar growth rate among each other. This result was explained by the higher local concentration of 1H spins on the surfaces of silica regions in QM resins.

Dipolar relaxation of multiple quantum NMR coherences in one-dimensional systems

Dipolar relaxation of multiple quantum (MQ) NMR coherences is investigated theoretically on the evolution period of the MQ NMR experiment in chains with an arbitrary number of spins. The dependencies of the intensities of these coherences on the lengths of the evolution and preparation periods are obtained. It is shown that the intensity of the MQ NMR coherence of the zeroth order does not decay completely in the relaxation process. The experimental results obtained for a quasi-one-dimensional chain of 19F nuclear spins in calcium fluorapatite qualitatively agree with the results of the developed theory.

Multiple Quantum Coherences (MQ) NMR and Entanglement Dynamics in the Mixed-Three-Spin XXX Heisenberg Model with Single-Ion Anisotropy

We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants and , by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.

Relaxation of Multiple Quantum NMR Coherences in Quasi-One-Dimensional Spin Systems

Abstract Dynamics and relaxation of the multiple quantum (MQ) NMR coherences of the zeroth and second orders are studied experimentally and theoretically in a quasi-one-dimensional chain of nuclear spins 19F in calcium fluorapatite. The dependencies of the intensities of those coherences on the time of the preparation period of the MQ NMR experiment is obtained. A good agreement of the experiment with theoretical predictions is demonstrated. Dipolar relaxation of the MQ NMR coherences is investigated on the evolution period of the MQ NMR experiment. A theory of dipolar relaxation of the MQ NMR coherences is developed for the model in which only the ZZ part of the secular dipole–dipole interactions is taken into account (ZZ model). It is shown that the MQ NMR coherence of the zeroth order is not subject to dipolar relaxation in the ZZ model. The experimental data qualitatively agree with the results of the developed theory for the MQ NMR coherence of the second order.

Dynamics and relaxation of multiple quantum NMR coherences in a quasi-one-dimensional chain of nuclear spins 19F in calcium fluorapatite

Multiple quantum experiments on nuclear magnetic resonance on spins of 19F 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.

Intermediate length scale organisation in tin borophosphate glasses: new insights from high field correlation NMR.

The structure of tin borophosphate glasses, considered for the development of low temperature sealing glasses or anode materials for Li-batteries, has been analysed at the intermediate length scale by a combination of high field standard and advanced 1D/2D nuclear magnetic resonance techniques. The nature and extent of B/P mixing were analysed using the (11)B((31)P) dipolar heteronuclear multiple quantum coherence NMR sequence and the data interpretation allowed (i) detecting the presence and analysing the nature of the B-O-P linkages, (ii) re-interpreting the 1D (31)P spectra and (iii) extracting the proportion of P connected to borate species. Interaction between the different borate species was analysed using the (11)B double quantum-simple quantum experiment to (i) investigate the presence and nature of the B-O-B linkage, (ii) assign the different borate species observed all along the composition line and (iii) monitor the borate network formation. In addition, (119)Sn static NMR was used to investigate the evolution of the chemical environment of the tin polyhedra. Altogether, the set of data allowed determining the structural units constituting the glass network and quantifying the extent of B/P mixing. The structural data were then used to explain the non-linear and unusual evolution of the glass transition temperature.

Multiple Quantum NMR in One-Dimensional and Nano-Scale Systems: Theory and Computer Simulations

We investigate several exactly solvable models of multiple quantum (MQ) NMR dynamics. We study MQ NMR dynamics of one-dimensional systems (chains and rings) and nano-voids filled with spin-carrying atoms or molecules in a strong external magnetic field. Our focus is the problem of the profile of MQ NMR coherences (i.e., the dependence of the intensities of MQ NMR coherences on their orders). We find that integrable one-dimensional systems exhibit peculiar behavior that does not shed much light on a more generic situation. On the other hand, important lessons can be extracted from our solution for the nano-scale systems. We find that the profile of the intensities of the MQ NMR coherences is rather exponential than Gaussian as was proposed earlier. We also address the cluster growth in the course of the evolution of MQ NMR coherences.

Solid-state multiple quantum NMR in quantum information processing: exactly solvable models

Multiple quantum (MQ) NMR is an effective tool for the generation of a large cluster of correlated particles, which, in turn, represent a basis for quantum information processing devices. Studying the available exactly solvable models clarifies many aspects of the quantum information. In this study, we consider two exactly solvable models in the MQ NMR experiment: (i) the isolated system of two spin-1/2 particles (dimers) and (ii) the large system of equivalent spin-1/2 particles in a nanopore. The former model is used to describe the quantum correlations and their relations with the MQ NMR coherences, whereas the latter helps one to model the creation and decay of large clusters of correlated particles.

Quantum discord versus second-order MQ NMR coherence intensity in dimers

We consider the quantum discord in a two-particle spin-1/2 system (dimer) governed by the standard multiple quantum (MQ) Hamiltonian and reveal the relation between the discord and the intensity of the second-order MQ coherence. Since the coherence intensities may be measured in experiment, we obtain a method of detecting the quantum discord in experiment. Comparison of discord and concurrence is represented.

Multiple quantum NMR dynamics in a gas of spin-carrying molecules in fluctuating nanopores

The effect of Gaussian fluctuations of nanopores filled with a gas of spin-carrying molecules ( s = 1/2) on the multiple quantum (MQ) NMR dynamics is investigated at different variances and correlation times of the fluctuations. We show that the fluctuations smooth out the evolution of MQ NMR coherence intensities which rapidly oscillate as functions of time in the absence of fluctuations. The growth and decay of the MQ coherence clusters in the fluctuating nanopore are also investigated.

The multiple quantum NMR dynamics in systems of equivalent spins with a dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an investigation of the MQ NMR dynamics in the systems consisting of hundreds of spins from "the first principles". We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for the systems of $200 - 600$ spins. It is shown that these profiles may be well approximated by the exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, namely the dipolar ordered state and the thermal equilibrium state in the strong external magnetic field.

Multiple quantum NMR dynamics of spin-12 carrying molecules of a gas in nanopores

We consider the multiple quantum (MQ) NMR dynamics of a gas of spin carrying molecules in nanocavities. MQ NMR dynamics is determined by the residual dipole-dipole interactions, which are not averaged completely due to the molecular diffusion in nanopores. Since the averaged nonsecular Hamiltonian describing MQ NMR dynamics depends on only one coupling constant, this Hamiltonian commutes with the square of the total spin angular momentum Î2. We use the basis of common eigenstates of Î2 and the projection of I on the external magnetic field for investigation of MQ NMR dynamics. This approach allows us to study MQ NMR dynamics in systems consisting of several hundreds of spins. The analytical approximation of the stationary profile of MQ coherences is obtained. The analytical expressions for MQ NMR coherence intensities of the five-spin system in a nanopore are found. Numerical investigations allow us to find the dependencies of intensities of MQ coherences on their orders (the profiles of MQ coherences) in systems consisting of 600 spins and even more. It is shown that the stationary MQ coherence profile in the considered system is an exponential one.