Intensities Of Multiple Quantum Coherences Research Articles

1H multiple quantum NMR in alternating quasi-one-dimensional spin chains of hambergite

Multiple quantum (MQ) dynamics was investigated in quasi-one-dimensional 1H zigzag spin chains in hambergite (Be2BO3OH) single crystals. Due to the non-linear arrangement of the spins, dipolar coupling strengths alternate along the chain. To solve the problem of MQ NMR experiments taking too much time due to extremely long 1H spin–lattice relaxation times, the samples were exposed to gamma irradiation to produce the defects accelerating the relaxation. The influence of the radiation dose was investigated. The experimental dependencies of MQ coherence intensities on the MQ excitation time in alternating spin chains were obtained and compared with the theory for inhomogeneous spin chains with nearest neighbor interactions developed earlier. The correspondence of the observed MQ dynamics to the alternating spin chain was demonstrated.

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.

Order dependence of the profile of the intensities of multiple-quantum coherences

A modification of the widespread phenomenological model theory of multiple-quantum (MQ) nuclear magnetic resonance spectra of a single cluster of correlated spins has been developed. In contrast to the mentioned theory, the size distribution of such clusters has been consistently taken into account. To obtain the distribution, solutions for the amplitudes of the expansion in the complete set of orthogonal operators are used. Expressions specifying the dependence of the profile of the intensities of MQ coherences on their number n (order) have been obtained. The total form of the dependence has been evaluated by means of the numerical implementation of the resulting expressions. The asymptotic expressions for large n values (wings of the spectrum) have been obtained analytically by the saddle-point method. It has been shown that the dependence under study has a Gaussian central part and exponential wings. The results obtained are in agreement with the previous calculations for some model systems and existing experimental data.

MQ NMR dynamics in dipolar ordered state at negative temperature

We investigate theoretically the Multiple Quantum (MQ) NMR dynamics at negative absolute temperatures in systems of nuclear spins 1/2 coupled by the dipole–dipole interactions and with the initial conditions determined by the dipolar ordered state. Two different methods of MQ NMR are used. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)y-pulse after the preparation period of the standard MQ NMR experiment. It is shown that at negative temperatures many-spin clusters and spin correlations are created faster, and the intensities of MQ coherences are higher than in the usual MQ NMR experiments. So, the eighth-order MQ coherence in 10-spin system of the cyclopentane molecule appears to be 1.5 times faster and its intensity is four orders higher than at positive temperatures. The proposed MQ NMR methods at negative absolute temperatures can be used for the investigation of many-spin dynamics of nuclear spins in solids.

Low temperature MQ NMR dynamics in dipolar ordered state

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in dipolar ordered spin systems of nuclear spins 1/2 at low temperatures. We consider two different methods of MQ NMR. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)y-pulse after the preparation period of the standard MQ NMR experiment in solids and allows one to measure the Zeeman energy. Both considered methods are sensitive to the contribution of remote spins in the interaction and to the spin system structure. The QS method is sensitive to the spin number in the molecule while the PS method gives very similar time dependencies of the intensities of MQ coherences for different spin numbers. It is shown that the use of the dipolar ordered initial state has the advantage of exciting the highest order MQ coherences in clusters of 4m identical spins, where m=1,2,3,…, that is impossible to do with the standard MQ method. MQ NMR methods based on the dipolar ordered initial states at low temperatures complement the standard NMR spectroscopy for better studying structures and dynamic processes in solids.

Multiple quantum NMR of spin-carrying molecules in nanopores: high order corrections to the two-spin/two-quantum Hamiltonian

This paper is devoted to multiple quantum (MQ) NMR spectroscopy in nanopores filled by a gas of spin-carrying molecules (s = 1/2) in a strong external magnetic field. It turns out that the high symmetry of the spin system in nanopores yields a possibility to overcome the problem of the exponential growth of the Hilbert space dimension with an increase in the number of spins and to investigate MQ NMR dynamics in systems consisting of several hundred spins. We investigate the dependence of the MQ coherence intensities on their order (the profile of the MQ coherence intensities) for a spin system governed by the standard MQ NMR Hamiltonian (the nonsecular two-spin/two-quantum Hamiltonian) together with the second order correction of average Hamiltonian theory. It is shown that the profile depends on the value of this correction and varies from an exponential to a logarithmic one.

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.

Exact solutions in the dynamics of alternating open chains of spins s = 1/2 with the XY Hamiltonian and their application to problems of multiple-quantum dynamics and quantum information theory

A method for exactly diagonalizing the XY Hamiltonian of an alternating open chain of spins s = 1/2 has been proposed on the basis of the Jordan-Wigner transformation and analysis of the dynamics of spinless fermions. The multiple-quantum spin dynamics of alternating open chains at high temperatures has been analyzed and the intensities of multiple-quantum coherences have been calculated. The problem of the transfer of a quantum state from one end of the alternating chain to the other is studied. It has been shown that the ideal transfer of qubits is possible in alternating chains with a larger number of spins than that in homogeneous chains.

Exact diagonalization of the XY-Hamiltonian of open linear chains with periodic coupling constants and its application

A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open linear chains with periodic (in space) changing Larmor frequencies and coupling constants is developed. As an example of application, multiple quantum dynamics of an inhomogeneous chain consisting of 1001 spins is investigated. Intensities of multiple quantum coherences are calculated for arbitrary inhomogeneous chains in the approximation of the next nearest interactions. {\it Key words:} linear spin chain, nearest--neighbour approximation, three--diagonal matrices, diagonalisation, fermions, multiple--quantum NMR, multiple--quantum coherence, intensities of multiple--quantum coherences. {\it PACS numbers:} 05.30.-d; 76.20.+q

Line shapes of multiple quantum NMR coherences in one-dimensional quantum spin chains in solids

General formulae for intensities of multiple quantum (MQ) NMR coherences in systems of nuclear spins coupled by the dipole–dipole interactions are derived. The second moments of the MQ coherences of zero- and second orders are calculated for infinite linear chains in the approximation of the nearest neighbor interactions. Supercomputer simulations of intensities of MQ coherences of linear chains are performed at different times of preparation and evolution periods of MQ NMR experiments. The second moments obtained from the developed theory are compared with the results of the supercomputer analysis of MQ NMR dynamics. The linewidth information in MQ NMR experiments is discussed.

Multiple Quantum Dynamics in Linear Chains and Rings of Nuclear Spins in Solids at Low Temperatures

Multiple quantum spin dynamics is studied using analytical and numerical methods for one-dimensional finite systems of nuclear spins 1 2 coupled by dipole–dipole interactions at low temperatures. Exact expressions for intensities of multiple quantum coherences at low temperatures were obtained in the approximation of the nearest neighbor interactions. The time growth of multiple quantum coherences was analyzed numerically when all the dipole–dipole interactions in one-dimensional systems consisting of 6÷8 spins were taken into account. It is shown that the growth of multiple quantum coherences gets faster when the temperature decreases, and the intensities of multiple quantum coherences can be negative at low temperatures.

Intensities of multiple-quantum coherences in a dilute spin system

The temporal evolution of the intensities of multiple-quantum coherences in a magnetically dilute system of dipole-dipole coupled spins is calculated. It is shown that not only the temporal scale but also the form of the time dependence itself are different from those in concentrated systems.