Triple-quantum Coherences Research Articles

Triple-quantum NMR by selective triple resonance

In high-resolution nuclear magnetic resonance spectra of scalar coupled spins in isotropic phase, it is possible to convert single-into triple-quantum coherences and vice versa by irradiating simultaneously at the frequencies of three chemical shifts. A triple resonance condition can be achieved by modulating a radio-frequency carrier by a product of two cosinusoidal audiowaves, chosen so that three of the four sidebands coincide with three selected chemical shifts. When used in conjunction with two-dimensional Fourier transform spectroscopy, it is possible to obtain triple-quantum multiplets with very high resolution within a limited time span. The linewidths can give an accurate measure of the relaxation rates of triple-quantum coherences.

Transverse relaxation times of spin [formula omitted] nuclei in the quadrupole nutation NMR experiment

Transverse relaxation times in the rotating frame of quadrupolar nuclei with half-integer spins are inversely proportional to the linewidth of quadrupole nutation NMR spectra. We apply fictitious spin −1 2 operators to I = 3 2 nuclei to derive correlations between the transitions of a multi-level system which affect nuclear relaxation. When ω rf ⪡ ω Q, all possible multiple-quantum transitions contribute to the transverse quadrupolar relaxatio time in the rotating frame T 2Q ϱ . When ω rf ⪢ ω Q, two of the three single-quantum transitions do not contribute. In the low-temperature region (outside the extreme narrowing limit), the contribution of double- and triple-quantum coherences to T 2Q ϱ goes through a minimum for ω rf ⪡ ω Q, while the triple-quantum coherence appears at zero frequency and corresponds to a short transverse relaxation time for ω rf ⪢ ω Q.

Complete elimination of the extracellular 23Na NMR signal in triple quantum filtered spectra of rat hearts in the presence of shift reagents

A method is suggested whereby the shifted extracellular triple quantum filtered 23Na signal of an isolated organ is completely eliminated. The method is based on the long relaxation time of the triple quantum coherence and on its fast evolution rate. When the carrier frequency is set on top of the intracellular sodium signal and the time interval between the last two pulses to (12 delta nu)-1 (delta nu is the frequency difference between the intracellular and the extracellular signals), a complete elimination of the extracellular 23Na signal is achieved. The method is demonstrated for isolated rat hearts and the quantification of intracellular sodium using triple quantum filtered spectroscopy is discussed.

Nuclear magnetic resonance line shapes of double and triple quantum coherences of spin 3/2 nuclei

Nuclear magnetic resonance (NMR) line shapes of double and triple quantum coherences were calculated for spin 3/2 nuclei over a wide range of reorientation times. It is shown that for slow rotating molecules the dynamic shifts of all the coherences are a result of adiabatic averaging of the powder spectra. Line shapes are shown to be single Lorentzians far beyond the range of rotational motion, where Redfield’s theory is valid. Analytical expressions for linewidths and dynamic shifts are given for the whole range of motion for which the line shape is Lorentzian. It is suggested that the high ratio between the dynamic shift and the linewidth for the triple quantum coherence can make it possible to distinguish between sodium nuclei in environments with different rotational mobility and quadrupole interactions.

An observation of 23Na NMR triple-quantum dynamic shift in solution

Mult iplequantum-coherence spectroscopy of spin-: nuclei in solution has become recently a subject of intensive research, particularly in reference to biological systems. It was found, both theoretically and experimentally, that in all cases where the singlequantum-coherence decay is biexponential, higher-order coherences may be observed ( 1, 2). This situation occurs when the nucleus is bound in a slowly tumbling site, i.e., with a reorientation time, rR, of the order of the inverse of the kumor frequency, G’, or larger, or when it exchanges with such a site (3, 4). According to relaxation theory (5) the resonance frequency in such systems is shifted relative to the Larmor frequency. This shift is referred to as a dynamic frequency shift (DFS). The measurement of the DFS for single-quantum (SQ) coherences has been very difficult since the shifts are comparable to the linewidths (6-8). However, it has been found to have a pronounced effect in ESR spectra ( 9). Theory predicts that this shift is smaller than the linewidth for double-quantum (DQ) coherence ( 10) but significantly larger for tr iple-quantum ( TQ ) coherence ( 20, 2 I ) . In the present Communicat ion we report the first experimental observation of a TQ DFS in solution. In order to have a system without complications due to the presence of several species and chemical exchange we have chosen the stable complex of Na+ with 4,7,13,16,21-pentaoxa-l,lO-diazabicyclo[S.8.5] tricosane (Kryptofix 221) ( 12 ) , dissolved in glycerol. In the following we shall denote the complex as Na cryptate. G lycerol was selected as the solvent due to the steep ,temperature dependence of its viscosity, allowing the rotational correlation time to vary over a wide range. The relaxation times of the TQ coherence and the TQ DFS were measured by the pulse sequence (1, 2, 13, 14)

Measurement of the quadrupolar coupling with two pulses of opposite phase

The central line intensity of a spin- 3 2 system following excitation by two RF pulses of opposite phase is calculated using the fictitious spin- 1 2 operator formalism. Measurement of this line intensity as a function of the duration of the second pulse enables the quadrupolar coupling ω Q to be determined. Moreover, alternating the phase of the second pulse will filter the polarizations and the double-quantum coherences; only the single- and the triple-quantum coherences are detected. The opposite case happens when the receiver phase is also alternated. These methods are illustrated in a study of 7Li nuclei in a single crystal of LiTaO 3. In the particular case of the rotary-echo sequence, signals having small or large ω Q values compared to the amplitude of the pulse are filtered.

Relaxation of spin quantum number S=3/2 under multiple-pulse quadrupolar echoes

The time evolution of the spin S=3/2 density operator due to relaxation in the presence of a sequence of (π/2) pulses has been calculated using perturbation theory in an interaction representation in which no external time-dependent rf fields occur. It is shown that the relaxation under the effect of the pulse train is similar to T1ρ relaxation. If the magnetization is sampled between the pulses, outside extreme narrowing conditions the observed signal is characterized by a biexponential decay. The amplitude ratio of the fast and slowly relaxing component equals 0.8:0.2. The rate of the fast relaxing component is sensitive to the pulse cycle time in the presence of slowly fluctuating electric-field gradients. A full expression of the relevant spectral density function valid for (π/2) pulses with arbitrary pulse width has been derived. In this derivation, the processes involved in determining the loss of correlation of the quadrupolar interaction are assumed to be independent and characterized by exponential correlation functions. Due to relaxation under the effect of the (π/2) pulse train triple-quantum coherences may be excited. The latter coherences can be monitored by applying an additional coherence transfer pulse after the pulse train. The relaxation of sodium in an ion exchange resin in the presence of the (π/2) pulse sequence has experimentally been studied and agrees with the theoretical analysis.

Spin S= [formula omitted]T1ρ relaxation; the excitation of triple-quantum coherences

A T 1ρ experiment on 23Na in a sodium poly(methylacrylate) ion-exchange resin is reported. It is shown that due to spin S= 3 2 T 1ρ relaxation outside the extreme narrowing limit, triple-quantum coherences are excited. The detected line-shape of the single- as well as the triple-quantum signal contribution consists of a sum of two Lorentzians. These line-shapes and the relative intensity ratio of the single- and triple-quantum signals are in agreement with the theoretical expressions based on previously reported density-operator calculations. The spectral density at two times the precession frequency with respect to the spin-lock field is extracted from the broad component of the detected signals.

Triple‐quantum‐coherence‐filtered imaging of sodium ions in vivo at 4.7 tesla

The tissue distribution of sodium ions which generate triple-quantum coherence (TQC) in vivo is determined from images. A technique for filtering conventional sodium images, so that signal is obtained only from sodium ions which have a correlation time appropriate for producing TQC, is described. The utility of TQC-filtered sodium images is demonstrated in a study of tumors implanted in a nude rat model, where the intensity of the TQC signal from sodium ions in the growing margin of the tumor is observed to be 200-250% greater than that from surrounding tissue.

Relaxation of spin S=3/2 in the doubly rotating tilted frame

For spin S=3/2 the time evolution of the density operator under spin–locking is described. It is shown that outside the extreme narrowing limit triple-quantum coherences are excited. An experiment is proposed to monitor these coherences. The corresponding signal evolves according to a simple relaxation function which is suitable for fitting.

Multipole NMR. VII. Bromine NMR quadrupolar echoes in crystalline KBr

Multipole NMR is used to calculate the responses during various pulse sequences for a solid system of spin- 1 2 nuclei subject to a strong do magnetic field and an inhomogeneous distribution of quadrupole and dipole-dipole interactions. The following sequences were treated: 90° X−τ 1, 90° X−τ 1−90° X−τ 2 90° X−τ 1−90° Y−τ 2, 90° X−τ 1−90° X−τ 2−90° X−τ 3 , 90° X−τ 1−90° Y−τ 2−90° Y−τ 3, and 90° X−τ 1−45° Y−τ 2−45° Y−τ 3 . The calculations show that all of the 15 multipole polarizations (3 alignments, 6 single-, 4 double-, and 2 triple-quantum coherences) can be created in significant amounts by appropriate sequences. The calculations for each sequence have been verified by a detailed experimental study of the sequence responses for Br in a deformed single-crystal of KBr. Seven independent relaxation times were determined. The experiments provide the first evidence for octupole alignment in spin systems.

Triple quantum NMR on spin systems with I = 3/2 in solids

Pulsed NMR experiments are developed for the excitation and the detection of triple quantum coherences in quadrupolar spin systems with I = 3/2. Two experimental methods are used: For systems with small quadrupolar frequencies direct triple quantum excitation and detection is accomplished by weak rf irradiation pulses. For large quadrupolar frequencies modulated rf pulses are applied to create and to monitor triple quantum coherences. Modulated rf pulse techniques are also used to search for quadrupolar frequencies and to excite selectively center frequency spectral lines of I = 3/2 nuclei. Applications of these techniques are demonstrated by 23Na(I = 3/2) NMR experiments on an oriented single crystal of sodium ammonium tartarate tetrahydrate.

Multiple-quantum cross-polarization NMR on spin systems withI=12andS=32in solids

Triple-quantum NMR on spins with $S=\frac{3}{2}$ in solids can be of much help by the determination of the chemical shielding parameters. Excitation and detection of the triple-quantum coherences of $S$ spins with small quadrupolar frequencies (${\ensuremath{\omega}}_{Q}\ensuremath{\lesssim}300$ ${\mathrm{sec}}^{\ensuremath{-}1}$), was accomplished by weak rf pulses. On spins with large quadrupolar frequencies modulated rf-pulse techniques have been explored in order to obtain their narrow-line triple-quantum spectra. In this publication cross-polarization-enhancement techniques on the single-, double-, and triple-quantum transitions of $S=\frac{3}{2}$ spins, in systems with abundant $I=\frac{1}{2}$ spins and rare $S=\frac{3}{2}$ spins, are developed. The theory of these experiments is an extension of the theory of double-quantum cross polarization. The $S=\frac{3}{2}$ spin Hamiltonian can always be divided in three commuting parts, of which two are fictitious spin-1/2 Hamiltonians. Cross polarization can occur between one of these transitions and the $I$ spins in the system. Hartmann-Hahn conditions for these processes are derived. Nonmodulated and partially modulated rf irradiation fields are used for the enhancement of single- and triple-quantum coherences. Efficiency factors of the different cross-polarization experiments are calculated. $^{23}\mathrm{Na}$-$^{1}\mathrm{H}$ spin-lock cross-polarization measurements are performed on an oriented single crystal of sodium ammonium tartarate tetrahydrate in order to verify the different Hartmann-Hahn conditions. A full modulation cross-polarization experiment is designed to obtain large enhancements of the signal intensities of center-frequency lines of $S=\frac{3}{2}$ spectra from single crystals.