Shimon Vega

Chemical shift correlation spectroscopy in rotating solids: Radio frequency‐driven dipolar recoupling and longitudinal exchange

We present a new method of performing chemical shift correlation spectroscopy in solids with magic angle spinning (MAS). Its key feature is a longitudinal mixing period of π pulses that recouples the dipolar interaction. We discuss experimental results for triply‐13C‐labeled alanine and a theory combining MAS and π pulses.

Operator formalism for double quantum NMR

An operator formalism is presented which conveniently treats the interaction of a spin‐1 nucleus with a weak radio frequency field. The Hamiltonian in the rotating frame is H=−Δω Iz−ω1Ix+(1/3) ωQ[3 I2z−I (I+1)], where Δω is the resonance offset (Δω=ω0−ω), ω1 is the intensity of the rf field, and ωQ is the quadrupolar splitting. Nine fictitious spin−1/2 operators, Ip,i where p=x,y,z and i=1,2,3, are defined where p refers to the transition between two of the levels and i the Cartesian component. The operators, which are the generators of the group SU (3), satisfy spin‐1/2 commutation relations [Ip,j, Ip,k]=i Ip,l, where j,k,l=1,2,3 or cyclic permutation. Thus each p defines a three‐dimensional space termed p space. For irradiation near one of the quadrupolar satellites, for example, Δω=ωQ+δω with δω, ω1≪ωQ, it is shown that the effective Hamiltonian can be written H?−δωIx,3−√2 ω1Ix,1, i.e., a fictitious spin‐1/2 Hamiltonian in x space with effective magnetogyric ratio γ along the 3 (resonance offset) axis ...

Fictitious spin 1/2 operator formalism for multiple quantum NMR

A formalism is presented that describes the time behavior of the spin density matrix of a nuclear spin system with arbitrary spin in terms of fictitious spin −(1/2) operators. This formalism is an extension of that used earlier for nuclei with spin I=1. For a spin system with n eigenstates we define for every pair of eigenstates ‖i〉 and ‖j〉 three operators Ii−jp, with p=x, y, and z, according to the three 2×2 Pauli matrices σx, σy, and σz. These operators together constitute a complete set of n2−1 independent Hermitian operators, and we can write the n×n density matrix and the spin Hamiltonian of the system in terms of the Ii−jp operators. The commutation relations among the operators make it possible in many cases to solve the equation of motion of the density matrix analytically. Three examples of the use of the Ii−jp operators are presented. Firstly a system of noninteracting spins with I=1 is considered. The Ii−jp operators for this case are compared with the Iq,k operator defined earlier. The cw sign...

High-resolution proton solid-state NMR spectroscopy by phase-modulated Lee–Goldburg experiment

Abstract In this Letter, we present a pulse scheme for coherent averaging of spin–spin interactions called phase-modulated Lee–Goldburg (PMLG) which is aimed at achieving high-resolution proton NMR spectra in the solid state. Our objective is mainly to discuss the design and execution of this experiment and to show some preliminary experimental results as evidence of the far-reaching potentials of this technique.

Sensitivity enhancement of the MQMAS NMR experiment by fast amplitude modulation of the pulses

Abstract We report here an improved way of doing the multiple-quantum magic-angle spinning (MQMAS) NMR experiment that relies on the use of amplitude modulated pulses. These pulses were found to yield MQMAS NMR signals that are considerably stronger (≈200–300%) than the ones arising from the usual continuous wave pulse schemes by virtue of a superior efficiency of the triple- to single-quantum conversion process. Numerical simulations and experimental results taking 23 N a and 87 R b nuclei as examples are presented that corroborate the usefulness of this approach.

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.

A simple magic angle spinning NMR experiment for the dephasing of rotational echoes of dipolar coupled homonuclear spin pairs

Abstract A simple NMR experiment for the dephasing of the rotational echo amplitudes of homonuclear dipolar coupled spin pairs in solids rotating at the magic angles is described. The dephasing is generated by π pulses applied synchronously with the sample rotation. One π pulse per rotor cycle is sufficient to cause an echo decay when the homonuclear dipole interaction is present. The dephasing effect of the π pulses is described using Floquet theory. Experimental results obtained on a doubly 13C-labeled alanine are presented and compared with numerical calculations. Effects arising from finite pulse lengths are also demonstrated and discussed.

Recoupling of Homo- and Heteronuclear Dipolar Interactions in Rotating Solids

The measurement of homo- and heteronuclear dipolar couplings by nuclear magnetic resonance (NMR) techniques is an important tool for the determination of molecular structure in solids. In a static polycrystalline solid, the dipolar coupling between two magnetically dilute spins results in the characteristic “Pake pattern” [1], first observed in the 1H spectrum of gypsum, CaSo4-2H2O, which arises from the interaction between the two protons in the water molecules of hydration. The splitting between the singularities provides a straightforward measurement of the dipolar coupling constant and therefore the internuclear distance between the two spins. Unfortunately, in the more general case, the structural information revealed by internuclear distances cannot be obtained directly from the static 1H NMR spectrum because of the multiplicity of couplings. In situations involving other nuclei, such as 13C, 15N, and 31P, large chemical shift anisotropics, as well as other line-broadening mechanisms, obscure the lineshape perturbations from the through-space dipolar couplings.

Proton spectroscopy in solid state nuclear magnetic resonance with windowed phase modulated Lee-Goldburg decoupling sequences

We demonstrate here a new windowed multiple pulse sequence for the detection of protons in solid state NMR. Acquisition windows are inserted in the phase modulated Lee–Goldburg scheme (PMLG). This enables one-dimensional acquisition as against two-dimensional in windowless schemes. The pulse scheme, theoretical justifications and experimental spectra of a few samples are presented. In addition two-dimensional proton–proton and carbon–proton correlation experiments are performed with windowed PMLG proton detection.

The Floquet theory of nuclear magnetic resonance spectroscopy of single spins and dipolar coupled spin pairs in rotating solids

The Floquet theory for the description of magic angle sample spinning (MASS) nuclear magnetic resonance (NMR) experiments is introduced. MASS NMR signals of single spin systems and homonuclear two‐spin system in the presence of direct and indirect dipolar couplings are evaluated. The single spin system is utilized to develop our Floquet formalism for the MASS NMR experiments and the coupled spin system is discussed to demonstrate its methodology and its applicability. This theoretical approach enables the calculation of the positions, the amplitudes, and line shapes of MASS center and sideband. The diagonalization of the MASS Floquet matrices of the different spin systems provides eigenvalues and eigenvectors which in turn determine the frequencies and intensities of the various bands in the MASS spectra. Their frequency shifts can be explained in terms of anticrossing of Floquet states and their amplitudes can be calculated via the matrix elements of transition–amplitude Floquet operator. New Floquet ope...