Molecular dynamics of half-integer quadrupolar nuclei studied by QCPMG solid-state NMR experiments on static and rotating samples. Theory and simulations

Simulations of QCPMG NMR type experiments have been used to explore dynamic processes of half-integer quadrupolar nuclei in solids. By setting up a theoretical approach that is well suited for efficient numerical simulations the QCPMG type experiments have been analyzed regarding the effect of the magnitude of the EFG- and CSA-tensors, the spin-quantum number, different dynamical processes and MAS. Compared to the QE experiment the QCPMG experiment offers not only intensity gain by an order of magnitude and changes in overall lineshape as a function of the kinetic rate constant but the lineshape of the individual spin-echo sidebands is also very sensitive towards dynamics. Hereby a visual identification of the dynamics is obtained. In common for all the simulations the spin-echo sidebands are narrow in the slow (k< or =10(2) Hz) and the fast (k> or =10(7) Hz) dynamic regime whereas they are broadened in the intermediate regime 10(3)< or =k< or =10(7) Hz. The maximum intensity of the spin-echo sidebands for two-site jumps is highly dependent on the type of anisotropic interactions involved and the type of QCPMG experiment. Hence, in the fast limit the maximum intensity was 140% of the initial intensity when significant CSA was present or under the QCPMG-MAS experiment compared to 89 or 71% for the static experiment influenced by the quadrupolar interaction only. For 3-, 4-, and 6-site jumps the maximum intensity in the fast limit reached up to 339% of the intensity in the static limit.     

13C/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling

A two-dimensional (13)C/(14)N heteronuclear multiple quantum correlation (HMQC) experiment using dipolar recoupling under magic-angle spinning (MAS) is described. The experiment is an extension of the recent indirect (13)C detection scheme for measuring (14)N quadrupolar coupling under MAS. The recoupling allows the direct use of the much larger dipolar interaction instead of the small J and residual dipolar couplings for establishing (13)C/(14)N correlations. Two recoupling methods are incorporated into the HMQC sequence, both applying rf only to the observed (13)C spin. The first one uses the REDOR sequence with two pi-pulses per rotor cycle. The second one uses a cw rf field matching the spinning frequency, known as rotary resonance. The effects of CSA, T(2)(') signal loss, MAS frequency and stability and t(1)-noise are compared and discussed.     

59Co chemical shift anisotropy and quadrupole coupling for K3Co(CN)6 from MQMAS and MAS NMR spectroscopy

59Co triple-quantum (3Q) MAS and single-pulse MAS NMR spectra of K3Co(CN)6 have been obtained at 14.1 T and used in a comparison of these methods for determination of small chemical shift anisotropies for spin I = 7/2 nuclei. From the 3QMAS NMR spectrum a spinning sideband manifold in the isotropic dimension with high resolution is reconstructed from the intensities of all spinning sidebands in the 3QMAS spectrum. The chemical shift anisotropy (CSA) parameters determined from this spectrum are compared with those obtained from MAS NMR spectra of (i) the complete manifold of spinning sidebands for the central and satellite transitions and of (ii) the second-order quadrupolar lineshapes for the centerband and spinning sidebands from the central transition. A good agreement between the three data sets, all of high precision, is obtained for the shift anisotropy (delta(sigma) = delta(iso) - delta(zz)) whereas minor deviations are observed for the CSA asymmetry parameter (eta(sigma)). The temperature dependence of the isotropic 59Co chemical shift has been studied over a temperature range from -28 to +76 degrees C. A linear and positive temperature dependence of 0.97 ppm/degree C is observed.     

A solid-state 14N magic-angle spinning NMR study of some amino acids

Experimental strategies for the acquisition of high-quality 14N magic-angle spinning (MAS) NMR spectra of the simple amino acids, which exhibit 14N quadrupole coupling constants (C(Q)) on the order of 1.2 MHz, are devised. These are the first useful 14N MAS spectra reported for nitrogen compounds having a C(Q)(14N) value in excess of 1 MHz. The complete manifolds of spinning sidebands (ssbs), i.e., about 300 ssbs for a spinning frequency of 6.0 kHz, have been observed in the 14N MAS NMR spectra of a series of amino acids. In their crystal structure these amino acids all exhibit the zwitterionic form and thus the 14N MAS NMR spectra represent those of a rotating -NH(3)(+) group and not of an amino (-NH(2)) group. Computer simulations combined with fitting of simulated to the experimental ssb intensities result in the determination of precise values for the 14N quadrupole coupling (C(Q)) and its associated asymmetry parameter (eta(Q)) for the nitrogen sites in these molecules. For some of the amino acids the 14N MAS NMR spectra exhibit overlap between the manifolds of ssbs from two different nitrogen sites in accordance with their crystal structures. Computer analysis of these spectra results in two different sets of (C(Q), eta(Q)) values which mainly differ in the magnitudes for eta(Q).     

A solid-state N magic-angle spinning NMR study of some amino acids

Experimental strategies for the acquisition of high-quality 14N magic-angle spinning (MAS) NMR spectra of the simple amino acids, which exhibit 14N quadrupole coupling constants (C(Q)) on the order of 1.2 MHz, are devised. These are the first useful 14N MAS spectra reported for nitrogen compounds having a C(Q)(14N) value in excess of 1 MHz. The complete manifolds of spinning sidebands (ssbs), i.e., about 300 ssbs for a spinning frequency of 6.0 kHz, have been observed in the 14N MAS NMR spectra of a series of amino acids. In their crystal structure these amino acids all exhibit the zwitterionic form and thus the 14N MAS NMR spectra represent those of a rotating -NH(3)(+) group and not of an amino (-NH(2)) group. Computer simulations combined with fitting of simulated to the experimental ssb intensities result in the determination of precise values for the 14N quadrupole coupling (C(Q)) and its associated asymmetry parameter (eta(Q)) for the nitrogen sites in these molecules. For some of the amino acids the 14N MAS NMR spectra exhibit overlap between the manifolds of ssbs from two different nitrogen sites in accordance with their crystal structures. Computer analysis of these spectra results in two different sets of (C(Q), eta(Q)) values which mainly differ in the magnitudes for eta(Q).     

Satellite transitions in natural abundance solid-state (33)S MAS NMR of alums--sign change with zero-crossing of C(Q) in a variable temperature study

Experiences obtained from recent improvements in the performance of solid-state (14)N MAS NMR spectroscopy have been used in a natural abundance (33)S MAS NMR investigation of the satellite transitions for this interesting spin I=3/2 isotope. This study reports the first observation of manifolds of spinning sidebands for these transitions in (33)S MAS NMR as observed for the two alums XAl(SO(4))(2) x 12H(2)O with X=NH(4) and K. For the NH(4)-alum a variable temperature (33)S MAS NMR study, employing the satellite transitions, shows that the (33)S quadrupole coupling constant (C(Q)) exhibits a linear temperature dependence (in the range -35 degrees C to 70 degrees C) with a temperature gradient of 3.1 kHz/ degrees C and undergoes a sign change with zero-crossing for C(Q) at 4 degrees C (277 K). For the isostructural K-alum a quite similar increase in the magnitude of C(Q) with increasing temperature is observed, and with a temperature gradient of 2.3 kHz/ degrees C. Finally, for optimization purposes, a study on the effect of the applied pulse widths at constant rf field strength on the intensity and variation in second-order quadrupolar lineshape for the central (1/2<-->-1/2) transition of the K-alum has been performed.     

Small 51V chemical shift anisotropy for LaVO4 from MQMAS and MAS NMR spectroscopy

51V MQMAS NMR of the triple-quantum transitions is shown to be particularly useful in the determination of the sign and magnitude of the chemical shift anisotropy (CSA) parameter delta(sigma)(= delta(iso)-delta(zz)) along with the asymmetry parameter (eta(sigma)) for a vanadium environment with a small CSA and a rather strong quadrupole coupling. This is demonstrated for the orthovanadate LaVO(4) for which 51V magic-angle spinning (MAS) NMR of the central and satellite transitions at 14.1T gives precise values for the quadrupole coupling parameters, however, an ambiguous sign for delta(sigma). The CSA parameters are reliably obtained from analysis of the spinning sidebands observed in a 51V triple-quantum MAS experiment. Combining these data with least-squares analysis of the manifold of spinning sidebands in the single-pulse MAS NMR spectrum results in a precise determination of the magnitudes and relative orientation of the 51V quadrupole coupling and CSA tensors for LaVO(4).     

Molecular dynamics as studied by static-powder and magic-angle spinning 2H NMR

The 2H NMR magic-angle spinning (MAS) technique is compared to the static-powder quadrupole echo (QE) and Jeener-Brockaert (JB) pulse sequences for a quantitative investigation of molecular dynamics in solids. The linewidth of individual spinning sidebands of the one-dimensional MAS spectra are observed to be characteristic of the correlation time from approximately 10(-2) to approximately 10(-8) s so that the dynamic range is increased by approximately three orders of magnitude when compared to the QE experiment. As a consequence, MAS 2H NMR is found to be more sensitive to the presence of an inhomogeneous distribution of correlation times than the QE and JB experiments which rely upon lineshape distortions due to anisotropic T2 and T1Q relaxation, respectively. All these results are demonstrated experimentally and numerically using the two-site flip motion of dimethyl sulfone and of the nitrobenzene guest in the alpha-p-tert-butylcalix[4]arene-nitrobenzene inclusion compound.     

A study of the 14C(6Li, 6He)14N reaction at 93 MeV

The reaction ¹⁴C(⁶Li, ⁶He)¹⁴N was investigated with 93 MeV ⁶Li ions in an angular interval of 7–26°. Angular distributions were analysed for the four most intense groups of ⁶He nuclei, corresponding to transitions to the ground (1₁⁺) and the excited (1₂⁺, 2₁^?, 4₁^?) states of ¹⁴N. In the theoretical analysis a mechanism of the spin-isospin excitation was suggested in the DWBA frame with the finite range of interaction and recoil in the light system (⁶Li⁶He) taken into account. In the calculations both shell-model wave functions and transition densities obtained in the theory of finite Fermi systems (FFS) were used. From the comparison between theory and experiment the Landau-Migdal force constant g′ is estimated in order to obtain some information on the degree of nuclear proximity to the threshold of pion condensation.     

6Li and 7li solid-state NMR spectroscopy of nitrogen ceramic phases

Two nitrogen ceramic phases, the oxynitride LiSiON and the nitride LiSi2N3, have been studied by 6Li and 7Li NMR. Magic angle spinning (MAS) NMR experiments have been carried out at two magnetic field strengths (7.05 and 14.1 T). The spectra give evidence of the relative effects of the quadrupolar and chemical shift interactions. The electric field gradient tensor of both phases has been determined accurately by iterative fitting of the 6Li and 7Li MAS NMR line shapes at the two magnetic field strengths. Due to the fact that for 7Li the quadrupolar interaction is much larger than the chemical shift interaction, it is shown that neither the small chemical shift anisotropy nor the relative orientation of the two interaction tensors can be determined accurately by 7Li MAS NMR. For 6Li, the two interactions are comparable and the value of these parameters obtained from the fits of the 6Li experimental MAS line shapes are therefore much more reliable.     

Chemical shift anisotropy amplification

A new NMR experiment which allows a measurement of the chemical shift anisotropy (CSA) tensor under magic angle spinning (MAS) is described. This correlates a fast MAS spectrum in the omega2 dimension with a sideband pattern in omega1 in which the intensities mimic those for a sample spinning at a fraction of the rate omega r/N, and these sidebands result from an amplification by a factor N of the modulation caused by the CSA. Standard methods can be used to extract the principal tensor components from the omega1 sideband patterns, and the nature of the experiment is such that the use of a large number of t1 increments can be avoided without compromising the resolution of different chemical sites. The new experiment is useful for accurately measuring narrow shift anisotropies.     

Dynamic properties of P4O6S and P4O7:31P spin-echo and 31P MAS-NMR investigations.

The rotational dynamics of P₄O₆S and P₄O₇ in the solid state were studied by means of ³¹P NMR spectra of spinning and static powder samples in the temperature range of 153–295 K and 295–388 K, respectively. All spectra were simulated to confirm the type of the motion and to extract the time scales as a function of the temperature. Good agreement between experimental and theoretical data was obtained on the basis of a three-site jump model. For P₄O₆S, the activation energy and the pre-exponential factor derived from the lineshape simulations amount to 51(2) kJ/mol and 6(3)·10¹⁵ s⁻¹. For P₄O₇, the spectral analysis yields an activation energy of 67(1) kJ/mol and a pre-exponential factor of 6(2)·10¹⁴ s⁻¹. The dynamic behavior was checked independently by lineshape analyses under both MAS and static conditions. Activation energies are consistent within the errors for the lineshape analyses. Additionally, we have analyzed spin–lattice relaxation measurements, which show the correct trends for the activation energies.     

Evidence for critical angular momenta in the formation of 26Al via the 14N + 12C channel

States in ²⁰Ne have been studied through the ¹²C(¹⁴N, ⁶Li)²⁰Ne reaction. Excitation functions have been measured from 20 MeV to 60 MeV in steps of 5 MeV at different angles for ²⁰Ne states up to 10 MeV excitation energy. States of ²⁴Mg have been also populated using the ¹²C(¹⁴N, d)²⁴Mg reaction; excitation functions of ²⁴Mg states up to 9 MeV excitation energies as well as angular distributions at 35 MeV bombarding energy have been obtained. Comparisons of data with Hauser-Feshbach calculations show clearly that the compound nucleus mechanism is the main process for both ¹²C(¹⁴N, ⁶Li)²⁰Ne and ¹²C(¹⁴N, d)²⁴Mg reactions. Strong evidence has been provided for inhibition of the ²⁶Al compound nucleus formation for angular momenta higher than critical values. The location of the yrast line in the ²⁶Al nucleus is discussed.     

<Superscript>33</Superscript>S MAS NMR of a disordered sulfur-doped silicate: Signal enhancement via RAPT,QCPMG and adiabatic pulses

Three different signal enhancement techniques have been applied to ³³S magic-angle spinning nuclear magnetic resonance (MAS NMR) of a disordered silicate containing 1.15 wt% ³³S. Partial saturation of the satellite transitions was achieved using a rotor-assisted population transfer (RAPT) pulse sequence, resulting in a signal enhancement of 1.63, albeit with a slight distortion of the line shape due to selective excitation. Adiabatic inversion of the satellite transitions by various amplitude-and frequency-modulated pulse shapes (such as hyperbolic secant and wideband uniform-rate smooth truncation) was also attempted, resulting in a signal enhancement of up to 1.85, with no apparent line shape distortion. Quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) and RAPT-QCPMG sequences were also used, both of which yielded spikelet spectra that accurately reflected the MAS line shape with a greatly improved signal-to-noise ratio. It is hoped that this study demonstrates that ³³S solid-state MAS NMR is now feasible even on disordered, low-sulfur-content systems.     

The role of (15)N CSA and CSA/dipole cross-correlation in (15)N relaxation in solid proteins

The influence of the (15)N CSA on (15)N longitudinal relaxation is investigated for an amide group in solid proteins in powder form under MAS. This contribution is determined to be typically 20-33% of the overall longitudinal relaxation rate, at 11.74 and 16.45 T, respectively. The improved treatment is used to analyze the internal dynamics in the protein Crh, in the frame of a motional model of diffusion in a cone, using the explicit average sum approach. Significant variations with respect to the determined dynamics parameters are observed when properly accounting for the contribution of (15)N CSA fluctuations. In general, the fit of experimental data including CSA led to the determination of diffusion times (tau(w)) which are longer than when considering only an (15)N-(1)H dipolar relaxation mechanism. CSA-Dipole cross-correlation is shown to play little or no role in protonated solids, in direct contrast to the liquid state case.     

Transfer reaction studies to states in 14N and 14C

States in ¹⁴N and ¹⁴C have been populated by the Li-induced reactions ¹⁰B(⁶Li, d), ¹¹B(⁶Li, t/³He), ¹¹B(⁷Li, α), ¹²C(⁶Li, α), and ¹³C(⁷Li, ⁶He/⁶Li) at E_Li = 32 and 34 MeV. Selective population of states is observed with these reactions. Angular distributions were measured for the ¹¹B(⁶Li t/³He) analog reactions. Experimental criteria are developed to allow the identification of analog states up to 18.40 and 16.45 MeV excitation in ¹⁴N and ¹⁴C, respectively.     

Solid-state 25Mg QCPMG NMR of bis(cyclopentadienyl)magnesium

Application of the "quadrupolar Carr-Purcell Meiboom-Gill" (QCPMG) sequence permits the first natural abundance solid-state 25Mg NMR study of an organometallic magnesium compound, bis(cyclopentadienyl)magnesium. Analytical and numerical simulations of both static and magic-angle spinning QCPMG NMR spectra beget an axially symmetric 25Mg electric field gradient (EFG) tensor (quadrupolar asymmetry parameter, eta(Q)=0.01(1)) with a nuclear quadrupole coupling constant of C(Q)=5.80(5)MHz. Restricted Hartree-Fock and hybrid density functional theory (B3LYP) calculations are in good agreement with experimental EFG values and predict a chemical shielding anisotropy of about 40-50 ppm, which we attempt to elucidate by numerical simulations. The parameters and orientation of the 25Mg EFG tensor are rationalized from examination of the crystal structure and molecular symmetry. The NMR properties of the cyclopentadienyl rings are examined by 13C[1H] CPMAS NMR, RHF and hybrid-DFT (B3LYP) calculations, and simulations of the effects of chemical exchange on the 13C powder pattern.     

Dipole excitation of alpha clusters in (6)Li and (7)Li

Dipole excitations in highly excited energy regions of (6)He and (7)He nuclei were investigated via the ((7)Li,(7)Be) reaction with an incident energy of 65A MeV at forward scattering angles. The resonances at Q approximately equal to -30 MeV observed commonly for both (6)Li and (7)Li targets were found to be excited via both spin-flip and spin-nonflip transitions with DeltaL = 1. Based on the observed excitation energy, width, and cross section of each resonance, the relevant resonances are inferred to be analogs of the dipole resonances of alpha clusters in the (6)Li and (7)Li nuclei.     

Dynamic properties of P4O6S and P4O7: P spin–echo and P MAS–NMR investigations

The rotational dynamics of P₄O₆S and P₄O₇ in the solid state were studied by means of ³¹P NMR spectra of spinning and static powder samples in the temperature range of 153–295 K and 295–388 K, respectively. All spectra were simulated to confirm the type of the motion and to extract the time scales as a function of the temperature. Good agreement between experimental and theoretical data was obtained on the basis of a three-site jump model. For P₄O₆S, the activation energy and the pre-exponential factor derived from the lineshape simulations amount to 51(2) kJ/mol and 6(3)·10¹⁵ s⁻¹. For P₄O₇, the spectral analysis yields an activation energy of 67(1) kJ/mol and a pre-exponential factor of 6(2)·10¹⁴ s⁻¹. The dynamic behavior was checked independently by lineshape analyses under both MAS and static conditions. Activation energies are consistent within the errors for the lineshape analyses. Additionally, we have analyzed spin–lattice relaxation measurements, which show the correct trends for the activation energies.     

Lineshape asymmetry for joint coherent population trapping and three-photon N resonances

We show that a characteristic two-photon lineshape asymmetry arises in coherent population trapping (CPT) and three-photon (N) resonances, because both resonances are simultaneously induced by modulation sidebands in the interrogating laser light. The N resonance is a three-photon resonance in which a two-photon Raman excitation is combined with a resonant optical pumping field. This joint CPT and N resonance can be the dominant source of lineshape distortion, with direct relevance for the operation of miniaturized atomic frequency standards. We present the results of both an experimental study and theoretical treatment of the asymmetry of the joint CPT and N resonance under conditions typical to the operation of an N resonance clock.