Sensitivity enhancement of solid-state NMR spectra of half-integer spin quadrupolar nuclei using hyperbolic secant pulses: Applications to spin-5/2 nuclei

On the use of frequency-swept pulses and pulses designed with optimal control theory for the acquisition of ultra-wideline NMR spectra

Frequency-swept (FS) pulses, such as wideband uniform-rate smooth-truncation (WURST) pulses, have found much success for the acquisition of ultra-wideline (UW) solid-state NMR spectra. In this preliminary study, new pulses and pulse sequences are explored in simulation and experimentally for several nuclei exhibiting UWNMR powder patterns under static conditions, including ¹¹⁹Sn (I = 1/2), ¹⁹⁵Pt (I = 1/2), ²H (I = 1), and ⁷¹Ga (I = 3/2). First, hyperbolic secant (HS) and tanh/tan (THT) pulses are tested and implemented as excitation and refocusing pulses in spin-echo and Carr-Purcell/Meiboom Gill (CPMG)-type sequences, and shown to have comparable performances to analogous WURST pulses. Second, optimal control theory (OCT) is utilized for the design of new Optimal Control Theory Optimized Broadband Excitation and Refocusing (OCTOBER) pulses, using carefully parameterized WURST, THT, and HS pulses as starting points. Some of the new OCTOBER pulses used in spin-echo sequences are capable of efficient broadband excitation and refocusing, in some cases resulting in spectra with increased signal enhancements over those obtained in experiments using conventional FS pulses. Finally, careful consideration of the spin dynamics of several systems, by monitoring of the time evolution of the density matrix via the Liouville-von Neumann equation and analysis of the time-resolved Fourier transforms of the pulses, lends insight into the underlying mechanisms of the FS and OCTOBER pulses. This is crucial for understanding their performance in terms of generating uniformly excited patterns of high signal intensity, and for identifying trends that may offer pathways to generalized parameterization and/or new pulse shapes.

Signal enhancement in solid-state NMR of quadrupolar nuclei

Recent progress in the development and application of signal enhancement methods for NMR of quadrupolar nuclei in solids is presented. First, various pulse schemes for manipulating the populations of the satellite transitions in order to increase the signal of the central transition (CT) in stationary and rotating solids are evaluated (e.g., double-frequency sweeps, hyperbolic secant pulses). Second, the utility of the quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) and WURST-QCPMG pulse sequences for the rapid and efficient acquisition of particularly broad CT powder patterns is discussed. Third, less frequently used experiments involving polarization transfer from abundant nuclear spins (cross-polarization) or from unpaired electrons (dynamic nuclear polarization) are assessed in the context of recent examples. Advantages and disadvantages of particular enhancement schemes are highlighted and an outlook on possible future directions for the signal enhancement of quadrupolar nuclei in solids is offered.

Enhancing the central-transition NMR signal of quadrupolar nuclei by spin population transfer using SW-FAM pulse trains with a tangent-shaped sweep profile

Solid-state NMR of quadrupolar nuclei with half-integer spin, such as (25)Mg (I=5/2) or (43)Ca (I=7/2), suffers from low sensitivity, which may be improved using spin population transfer (SPT) from the satellite transitions. Effecting SPT with good efficiency is especially challenging under static conditions, and several techniques such as double-frequency sweeps (DFS), hyperbolic secant pulses (HS) and frequency-swept fast-amplitude modulated pulses (SW-FAM) have been suggested for achieving the necessary manipulations of the satellite transitions. We here investigate the SPT properties of an SW-FAM sequence with a tangent-shaped profile. The new SW(tan)-FAM pulse train is shown to possess superior SPT performance to the SW(1/τ)-FAM sequence, which hitherto has been considered to be the best FAM method for signal enhancement of static spectra, by both numerical simulations on a (27)Al model system, and experimental results on aluminium acetyl acetonate, Al(acac)(3). In addition, the CT enhancement of individual crystallites from the polycrystalline sample with a defined angle between principal z-axis of the diagonal Q-tensor and the external field was considered by numerical simulations. In the vicinity of the magic angle θ(m)=54.7°, a region of zero enhancement exists. Use of the SW(tan)-FAM sequence allows extending the frequency sweep further into this region, with beneficial effects for the overall enhancement and the faithfulness of the line shape. In agreement with previously published studies, our numerical simulations on SPT for single crystals again evidence that the enhancement factors for a polycrystalline sample range from zero enhancement to the maximum gain of 2I, with the total enhancement factor of the full powder pattern being the summation of these strongly varying individual factors. This variation is the cause for line shape distortions in SPT-enhanced spectra. At the same time, these findings prove the capability of frequency sweeps (i.e., DFS and SW-FAM) to fully invert the satellite transitions under certain conditions.

Repetitive sideband-selective double frequency sweeps for sensitivity enhancement of MAS NMR of half-integer quadrupolar nuclei

A sensitivity enhancement scheme aiming at selective adiabatic inversion of a single set of satellite transition sidebands under magic angle spinning has been employed on samples of albite containing a single moderately distorted (27)Al site and zoisite containing two highly distorted octahedral (27)Al sites. Overall enhancements of ∼2.5 for albite and ∼3 for the two AlO(6) sites of zoisite are reported by applying this scheme at different spinning speeds reflecting the versatility of this enhancement scheme which achieves significant signal-to-noise enhancements for the systems with moderately high quadrupolar coupling and high quadrupolar coupling. Repeating the sensitivity enhancement scheme and signal readout several times without allowing for spin-lattice relaxation leads to sensitivity enhancements of factors of ∼4 for albite and ∼5 for zoisite which substantially increases the detectability of the quadrupolar sites. The effectiveness of this scheme at high magnetic field under very fast magic angle spinning has been demonstrated. Finally, the possibility of performing spectral editing by selective enhancement of one of the quadrupolar sites in zoisite whilst keeping the other site unaffected has been explored.

Sensitivity enhancement in MAS NMR of half-integer quadrupolar nuclei using sideband selective double-frequency sweeps

Sensitivity enhancement of the NMR signal of the half-integer spin quadrupolar nuclei under magic angle spinning (MAS) conditions is demonstrated using the DFS (Double Frequency Sweep) enhancement scheme. It has been shown, both through numerical simulations and by experiments, that with a sinusoidal amplitude profile a narrow band DFS scheme performs much better than a DFS scheme with a large bandwidth. The total enhancement compares favorably to the hyperbolic secant (HS) pulse scheme under MAS. Finally, we report the robustness of this DFS scheme with respect to variation of different experimental parameters, making it a very attractive choice for acquiring sensitivity-enhanced NMR experiments of half-integer quadrupolar nuclei.

Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances

Solid-state nuclear magnetic resonance (NMR) of quadrupolar nuclei has recently undergone remarkable development of capabilities for obtaining structural and dynamic information at the molecular level. This review summarizes the key achievements attained during the last couple of decades in solid-state NMR of both integer spin and half-integer spin quadrupolar nuclei. We provide a concise description of the first- and second-order quadrupolar interactions, and their effect on the static and magic angle spinning (MAS) spectra. Methods are explained for efficient excitation of single- and multiple-quantum coherences, and acquisition of spectra under low- and high-resolution conditions. Most of all, we present a coherent, comparative description of the high-resolution methods for half-integer quadrupolar nuclei, including double rotation (DOR), dynamic angle spinning (DAS), multiple-quantum magic angle spinning (MQMAS), and satellite transition magic angle spinning (STMAS). Also highlighted are methods for processing and analysis of the spectra. Finally, we review methods for probing the heteronuclear and homonuclear correlations between the quadrupolar nuclei and their quadrupolar or spin-1/2 neighbors.

Using hyperbolic secant pulses to assist characterization of chemical shift tensors for half-integer spin quadrupolar nuclei in MAS powder samples

Determination of the NMR anisotropic magnetic shielding parameters from magic angle spinning, MAS, powder samples containing half-integer spin quadrupolar nuclei is achieved by analysis of the difference spectrum obtained with and without application of a hyperbolic secant pulse. Application of a hyperbolic secant pulse to any spinning sideband associated with the central transition, m(I) = 1/2 to m(I) = - 1/2, results in 'saturation' of the entire central transition manifold. Similarly, if one spinning sideband associated with the m(I) = 3/2 to m(I) = 1/2 and m(I) = - 1/2 to m(I) = - 3/2 satellite transitions is perturbed, the entire satellite manifold associated with these transitions is 'saturated' while the central transition is enhanced by population transfer. Three 'difference spectrum' techniques are employed to selectively yield the spinning sidebands associated predominantly from the central transition. The success of these difference techniques is first demonstrated by examining (51)V NMR spectra of three metavanadate salts and (59)Co NMR spectra of Co(acac)(3). The vanadium and cobalt chemical shift tensors in these compounds have spans between 400 and 1400 ppm. Because the hyperbolic secant techniques proposed here yielded results that are in good agreement with earlier reports, they have been applied to characterize the (51)V chemical shift tensor of the dimer of bis(N, N-dimethylhydroxamido)-hydroxooxovanadate, {V(O)(ONMe(2))(2)}(2)O, whose chemical shift tensor has not been previously reported.

DFT calculations as a powerful technique to probe the crystal structure of Al(acac)3

(27)Al, (17)O and (13)C chemical shieldings of aluminum acetylacetonate complex, Al(acac)(3), were calculated at some Density Functional Theory (DFT) levels of theory. In these calculations the X-ray structures of its different polymorphs were used. Using these calculated data observed discrepancies between the X-ray crystallography and solid state NMR experiment were explained in terms of the quality of the NMR data. In this survey we resorted to the simulated spectra using our calculated chemical shifts. In order to confirm our conclusions, electric field gradient (EFG) tensors of the (27)Al and (17)O nuclei were calculated at the same levels of theory as used in the chemical shielding calculations. On the other hand, these calculated chemical shifts and nuclear quadrupole coupling constants (NQCCs) made a correlation between X-ray crystallography and solid state NMR experiments.

Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in solid-state NMR of spin-7/2 nuclei

We here investigate the sensitivity enhancement of central-transition NMR spectra of quadrupolar nuclei with spin-7/2 in the solid state, generated by fast amplitude-modulated RF pulse trains with constant (FAM-I) and incremented pulse durations (SW-FAM). Considerable intensity is gained for the central-transition resonance of single-quantum spectra by means of spin population transfer from the satellite transitions, both under static and magic-angle-spinning (MAS) conditions. It is also shown that incorporation of a SW-FAM train into the excitation part of a 7QMAS sequence improves the efficiency of 7Q coherence generation, resulting in improved signal-to-noise ratio. The application of FAM-type pulse trains may thus facilitate faster spectra acquisition of spin-7/2 systems.

Sensitivity enhancement of the central-transition signal of half-integer spin quadrupolar nuclei in solid-state NMR: features of multiple fast amplitude-modulated pulse transfer

Sensitivity enhancement of solid-state NMR spectrum of half-integer spin quadrupolar nuclei under both magic-angle spinning (MAS) and static cases has been demonstrated by transferring polarisation associated with satellite transitions to the central m=-1/2-->1/2 transition with suitably modulated radio-frequency pulse schemes. It has been shown that after the application of such enhancement schemes, there still remains polarisation in the satellite transitions that can be transferred to the central transition. This polarisation is available without having to wait for the spin system to return to thermal equilibrium. We demonstrate here the additional sensitivity enhancement obtained by making use of this remaining polarisation with fast amplitude-modulated (FAM) pulse schemes under both MAS and static conditions on a spin-3/2 and a spin-5/2 system. Considerable signal enhancement is obtained with the application of the multiple FAM sequence, denoted as m-FAM. We also report here some of the salient features of these multiple FAM sequences with respect to the nutation frequency of the pulses and the spinning frequency.

Solid-state 17O NMR spectroscopy of a phospholemman transmembrane domain protein: implications for the limits of detecting dilute 17O sites in biomaterials

The 17O-'diluted' glycine-14 sites in a phospholemman (PLM) transmembrane domain protein are characterized by solid-state 17O NMR spectroscopy. The PLM transmembrane domain is an alpha-helical tetramer unit of four 28-residue peptides and is rigidly embedded in a bilayer where each alpha-helix has an average tilt of 7.3 degrees against the membrane normal. The PLM sample investigated here consists of a high lipid/peptide molar ratio (25:1) with one glycine residue in each helix enriched to <40% (17)O; thus, this is a very dilute 17O-sample and is the most dilute 17O-membrane protein to date to be characterized by solid-state 17O NMR spectroscopy. Based on the spectral analysis of 17O magic angle spinning (MAS) at 14.1 and 18.8T, the PLM transmembrane domain protein consists of multiple crystallographic gly14 sites, suggesting that the tetramer protein is an asymmetric unit with either C2- or C1-rotational symmetry along the bilayer normal.

Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion

A sensitivity enhancement method based on selective adiabatic inversion of a satellite transition has been employed in a (pi/2)CT-(pi)ST1-(pi/2)CT spectral editing sequence to both enhance and resolve multisite NMR spectra of quadrupolar nuclei. In addition to a total enhancement of 2.5 times for spin 3/2 nuclei, enhancements up to 2.0 times is reported for the edited sites in a mixture of rubidium salts.

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m(I)=1/2-->m(I)=-1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The (87)Rb NMR enhancement obtained for RbClO(4) using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac)(3), the (27)Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.

Solid-State 25Mg NMR Spectroscopic and Computational Studies of Organic Compounds. Square-Pyramidal Magnesium(II) Ions in Aqua(magnesium) Phthalocyanine and Chlorophyll a

We report a solid-state (25)Mg NMR spectroscopic study of two magnesium-containing organic compounds: monopyridinated aqua(magnesium) phthalocyanine (MgPc.H(2)O.Py) and chlorophyll a (Chla). Each of these compounds contains a Mg(II) ion coordinating to four nitrogen atoms and a water molecule in a square-pyramidal geometry. Solid-state (25)Mg NMR spectra for MgPc.H(2)O.Py were obtained at 11.7 T (500 MHz for (1)H) for a (25)Mg-enriched sample (99.1% (25)Mg atom) using both Hahn-echo and quadrupole Carr-Purcell Meiboom-Gill (QCPMG) pulse sequences. Solid-state (25)Mg NMR spectra for Chla were recorded at (25)Mg natural abundance (10.1%) at 19.6 T (830 MHz for (1)H). The (25)Mg quadrupole parameters were determined from spectral analyses: MgPc.H(2)O.Py, C(Q) = 13.0 +/- 0.1 MHz and eta(Q) = 0.00 +/- 0.05; Chla, C(Q) = 12.9 +/- 0.1 MHz and eta(Q) = 1.00 +/- 0.05. This work represents the first time that Mg(II) ions in a square-pyramidal geometry have been characterized by solid-state (25)Mg NMR spectroscopy. Extensive quantum mechanical calculations for electric-field-gradient (EFG) and chemical shielding tensors were performed at restricted Hartee-Fock (RHF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) levels for both compounds. Computed (25)Mg nuclear quadrupole coupling constants at the RHF and MP2 levels show a reasonable basis-set convergence at the cc-pV5Z basis set (within 7% of the experimental value); however, B3LYP results display a drastic divergence beyond the cc-pVTZ basis set. A new crystal structure for MgPc.H(2)O.Py is also reported.

Ultrahigh-Field NMR Spectroscopy of Quadrupolar Transition Metals: 55Mn NMR of Several Solid Manganese Carbonyls

55Mn NMR spectra acquired at 21.14 T (nu(L)(55Mn) = 223.1 MHz) are presented and demonstrate the advantages of using ultrahigh magnetic fields for characterizing the chemical shift tensors of several manganese carbonyls: eta5-CpMn(CO)3, Mn2(CO)10, and (CO)5MnMPh3 (M = Ge, Sn, Pb). For the compounds investigated, the anisotropies of the manganese chemical shift tensors are less than 250 ppm except for eta5-CpMn(CO)3, which has an anisotropy of 920 ppm. At 21.14 T, one can excite the entire m(I) = 1/2 <--> m(I) = -1/2 central transition of eta5-CpMn(CO)3, which has a breadth of approximately 700 kHz. The breadth arises from second-order quadrupolar broadening due to the 55Mn quadrupolar coupling constant of 64.3 MHz, as well as the anisotropic shielding. Subtle variations in the electric field gradient tensors at the manganese are observed for crystallographically unique sites in two of the solid pentacarbonyls, resulting in measurably different C(Q) values. MQMAS experiments are able to distinguish four magnetically unique Mn sites in (CO)(5)MnPbPh3, each with slightly different values of delta(iso), C(Q), and eta(Q).

Sensitivity Enhancement and Heteronuclear Distance Measurements in Biological 17O Solid-State NMR

In this contribution we present a comprehensive approach to study hydrogen bonding in biological and biomimetic systems through 17O and 17O-1H solid-state NMR combined with density functional theory calculations of 17O and 1H NMR parameters. We explore the signal enhancement of 17O in L-tyrosine.HCl using repetitive double-frequency swept radio frequency pulses in solid-state NMR. The technique is compatible with high magnetic fields and fast magic-angle spinning of the sample. A maximum enhancement by a factor of 4.3 is obtained in the signal-to-noise ratio of the selectively excited 17O central transition in a powdered sample of 17Oeta-L-tyrosine.HCl at an external field of 14.1 T and a spinning frequency of 25 kHz. As little as 128 transients lead to meaningful 17O spectra of the same sample at an external field of 18.8 T and a spinning frequency of 50 kHz. Furthermore we employed supercycled symmetry-based pulse sequences on the protons to achieve heteronuclear longitudinal two-spin-order (IzSz) recoupling to determine 17O-1H distances. These sequences recouple the heteronuclear dipolar 17O-1H couplings, where dipolar truncation is absent, while decoupling the homonuclear proton dipolar interactions. They can be applied at fast magic-angle-spinning frequencies up and beyond 50 kHz and are very robust with respect to 17O quadrupolar couplings and both 17O and 1H chemical shift anisotropies, which makes them suitable for the use at high external magnetic fields. The method is demonstrated by determining the 17Oeta-1H distance in L-tyrosine.HCl at a spinning frequency of 50 kHz and an external field of 18.8 T.

Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in static NMR of half-integer spin quadrupolar nuclei

In solid-state NMR of quadrupolar nuclei with half-integer spin I, fast amplitude-modulated (FAM) pulse trains have been utilised to enhance the intensity of the central-transition signal, by transferring spin population from the satellite transitions. In this paper, the signal-enhancement performance of the recently introduced SW-FAM pulse train with swept modulation frequency [T. Bräuniger, K. Ramaswamy, P.K. Madhu, Enhancement of the central-transition signal in static and magic-angle-spinning NMR of quadrupolar nuclei by frequency-swept fast amplitude-modulated pulses, Chem. Phys. Lett. 383 (2004) 403-410] is explored in more detail for static spectra. It is shown that by sweeping the modulation frequencies linearly over the pulse pairs (SW1/tau-FAM), the shape of the frequency distribution is improved in comparison to the original pulse scheme (SWtau-FAM). For static spectra of 27Al (I=5/2), better signal-enhancement performance is found for the SW1/tau-FAM sequence, as demonstrated both by experiments and numerical simulations.