Accessing structure and dynamics of mobile phase in organic solids by real-time T1C filter PISEMA NMR spectroscopy

The structure and dynamic behavior of mobile components play a significant role in determining properties of solid materials. Herein, we propose a novel real-time spectrum-editing method to extract signals of mobile components in organic solids on the basis of the polarization inversion spin exchange at magic angle (PISEMA) pulse sequence and the difference in (13)C T(1) values of rigid and mobile components. From the dipolar splitting spectrum sliced along the heteronuclear dipolar coupling dimension of the 2D spectrum, the structural and dynamic information can be obtained, such as the distances between atoms, the dipolar coupling strength, the order parameter of the polymer backbone chain, and so on. Furthermore, our proposed method can be used to achieve the separation of overlapped NMR signals of mobile and rigid phases in the PISEMA experiment. The high efficacy of this 2D NMR method is demonstrated on organic solids, including crystalline L-alanine, semicrystalline polyamide-6, and the natural abundant silk fibroin.     

Towards measurement of homonuclear dipolar couplings in 1H solid-state NMR: recoupling with a rotor-synchronized decoupling scheme

We describe a magic-angle spinning NMR experiment for (1)H-(1)H homonuclear dipole-dipole coupling estimations in organic solids. The methodology involves reintroducing dipolar interactions with rotor-synchronized homonuclear decoupling pulse sequences. Frequency-selective DANTE pulses are used to isolate a specific spin pair from a natural isotopic abundance sample. The coupling of interest, between the selected spin pair, may be extracted by a non linear least-squares fit of the experimentally observed modulation of the signal intensity to an exact analytical formula. The experiment is demonstrated on natural isotopic abundance glycine and alanine powder samples.     

PITANSEMA-MAS, a solid-state NMR method to measure heteronuclear dipolar couplings under MAS

A 2D NMR method is presented for the measurement of the dipole-dipole interaction between a proton and a low-frequency nuclear spin species in the solid state under the magic angle spinning. It employs the time averaged nutation concept to dramatically reduce the required radio frequency (rf) power on the low γ nuclear channel and spin exchange at the magic angle is used to suppress (1)H-(1)H dipolar interactions and chemical shifts. The flexibility in choosing the spinning speed, rf power and the scaling factor of the pulse sequence are of considerable importance for the structural studies of biological solids. The performance of the pulse sequence has been numerically and experimentally demonstrated on several solids.     

A contribution to the theory of multiple-pulse narrowing of NQR lines

A theory of the high resolution NQR spectroscopy experiments is developed in the framework of an average Hamiltonian approach analogous to that used in the theory of the NMR line pulse narrowing in solids. A specially constructed unitary operator is found making it possible to treat r. f. excitation of spin systems with nonequidistant spectra, spin and EFG asymmetry parameter being arbitrary. Time averaging is used to get an average Hamiltonian appropriate to dealing with arbitrary periodic multiple-pulse sequences. Relations between the sequence parameters are found ensuring realization of the averaging above mentioned in different cases of interest. The theoretical results obtained are consistent with available data on NQR multiple-pulse experiments.     

Relaxations Studies of 2IZSZ Spin Order with Signal Enhancement by Coherence Transfer

The pulse sequence for generating coherence transfer (or polarization transfer) is invoked to enhance the signal of heteronuclear two spin order (e.g. 2I_ZS_Z) in a spin system with CH moiety. This allows the observation of selective conversion of Zeeman order, in a sample with natural abundant ¹³C nuclei, into two spin order for measuring cross-correlation of chemical shift anisotropy and dipole-dipole interactions. The molecular reorientational correlation time and the orientation of the C–H axis with respect to the principal axes of carboxyl CSA tensor may be determined simultaneously in the relaxation profile of two spin order.     

Selective double-quantum nmr in solids

A simple method for selective double-quantum NMR in solids is described. The spin system is first prepared in a state having only dipolar, or quadrupolar, order. Selective excitation and detection of double-quantum coherence is then achieved by the 90°_x,y-t-45°_y pulse sequence.     

Application of the superposition principle to the study of a charge transfer reaction in cyclic chronopotentiometry. Part II

The general analytical expressions corresponding to the response obtained for a charge transfer process in cyclic chronopotentiometry are presented. The different geometries considered for the mass transport operator are planar, tubular and spherical. In the case of spherical electrodes (such as the dropping mercury electrode and the static mercury dropping electrode), we have analyzed the following two cases: solution soluble product and electrode soluble product or amalgamation. The solutions deduced here are independent of the method used in solving the differential equations system since we have applied the superposition principle for which we have only used the properties of the linear operators.     

Analytical block-diagonalization of matrices using unit spherical tensors

A new method for block-diagonalizing large Hamiltonian matrices, in closed form, is described. The method is based on (i) a general unitary transformation due to Slichter, and (ii) Fano's unit spherical operatorsÛ _Q ^K (I _i,I _i). The method is illustrated with a simple three spin 1/2 dipolar coupled spin system, characterized by off-block-diagonal unit spherical tensorsÛ ₀ ² (3/2,1/2,) andÛ ₀ ² (3/2,1 /2,). In addition, it is pointed out that any Hamiltonian matrix can be re-labelled in terms of fictitious spin labels, enabling a wide variety of unit spherical tensors to be used in block-diagonalization. For example, a single spin 5/2 matrix can be re-labelled using three spin labels 1/2, 1/2, and 1/2, respectively. Thus the tensor algebra required to block-diagonalize a 6 x 6 matrix is determined solely by the properties of the Pauli spin matrices. Finally, it is shown that re-labelling within the unit spherical tensor framework provides a unifying framework for standard basis operators, fictitious spin 1/2 and 1 operators, and others. The fictitious spin 1 / 2 unit spherical operators discussed in this paper differ from those of Vega and Pines.     

Z-restored spin-echo 13C 1D spectrum of straight baseline free of hump, dip and roll

A pulse sequence of z-restored spin echo, -pi-beta-tau-pi-tau-, employing a pi pulse in the middle of the delay (2tau) to form a spin echo and the two pi pulses together to restore the residual longitudinal magnetization back to + z direction, is described. (13)C spectra of organic compounds provide a wealth of structural information; however, (13)C 1D spectra acquired using reverse geometry probes can have significant baseline humps or rolls because of pulse ring-down within the coil. The baseline distortions are especially apparent in spectra acquired using cryogenically enhanced probes. The baseline problem may be alleviated by extending the delay between the last pulse and the starting point of acquisition. However, uses of long delay times introduce large negative first-order phase corrections which themselves produce baseline roll. The prescribed experiment can be used to completely remove the hump, roll or dip in the baseline of the (13)C spectrum and at the same time obtain sensitivity similar to the experiment of a single beta pulse. We believe that this experiment will be of general applications in acquiring high-quality (13)C NMR data with reverse geometry probes and spectral interpretation.     

Observation of satellite signals due to scalar coupling to spin-1/2 isotopes in solid-state nuclear magnetic resonance spectroscopy

A method is introduced to select the signal from a spin-1/2 nucleus I specifically bound to another spin-1/2 nucleus S for solid-state magic angle spinning nuclear magnetic resonance (NMR) spectroscopy via correlation through the heteronuclear J coupling. This experiment is analogous to the bilinear rotation decoupling (BIRD) sequence in liquid-state NMR spectroscopy which selects for signals from 1H directly bound to 13C. The spin dynamics of this modified BIRD experiment is described using the product-operator formalism, where experimental considerations such as rotor synchronization and the effect of large chemical shielding anisotropies on I and S are discussed. Two experiments are proposed that accommodate large chemical shielding anisotropies on S: (1) by stepping the inversion pulse frequency through the entire S spectral range or (2) by adiabatically inverting the S spins. Both these experiments are shown to successfully select the signal of 19F bound to 129Xe in XeF+ salts, removing the contributions from isotopomers containing non-spin-1/2 Xe isotopes. The feasibility in obtaining isotope-selective 19F spectra of inorganic fluoride compounds is discussed, and further modifications are proposed to expand the application to other chemical systems.     

Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms

Optimal control theory has recently been introduced to nuclear magnetic resonance (NMR) spectroscopy as a means to systematically design and optimize pulse sequences for liquid- and solid-state applications. This has so far primarily involved numerical optimization using gradient-based methods, which allow for the optimization of a large number of pulse sequence parameters in a concerted way to maximize the efficiency of transfer between given spin states or shape the nuclear spin Hamiltonian to a particular form, both within a given period of time. Using such tools, a variety of new pulse sequences with improved performance have been developed, and the NMR spin engineers have been challenged to consider alternative routes for analytical experiment design to meet similar performance. In addition, it has lead to increasing demands to the numerical procedures used in the optimization process in terms of computational speed and fast convergence. With the latter aspect in mind, here we introduce an alternative approach to numerical experiment design based on the Krotov formulation of optimal control theory. For practical reasons, the overall radio frequency power delivered to the sample should be minimized to facilitate experimental implementation and avoid excessive sample heating. The presented algorithm makes explicit use of this requirement and iteratively solves the stationary conditions making sure that the maximum of the objective is reached. It is shown that this method is faster per iteration and takes different paths within a control space than gradient-based methods. In the present work, the Krotov approach is demonstrated by the optimization of NMR and dynamic nuclear polarization experiments for various spin systems and using different constraints with respect to radio frequency and microwave power consumption.     

A triple resonance hyperfine sublevel correlation experiment for assignment of electron-nuclear double resonance lines

A new, triple resonance, pulse electron paramagnetic resonance (EPR) sequence is described. It provides spin links between forbidden electron spin transitions (DeltaM(S)=+/-1, DeltaM(I) not equal 0) and allowed nuclear spin transitions (DeltaM(I) = +/-1), thus, facilitating the assignment of nuclear frequencies to their respective electron spin manifolds and paramagnetic centers. It also yields the relative signs of the hyperfine couplings of the different nuclei. The technique is based on the combination of electron-nuclear double resonance (ENDOR) and electron-electron double resonance (ELDOR)-detected NMR experiments in a way similar to the TRIPLE experiment. The feasibility and the information content of the method are demonstrated first on a single crystal of Cu-doped L-histidine and then on a frozen solution of a Cu-histidine complex.     

Analogy between real irreducible tensor operator and molecular two-particle operator

. Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry. We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases. A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used. Received: 3 September 1996 / Accepted: 19 December 1996     

Rapid measurement of three-dimensional diffusion tensor

In this article, the authors demonstrate a rapid NMR method to measure a full three-dimensional diffusion tensor. This method is based on a multiple modulation multiple echo sequence and utilizes static and pulsed magnetic field gradients to measure diffusion along multiple directions simultaneously. The pulse sequence was optimized using a well-known linear inversion metric (condition number) and successfully tested on both isotropic (water) and anisotropic (asparagus) diffusion systems.     

Incompletely symmetric non-bloch electron states in perfect cubic crystals. III. Density of dynamical observables in the FCC lattice

The operators of dynamical observables of the crystal electron (velocity vector components. reciprocal mass tensor components and their functions) commute with the energy operator; hence, the averages of these observables can be adequately approximated by the eigenfunctions for the energy operator. Calculations of the averages were based on the LCAO eigenfunctions classified according to incompletely symmetric irreducible representations of the point group of the cubic crystal, and a similar classification was made for the averages.     

“Basis” lie algebra of electronic fock space: Application to evaluation of matrix elements of spin tensor operators

A new set of generators of the operator algebra over the electronic Fock space is introduced. It is shown that with this set of generators the “basis” Lie algebra can be associated and that the operator algebra of the Fock space is the homomorphic image of the corresponding universal enveloping algebra. The algebraic structure revealed is used for deriving the reduction formulas for the elements of the simplest spin tensor operators between the Gelfand states.     

Frequency selective heteronuclear dipolar recoupling in rotating solids: accurate (13)C-(15)N distance measurements in uniformly (13)C,(15)N-labeled peptides

We describe a magic-angle spinning NMR experiment for selective (13)C-(15)N distance measurements in uniformly (13)C,(15)N-labeled solids, where multiple (13)C-(15)N and (13)C-(13)C interactions complicate the accurate measurement of structurally interesting, weak (13)C-(15)N dipolar couplings. The new experiment, termed FSR (frequency selective REDOR), combines the REDOR pulse sequence with a frequency selective spin-echo to recouple a single (13)C-(15)N dipolar interaction in a multiple spin system. Concurrently the remaining (13)C-(15)N dipolar couplings and all (13)C-(13)C scalar couplings to the selected (13)C are suppressed. The (13)C-(15)N coupling of interest is extracted by a least-squares fit of the experimentally observed modulation of the (13)C spin-echo intensity to the analytical expression describing the dipolar dephasing in an isolated heteronuclear spin pair under conventional REDOR. The experiment is demonstrated in three uniformly (13)C,(15)N-labeled model systems: asparagine, N-acetyl-L-Val-L-Leu and N-formyl-L-Met-L-Leu-L-Phe; in N-formyl-[U-(13)C,(15)N]L-Met-L-Leu-L-Phe we have determined a total of 16 internuclear distances in the 2.5-6 A range.     

Disentangling diffusion information of individual components in a mixture with a 3D COMPACT‐IDOSY NMR experiment

A new 3D diffusion‐ordered heteronuclear NMR experiment COMPACT‐IDOSY (cross‐polarization optimized multisite polarized accelerated time internally encoded diffusion ordered spectroscopy) has been designed and experimentally implemented on a mixture of flavonoids rutin and quercetin. The pulse sequence uses a cross‐polarization mixing period and diffusion encoding gradients internally incorporated into the coherence transfer interval of a long‐range heteronuclear correlation experiment. Substantial reduction in experimental time, good sensitivity and excellent resolution of signal overlap lead to the accurate determination of translational diffusion coefficients of individual components in the mixture. Copyright © 2012 John Wiley & Sons, Ltd.     

Broadband inversion for MAS NMR with single-sideband-selective adiabatic pulses

We explain how and under which conditions it is possible to obtain an efficient inversion of an entire sideband family of several hundred kHz using low-power, sideband-selective adiabatic pulses, and we illustrate with some experimental results how this framework opens new avenues in solid-state NMR for manipulating spin systems with wide spinning-sideband (SSB) manifolds. This is achieved through the definition of the criteria of phase and amplitude modulation for designing an adiabatic inversion pulse for rotating solids. In turn, this is based on a framework for representing the Hamiltonian of the spin system in an NMR experiment under magic angle spinning (MAS). Following earlier ideas from Caravatti et al. [J. Magn. Reson. 55, 88 (1983)], the so-called "jolting frame" is used, which is the interaction frame of the anisotropic interaction giving rise to the SSB manifold. In the jolting frame, the shift modulation affecting the nuclear spin is removed, while the Hamiltonian corresponding to the RF field is frequency modulated and acquires a spinning-sideband pattern, specific for each crystallite orientation.