Theory of heteronuclear decoupling in solid-state nuclear magnetic resonance using multipole-multimode Floquet theory

A formal theory for heteronuclear decoupling in solid-state magic angle spinning (MAS) nuclear magnetic resonance experiments is presented as a first application of multipole-multimode Floquet theory. The method permits a straightforward construction of the multispin basis and describes the spin dynamics via effective Floquet Hamiltonians obtained using the van Vleck transformation method in the Floquet-Liouville space. As a test case, we consider a model three-spin system (I2S) under asynchronous time modulations (both MAS and rf irradiation) and derive effective Hamiltonians for describing the spin dynamics in the Floquet-Liouville space during heteronuclear decoupling. Furthermore, we describe and evaluate the origin of cross terms between the various anisotropic interactions and illustrate their exact contributions to the spin dynamics. The theory presented herein should be applicable to the design and understanding of pulse sequences for heteronuclear and homonuclear recoupling and decoupling.     

Description of depolarization effects in double-quantum solid state nuclear magnetic resonance experiments using multipole-multimode Floquet theory

Using an analytical model based on multipole-multimode Floquet theory (MMFT), we describe the polarization loss (or depolarization) observed in double-quantum (DQ) dipolar recoupling magic angle spinning (MAS) experiments. Specifically, the factors responsible for depolarization are analyzed in terms of higher order corrections to the spin Hamiltonian in addition to the usual phenomenological decay rate constant. From the MMFT model and the effective Hamiltonians, we elucidate the rationale behind the inclusion of a phenomenological damping term in DQ recoupling experiments. As a test of this theoretical approach, the recoupling efficiency of one class of (13)C-(13)C and (13)C-(15)N resonance width dipolar recoupling experiments are investigated at different magnetic field strengths and compared with the more exact numerical simulations. In contrast to existing analytical treatments, the role of higher order corrections is clearly explained in the context of the MMFT approach leading to a better understanding of the underlying spin physics. Furthermore, the analytical model presented herein provides a general framework for describing coherent and incoherent effects in homonuclear and heteronuclear DQ MAS recoupling experiments.     

Bimodal Floquet description of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance

A theoretical treatment of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance is presented here based on bimodal Floquet theory. The conditions necessary for good heteronuclear decoupling are derived. An analysis of a few of the decoupling schemes implemented until date is presented with regard to satisfying such decoupling conditions and efficiency of decoupling. Resonance conditions for efficient heteronuclear dipolar decoupling are derived with and without the homonuclear (1)H-(1)H dipolar couplings and their influence on heteronuclear dipolar decoupling is pointed out. The analysis points to the superior efficiency of the newly introduced swept two-pulse phase-modulation (SW(f)-TPPM) sequence. It is shown that the experimental robustness of SW(f)-TPPM as compared to the original TPPM sequence results from an adiabatic sweeping of the modulation frequencies. Based on this finding alternative strategies are compared here. The theoretical findings are corroborated by both numerical simulations and representative experiments.     

A first principles theory of nuclear magnetic resonance J-coupling in solid-state systems

A method to calculate NMR J-coupling constants from first principles in extended systems is presented. It is based on density functional theory and is formulated within a planewave-pseudopotential framework. The all-electron properties are recovered using the projector augmented wave approach. The method is validated by comparison with existing quantum chemical calculations of solution-state systems and with experimental data. The approach has also been applied to the silicophosphate, Si(5)O(PO(4))(6), giving (31)P-(29)Si-couplings which are in excellent agreement with experiment.     

Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning

Spin dynamics under magic angle spinning has been studied using different theoretical approaches and also by extensive numerical simulation programs. In this article we present a general theoretical approach that leads to analytic forms for effective Hamiltonians for an N-spin dipolar and quadrupolar coupled system under magic angle spinning (MAS) conditions, using a combination of Floquet theory and van Vleck (contact) transformation. The analytic forms presented are shown to be useful for the study of MAS spin dynamics in solids with the help of a number of simulations in two, three, and four coupled, spin-1/2 systems as well as spins in which quadrupolar interactions are also present.     

Covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy is introduced, which is a new scheme for establishing nuclear spin correlations from NMR experiments. In this method correlated spin dynamics is directly displayed in terms of a covariance matrix of a series of one-dimensional (1D) spectra. In contrast to two-dimensional (2D) Fourier transform NMR, in a covariance spectrum the spectral resolution along the indirect dimension is determined by the favorable spectral resolution obtainable along the detection dimension, thereby reducing the time-consuming sampling requirement along the indirect dimension. The covariance method neither involves a second Fourier transformation nor does it require separate phase correction or apodization along the indirect dimension. The new scheme is demonstrated for cross-relaxation (NOESY) and J-coupling based magnetization transfer (TOCSY) experiments.     

Two-photon two-color nuclear magnetic resonance

Two-photon excitation has recently been demonstrated to be a practical means of exciting nuclear magnetic resonance (NMR) signals by radio-frequency (rf) irradiation at half the normal resonance frequency. In this work, two-photon excitation is treated with average Hamiltonian theory and shown to be a consequence of higher order terms in the Magnus expansion. It is shown that the excitation condition may be satisfied not only with rf at half resonance, but also with two independent rf fields, where the two frequencies sum to or differ by the resonance frequency. The technique is demonstrated by observation of proton NMR signals at 400 MHz while simultaneously exciting at 30 and 370 MHz. Advantages of this so-called two-color excitation, such as a dramatic increase in nutation rate over half-frequency excitation, along with a variety potential applications are discussed.     

Introduction to nuclear magnetic resonance

The basic principles of nuclear magnetic resonance (NMR) are presented in an elementary form using classical and elementary quantum mechanics and the experimental technique 1s explained. The motion of the magnetization by r.f. pulses, free induction decay and spectrum, transverse and longitudinal relaxation, local field and spin echo are described and the effects of molecular motion are discussed. The concepts of spin temperature and spin diffusion are presented and the advantage of using quadrupole nuclei is stressed. Finally, the specific problems of NMR in interface studies are considered and a typical example is given.     

Shiftless nuclear magnetic resonance spectroscopy

The acquisition and analysis of high resolution one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectra without chemical shift frequencies are described. Many variations of shiftless NMR spectroscopy are feasible. A two-dimensional experiment that correlates the dipole-dipole and dipole-dipole couplings in the model peptide , (15)N labeled N-acetyl-leucine is demonstrated. In addition to the resolution of resonances from individual sites in a single crystal sample, the bond lengths and angles are characterized by the two-dimensional powder pattern obtained from a polycrystalline sample.     

Predicting 9Be nuclear magnetic resonance chemical shielding tensors utilizing density functional theory

The structures of a series of beryllium containing complexes have been optimized at the B3LYP/6-31G(d) level and their (9)Be magnetic shielding values have been determined using B3LYP/6-311G+g(2d,p) and the gauge-including atomic orbital (GIAO) method. The calculated chemical shifts are in excellent agreement with experimental values. The performance of a variety of NMR methods (SGO, IGAIM, CSGT) were also examined but were found to be inferior to the GIAO method at the chosen level of theory employed. The theoretical method has been utilized to predict the beryllium chemical shifts of structurally characterized complexes for which no measured (9)Be NMR spectrum exists, and to investigate a literature complex with an unusual (9)Be NMR chemical shift. A new standard for beryllium NMR in nonaqueous solvents has been suggested.     

A nuclear magnetic resonance study of toluene-polyisobutylene solutions. 2. Vrentas-Duda theory

The self-diffusion coefficients of toluene in polyisobutylene have been analyzed using the Vrentas-Duda free volume diffusion model. The diffusion coefficients were determined at different temperatures and concentrations, using the pulsed field gradient nuclear magnetic resonance technique. The data were satisfactorily described by the model and the size of the polymer jumping unit was extracted. Comparisons were made with the Fujita free volume theory and the Fujita free volume parameters were extracted from the Vrentas-Duda free volume parameters. From the diffusion data that now available, it can be concluded that for most polymers the jumping unit is about 1.5 times the polymer monomer molecular weight. The activation energy of the toluene diffusion in polyisobutylene is compared with the activation energies of other penetrants in the same polymer. The diffusion data presented in this work show that the energy per mole required to overcome the attractive forces which constrain a diffusing species to its neighbors should be considered to be zero, in order to be able to extract the free volume parameters (from viscosity and diffusion data) with an acceptable uncertainty. ©1995 John Wiley & Sons, Inc.     

Near neighbor approximation in nuclear magnetic resonance

A new way to deal with the excitation by multiple effective RF fields with interference is presented using the coherent averaging theory. It significantly simplifies the calculation of the effect of RF interference that occurs in the excitations by periodic pulses and phase-incremented pulses (PIPs). This approach shows that each neighboring RF field contributes to an excitation profile an offset shift, which is termed the Bloch-Siegert offset shift (BSOS). The BSOS depends not only on the strengths of both RF fields that interfere with each other but also on their relative phase between the two RF fields. Consequently, it can be positive, negative, and zero. In addition, the BSOS is also inversely proportional to the frequency separation of the two RF fields. Therefore, only a few near neighbors need to be taken into account in most cases, resulting in a near neighbor approximation (NNA). The BSOS for two multiband excitation profiles, one by a periodic pulse and the other by a PIP, are calculated using the NNA. The results are in good agreement with the computer simulated ones.     

Multinuclear solid-state nuclear magnetic resonance and density functional theory characterization of interaction tensors in taurine

A variety of experimental solid-state nuclear magnetic resonance (NMR) techniques has been used to characterize each of the elements in 2-aminoethane sulfonic acid (taurine). A combination of (15)N cross-polarization magic angle spinning (CPMAS), (14)N ultrawideline, and (14)N overtone experiments enabled a determination of the relative orientation of the nitrogen electric field gradient and chemical shift tensors. (17)O spectra recorded from an isotopically enriched taurine sample at multiple magnetic fields allowed the three nonequivalent oxygen sites to be distinguished, and NMR parameters calculated from a neutron diffraction structure using density functional theory allowed the assignment of the (17)O parameters to the correct crystallographic sites. This is the first time that a complete set of (17)O NMR tensors are reported for a sulfonate group. In combination with (1)H and (13)C MAS spectra, as well as a previously reported (33)S NMR study, this provides a very broad set of NMR data for this relatively simple organic molecule, making it a potentially useful structure on which to test DFT calculation methods (particularly for the quadrupolar nuclei (14)N, (17)O, and (33)S) or NMR crystallography approaches.     

Isotropic proton-detected local-field nuclear magnetic resonance in solids

A nuclear magnetic resonance method is presented which produces linear, isotropic proton-detected local-field spectra for INS spin systems in powdered samples. The method, heteronuclear isotropic evolution (HETIE), refocuses the anisotropic portion of the heteronuclear dipolar coupling frequencies by evolving the system under a series of specially designed Hamiltonians and evolution pathways. The theory behind HETIE is presented along with experimental studies conducted on a powdered sample of ferrocene, demonstrating the methodology outlined in this paper. Applications of HETIE for use in structure determination in the solid state are discussed.