Publications

In this study, we perform quantum calculations of the spin dynamics of a small spin system that includes nine coupled electrons and one nucleus placed in an external magnetic field and exposed to microwave irradiation. This is an extension of a previous work in which we have demonstrated on a system of 11 coupled electron spins the dynamics of the electron polarizations composing the electron paramagnetic resonance (EPR) line during static dynamic nuclear polarization (DNP) experiments. There we have shown that the electron polarizations are determined by a spectral diffusion process, induced by the dipolar interaction and cross-relaxation. Additionally, we showed that a distinction had to be made between strong and weak dipolar-coupled systems relative to the inhomogeneity of the EPR line with only the first behaving according to the thermal mixing DNP (with two electron spin temperatures) description. The EPR spectra in the weak and strong dipolar interaction cases show different types of spectral features. In the extended spin system, we again make a distinction between weak and strong electron electron interactions and show that the DNP spectra for the two cases are different in nature but that the DNP spectra can be derived in all cases from the EPR line shapes using the indirect cross effect.

Here, we present an integrated experimental and theoretical study of ¹H dynamic nuclear polarization (DNP) of a frozen aqueous glass containing free radicals at 7 T, under static conditions and at temperatures ranging between 4 and 20 K. The DNP studies were performed with a home-built 200 GHz quasi-optics microwave bridge, powered by a tunable solid-state diode source. DNP using monochromatic and continuous wave (cw) irradiation applied to the electron paramagnetic resonance (EPR) spectrum of the radicals induces the transfer of polarization from the electron spins to the surrounding nuclei of the solvent and solutes in the frozen aqueous glass. In our systematic experimental study, the DNP enhanced ¹H signals are monitored as a function of microwave frequency, microwave power, radical concentration, and temperature, and are interpreted with the help of electron spin-lattice relaxation times, experimental MW irradiation parameters, and the electron spectral diffusion (eSD) model introduced previously. This comprehensive experimental DNP study with mono-nitroxide radical spin probes was accompanied with theoretical calculations. Our results consistently demonstrate that eSD effects can be significant at 7 T under static DNP conditions, and can be systematically modulated by experimental conditions.

We present a bimodal Floquet analysis of the recently introduced refocused continuous wave (rCW) solid-state NMR heteronuclear dipolar decoupling method and compare it with the similar looking X-inverse X (XiX) scheme. The description is formulated in the rf interaction frame and is valid for both finite and ideal pi pulse rCW irradiation that forms the refocusing element in the rCW scheme. The effective heteronuclear dipolar coupling Hamiltonian up to first order is described. The analysis delineates the difference between the two sequences to different orders of their Hamiltonians for both diagonal and off-diagonal parts. All the resonance conditions observed in experiments and simulations have been characterised and their influence on residual line broadening is highlighted. The theoretical comparison substantiates the numerical simulations and experimental results to a large extent. (C) 2016 Elsevier Inc. All rights reserved.

Gd(iii) complexes have emerged as spin labels for distance determination in biomolecules through double-electron-electron resonance (DEER) measurements at high fields. For data analysis, the standard approach developed for a pair of weakly coupled spins with S = 1/2 was applied, ignoring the actual properties of Gd(iii) ions, i.e. S = 7/2 and ZFS (zero field splitting) ≠ 0. The present study reports on a careful investigation on the consequences of this approach, together with the range of distances accessible by DEER with Gd(iii) complexes as spin labels. The experiments were performed on a series of specifically designed and synthesized Gd-rulers (Gd-PyMTA-spacer-Gd-PyMTA) covering Gd-Gd distances of 2-8 nm. These were dissolved in D₂O-glycerol-d₈ (0.03-0.10 mM solutions) which is the solvent used for the corresponding experiments on biomolecules. Q- and W-band DEER measurements, followed by data analysis using the standard data analysis approach, used for S = 1/2 pairs gave the distance-distribution curves, of which the absolute maxima agreed very well with the expected distances. However, in the case of the short distances of 2.1 and 2.9 nm, the distance distributions revealed additional peaks. These are a consequence of neglecting the pseudo-secular term in the dipolar Hamiltonian during the data analysis, as is outlined in a theoretical treatment. At distances of 3.4 nm and above, disregarding the pseudo-secular term leads to a broadening of a maximum of 0.4 nm of the distance-distribution curves at half height. Overall, the distances of up to 8.3 nm were determined, and the long evolution time of 16 μs at 10 K indicates that a distance of up to 9.4 nm can be accessed. A large distribution of the ZFS parameter, D, as is found for most Gd(iii) complexes in a frozen solution, is crucial for the application of Gd(iii) complexes as spin labels for distance determination via Gd(iii)-Gd(iii) DEER, especially for short distances. The larger ZFS of Gd-PyMTA, in comparison to that of Gd-DOTA, makes Gd-PyMTA a better label for short distances.

Over the last two decades solid state Nuclear Magnetic Resonance has witnessed a breakthrough in increasing the nuclear polarization, and thus experimental sensitivity, with the advent of Magic Angle Spinning Dynamic Nuclear Polarization (MAS-DNP). To enhance the nuclear polarization of protons, exogenous nitroxide biradicals such as TOTAPOL or AMUPOL are routinely used. Their efficiency is usually assessed as the ratio between the NMR signal intensity in the presence and the absence of microwave irradiation ε_on/off. While TOTAPOL delivers an enhancement ε_on/off of about 60 on a model sample, the more recent AMUPOL is more efficient: >200 at 100 K. Such a comparison is valid as long as the signal measured in the absence of microwaves is merely the Boltzmann polarization and is not affected by the spinning of the sample. However, recent MAS-DNP studies at 25 K by Thurber and Tycko (2014) have demonstrated that the presence of nitroxide biradicals combined with sample spinning can lead to a depolarized nuclear state, below the Boltzmann polarization. In this work we demonstrate that TOTAPOL and AMUPOL both lead to observable depolarization at ≈110 K, and that the magnitude of this depolarization is radical dependent. Compared to the static sample, TOTAPOL and AMUPOL lead, respectively, to nuclear polarization losses of up to 20% and 60% at a 10 kHz MAS frequency, while Trityl OX63 does not depolarize at all. This experimental work is analyzed using a theoretical model that explains how the depolarization process works under MAS and gives new insights into the DNP mechanism and into the spin parameters, which are relevant for the efficiency of a biradical. In light of these results, the outstanding performance of AMUPOL must be revised and we propose a new method to assess the polarization gain for future radicals.

Dynamic Nuclear Polarization (DNP) experiments on solid dielectrics can be described in terms of the Solid Effect (SE) and Cross Effect (CE) mechanisms. These mechanisms are best understood by following the spin dynamics in electron-nuclear and electron-electron-nuclear model systems, respectively. Recently it was shown that the frequency swept DNP enhancement profiles can be reconstructed by combining basic SE and CE DNP spectra. However, this analysis did not take into account the role of the electron spectral diffusion (eSD), which can result in a dramatic loss of electron polarization along the EPR line. In this paper we extend the analysis of DNP spectra by including the influence of the eSD process on the enhancement profiles. We show for an electron-electron-nuclear model system that the change in nuclear polarization can be caused by direct MW irradiation on the CE electron transitions, resulting in a direct CE (dCE) enhancement, or by the influence of the eSD process on the spin system, resulting in nuclear enhancements via a process we term the indirect CE (iCE). We next derive the dependence of the basic SE, dCE, and iCE DNP spectra on the electron polarization distribution along the EPR line and on the MW irradiation frequency. The electron polarization can be obtained from ELDOR experiments, using a recent model which describes its temporal evolution in real samples. Finally, DNP and ELDOR spectra, recorded for a 40 mM TEMPOL sample at 10-40 K, are analyzed. It is shown that the iCE is the major mechanism responsible for the bulk nuclear enhancement at all temperatures.

The microwave frequency swept DNP enhancement, referred to as the DNP spectrum, is strongly dependent on the EPR spectrum of the polarizing radical and it reveals the underlying DNP mechanisms. Here we focus on two chlorinated trityl radicals that feature axially symmetric powder patterns at 95 GHz, the width of which are narrower than those of TEMPOL or TOTAPOL but broader than that of the trityl derivative OX63. The static DNP lineshapes of these commonly used radicals in DNP, have been recently analyzed in terms of a superposition of basic Solid Effect (SE) and Cross Effect (CE)-DNP lineshapes, with their relative contributions as a fit parameter. To substantiate the generality of this approach and further investigate an earlier suggestion that a ^35,37Cl-¹³C polarization transfer pathway, termed \u201chetero-nuclear assisted DNP\u201d, may be in effect in the chlorinated radicals (C. Gabellieri et al., Angew. Chem., Int. Ed., 2010, 49, 3360-3362), we measured the static ¹³C-glycerol DNP spectra of solutions of ca.∼10 mM of the two chlorinated trityl radicals as a function of temperature (10-50 K) and microwave power. Analysis of the DNP lineshapes was first done in terms of the SE/CE superposition model calculated assuming a direct e-¹³C polarization transfer. The CE was found to prevail at the high temperature range (40-50 K), whereas at the low temperature end (10-20 K) the SE dominates, as was observed earlier for ¹³C DNP with OX63 and ¹H DNP with TEMPOL and TOTAPOL, thus indicating that this is rather general behavior. Furthermore, it was found that at low temperatures it is possible to suppress the SE, and increase the CE by merely lowering the microwave power. While this analysis gave a good agreement between experimental and calculated lineshapes when the CE dominates, some significant discrepancies were observed at low temperatures, where the SE dominates. We show that by explicitly taking into account the presence of ^35/37Cl nuclei through a e-^35,37Cl-¹³C polarization pathway in the SE-DNP lineshape calculations, as proposed earlier, we can improve the fit significantly, thus supporting the existence of the \u201chetero-nuclear assisted DNP\u201d pathway.

To study the solid state ¹H-DNP mechanism of the biradical TOTAPOL under static conditions the frequency swept DNP enhancement spectra of samples containing 20 mM and 5 mM TOTAPOL were measured as a function of MW irradiation time and temperature. We observed that under static DNP conditions the biradical TOTAPOL behaves similar to the monoradical TEMPOL, in contrast to MAS DNP where TOTAPOL is considerably more effective. As previously done for TEMPOL, the TOTAPOL DNP spectra were analyzed taking a superposition of a basic SE-DNP lineshape and a basic CE-DNP lineshape with different amplitudes. The analysis of the steady state DNP spectra showed that the SE was dominant in the 6-10 K range and the CE was dominant above 10 K. DNP spectra obtained as a function of MW irradiation time allowed resolving the individual SE and CE buildup times. At low temperatures the SE buildup time was faster than the CE buildup time and at all temperatures the CE buildup time was close to the nuclear spin-lattice relaxation time, T_1n. Polarization calculations involving nuclear spin-diffusion for a model system of one electron and many nuclei suggested that the shortening of the T_1n for increasing temperatures is the reason why the SE contribution to the overall enhancement was reduced.

Deuterium (²H) magic angle spinning (MAS) NMR has been employed to monitor the restricted mobility of a molecule grafted at the inner surface of mesoporous SBA-15. The grafted linear moiety (O₃Si-CH ₂-CH₂-C(O)-N(H)-CD₂-CD₂-NH ₂) has two deuterated methylene groups toward the end terminus of the chain. A series of ²H-MAS (at 6 and 9 kHz) spectra of the grafted molecule at room temperature were recorded and decomposed into spectra with different quadrupolar tensor components {C_Q, η} to illustrate the mobility of the chain as function of the humidity. At very low water contents the MAS spectra resemble a static CD₂ spectrum. At high water concentrations the spectrum with the large symmetric quadrupolar tensor of CD₂ decomposes into two spectra, one with an asymmetric tensor and the other with a significantly smaller tensor depicting substantial mobility. Molecular dynamic (MD) simulations were employed to support the experimental data. The results from these MD studies show the possible binding of the molecule with silanol groups on the silica surface of SBA-15 through C(O)⋯HO, N(H)⋯OH, or NH₂⋯OH hydrogen bonding. Insights obtained from these MD calculations toward molecular mobility induced by single water molecules are discussed.

Dynamic nuclear polarization is a method which allows for a dramatic increase of the NMR signals due to polarization transfer between electrons and their neighboring nuclei, via microwave irradiation. These experiments have become popular in recent years due to the ability to create hyper-polarized chemically and biologically relevant molecules, in frozen glass forming mixtures containing free radicals. Three mechanisms have been proposed for the polarization transfer between electrons and their surrounding nuclei in such non-conducting samples: the solid effect and cross effect mechanisms, which are based on quantum mechanics and relaxation on small spin systems, and thermal mixing, which originates from the thermodynamic macroscopic notion of spin temperature. We have recently introduced a spin model, which is based on the density matrix formalism and includes relaxation, and applied it to study the solid effect and cross effect mechanisms on small spin systems. In this publication we use the same model to describe the thermal mixing mechanism, and the creation of spin temperature. This is obtained without relying on the spin temperature formalism. Simulations of small model systems are used on systems with homogeneously and inhomogeneously broadened EPR lines. For the case of a homogeneously broadened line we show that the nuclear enhancement results from the thermal mixing and solid effect mechanisms, and that spin temperatures are created in the system. In the inhomogeneous case the enhancements are attributed to the solid effect and cross effect mechanisms, but not thermal mixing.

Deuterium magic angle spinning (MAS) NMR is used to study the dynamics of an organic molecule, N-[triethoxysilylpropyl]acetamide-d₃, grafted at the inner surface of the mesoporous silica material, MCM-41. The grafted molecule has a deuterated methyl group at its free terminus to monitor its local mobility through changes in its dynamic ²H-MAS NMR spectrum. Different spectra were recorded as a function of temperature from two different water containing samples. Observation shows that a major part of the grafted molecule remains static, irrespective of the temperature and hydration state of the sample, whereas the rest shows spectral changes indicative of a two-site jump motion of the methyl groups. Experimental observations were substantiated using molecular dynamic (MD) simulations of the grafted molecule. Subsequently, the MD results corroborate a model for the grafted molecules experiencing an exchange between two conformations consistent with the analysis of the ²H-MAS NMR spectra.

Proton Dynamic Nuclear Polarization (DNP) experiments were conducted on a 3.4 T homebuilt hybrid pulsed-EPR-NMR spectrometer, on static samples containing 10 mM or 40 mM TEMPOL in frozen glassy solutions of DMSO/water. During DNP experiments proton-NMR signals are enhanced with the help of microwave (MW) irradiation on or close to the Electron Paramagnetic Resonance (EPR) spectrum of the free radicals in the sample, transferring polarization from the free electrons to the nuclei. In the solid state a distinction is made between three DNP enhancement mechanisms: the Solid Effect (SE), the Cross Effect (CE) and Thermal Mixing (TM). In an effort to determine the dominant DNP mechanisms responsible for the enhancement of the nuclear signals, electron and nuclear spin-lattice relaxation rates, enhancement buildup times and microwave (MW) swept DNP spectra were measured as a function of temperature and MW irradiation strength. We observed lineshape variations of the DNP spectra that indicated changes in the relative contributions of SE-DNP and CE-DNP with temperature and MW power. Using a theoretical model describing the SE-DNP and CE-DNP the DNP spectra could be analyzed without involving the TM-DNP mechanism and the relative SE-DNP and CE-DNP contributions to the nuclear enhancement could be determined. From this analysis it follows that lowering the temperature beyond 20 K increases the SE-DNP and decreases the CE-DNP contributions. Possible explanations for this behavior are suggested.

We present a Floquet theory approach for the analysis of homonuclear recoupling assisted by radio frequency (RF) irradiation of surrounding heteronuclear spins. This description covers a broad range of systems from fully protonated to deuterated proteins, focusing in detail on recoupling via protons and deuterons separately as well as simultaneously by the double nucleus enhanced recoupling (DONER) scheme. The theoretical description, supported by numerical simulations and compared to experimental results from a partially deuterated model compound, indicates that in perdeuterated systems setting the RF amplitude equal to the magic angle spinning (MAS) frequency is not necessarily optimal for recoupling via ¹H and/or ²H nuclei and modified recoupling conditions are identified.

The application of Floquet theory in solid-state nuclear magnetic resonance is discussed. The Floquet approach has been used in the study of various effects related to quadrupolar nuclei varying from the basic magic-angle spinning (MAS) Hamiltonian, rotational resonance, and rotary-resonance conditions to the effect of quadrupole nuclei on spin 1/2 coupled to them. An extension of Floquet theory, multimode-multipole Floquet theory (MMFT), in which a multipole operator basis has been used is applied to the analysis of heteronuclear decoupling, the calculation of the R² condition width, and depolarization effects in double-quantum recoupling experiments. Cross polarization (CP) is one of the most important techniques for the detection of rare spins in solid-state nuclear magnetic resonance (NMR). MAS leads to improvement in the spectral resolution making the various sites distinguishable and improving the signal to noise ratio but it complicates the analysis of the spectra resulting from dynamic processes.

Magnetic susceptibility measurements of WO ₃ crystals hydrogen doped on the surface suggest 2D local non-percolated superconductivity with an onset temperature of 120 K. Observed zero field cooled vs. field cooled magnetization response is characteristic of type II superconductivity. The diamagnetic response at the critical temperature is field dependent, and is suppressed by a magnetic field of ∼1700 Oe.

We present a rf scheme designed to excite triple quantum (TQ) coherences for proton solid state NMR. This recoupling scheme is based on the phase modulated Lee Goldburg sequence combined with echo pulses and applied nonsynchronous with the magic angle spinning period. Based on the effective bimodal Floquet Hamiltonian we optimize the conditions for TQ coherence excitation. Numerical simulations are used to further adjust the recoupling conditions as well as define the sequence limitations. Experimental TQ filtered one-dimensional spectra and two-dimensional correlations of TQ to single quantum coherences are presented for standard amino acids. These results are compared with the crystal structures showing that this scheme can aid in resonance assignments and in resolving local spin topologies.

The elimination by HF of the silica matrix from the composites obtained by the two-step reaction deposition of Cs_xH_3-xPW₁₂O₄₀ (CsHPW) salt nanocrystals with a Cs/W₁₂ ratio equal 2.5 on SBA-15 yields materials with substantially lower Cs/W₁₂ ratios of 1.7-2.0. The value of the Cs/W₁₂ ratio in the nanocasts is determined by the Cs-precursor (Cs n-propoxide or Cs-acetate) used at the first stage of materials preparation. The surface area of the CsHPW nanocasts is 41-45 times higher than their co-precipitated analogs at the same Cs/W₁₂ ratios. We report here that implementation of the nanocasting preparation technique yields for the first time a bulk CsHPW material that combines a high concentration of acid sites (Cs/W₁₂ = 1.7-2.0) with a high surface area of 41-93 m² g^-1. Co-precipitated analogues at the same Cs/W₁₂ ratios are nonporous and exhibit a surface area smaller than 5 m² g^-1. Our nanocasted CsHPW materials are stable against leaching and colloidization in polar solvents, and their catalytic performance exceeded that of bulk Cs_2.5H_0.5PW₁₂O₄₀, known as the most active among the acidic HPW salts. The catalytic activity of CsHPW nanocasts in MTBE synthesis and in the isopropanol dehydration reactions is shown to be higher by a factor of 2-3 than that of the standard Cs_2.5H_0.5PW₁₂O₄₀ material.

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 H1 - H1 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 (SWf -TPPM) sequence. It is shown that the experimental robustness of SWf -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.

The effects of grafting the alumina species at the surface of silica support on the H₃PW₁₂O₄₀ (HPW) immobilization capacity and performance of loaded HPW in acid-catalyzed reactions were studied with regular silica-gel and ordered mesostructured silica SBA-15. The states of alumina and HPW, in terms of the acidity/basicity, material texture, and structure of adsorbed HPW species, were characterized by XRD, XPS, NH ₃-TPD, UV-vis-, and FTIR-spectroscopy, as well as ¹H and ³¹P MAS NMR, NH₃- and CO₂-TPD, and N ₂ adsorption. It was demonstrated that grafting of silica with small alumina clusters at partial to full surface coverage produces isolated basic sites of the same strength as at the surface of pure alumina, but with a surface concentration that is an order of magnitude lower. These sites anchor the molecular species of HPW, retaining their polyanion structure and acidity-catalytic activity patterns in several acid-catalyzed reactions. The reason for the low activity of HPW moieties immobilized at the surface of pure alumina is a polydentate adsorption of polyanions yielding a high extent of HPW acidity neutralization. The use of mesostructured SBA-15 as a support yielded catalysts with 30-70% higher activity compared with that based on regular silica gel. This is a result of higher surface area and surface concentration of silanols in SBA-15, which makes it possible to immobilize more HPW as molecular species.

We here report on a high-resolution pulse scheme for double-quantum (DQ) proton NMR spectroscopy in the solid-state. The pulse scheme employs a combination of multiple-pulses and magic-angle spinning (MAS) for both the excitation and conversion of DQ coherences and their evolution under homonuclear dipolar decoupling. This is made possible in this two-dimensional experiment by an effective combination of homonuclear dipolar decoupling method of phase modulated Lee-Goldburg and symmetry adapted sequence for homonuclear dipolar recoupling under MAS. DQ spectra of monoethyl fumaric acid, glycine, and histidine are presented to highlight the utility of the pulse scheme together with some of the existing drawbacks.

The multispin dynamics occurring during LG-CP experiments were addressed. It was shown that the behavior of the carbon signals is a manifestation of the coherent nature of the polarization transfer processes during the LG-CP process. The coherent effects manifest themselves in the dependence of the oscillation frequencies and the levelling-off values on the dipolar couplings.

Recovery of the magnetic dipolar interaction between nuclei bearing the same gyromagnetic ratio in rotating solids can be promoted by synchronous rf irradiation. Determination of the dipolar interaction strength can serve as a tool for structural elucidation in polycrystalline powders. Spinning frequency dependent narrow-band (nb) RFDR and SEDRA experiments are utilized as simple techniques for the determination of dipolar interactions between the nuclei in coupled homonuclear spin pairs. The magnetization exchange and coherence dephasing due to a fixed number of rotor-synchronously applied π-pulses is monitored at spinning frequencies in the vicinity of the rotational resonance (R²) conditions. The powder nbRFDR and nbSEDRA decay curves of spin magnetizations and coherences, respectively, as a function of the spinning frequency can be measured and analyzed using simple rate equations providing a quantitative measure of the dipolar coupling. The effects of the phenomenological relaxation parameters in these rate equations are discussed and an improved methodology is suggested for analyzing nbRFDR data for small dipolar couplings. The distance between the labeled nuclei in the 1,3-¹³C₂-hydroxybutyric acid molecule is rederived using existing nbRFDR results and the new simulation procedure. A nbSEDRA experiment has been performed successfully on a powder sample of singly labeled 1-¹³C-L-leucine measuring the dipolar interaction between the labeled carboxyl carbon and the natural abundant β-carbon. Both narrowband techniques are employed for the determination of the nuclear distances between the side-chain carbons of leucine and its carbonyl carbon in a tripeptide Leu-Gly-Phe that is singly ¹³C-labeled at the leucine carbonyl carbon position.

We present a method for the synthesis of CdS and CdS_xSe_1-x nanocrystals by precipitation from a solution of cadmium carboxylate in dimethyl sulfoxide (DMSO) with or without elemental S (Se). The reaction in the presence of hydrazine has also been investigated. The CdS particle size, determined by X-ray diffraction, varied between 2 and 7 nm, depending on the reaction conditions. The CdS_xSe_1-x crystal size varied between 5 and 10 nm. UV spectra of the particles showed an increase of the optical band gap as the size of the crystals decreased. The surface structure of the CdS nanocrystals was characterized by IR and NMR spectroscopy. The spectra of CdS particles prepared with cadmium acetate and sulfur showed four types of binding sites at the crystallite surfaces: oxidized sulfur, acetate adsorbed to the surface cadmium in a bridging complex, oxygen-bound DMSO, and hydroxyl ions.

Dipolar recoupling techniques of homonuclear spin pairs are commonly used for distance or orientation measurements in solids. Accurate measurements are interfered with by broadening mechanisms. In this publication narrowband RF-driven dipolar recoupling magnetization exchange experiments are performed as a function of the spinning frequency to reduce the effect of zero-quantum T₂ relaxation. To enhance the exchange of magnetization between the coupled spins, a fixed number of rotor-synchronous π-pulses are applied at spinning frequencies approaching the rotational resonance (R²) conditions. The analysis of the powder averaged dipolar decay curves of the spin magnetizations as a function of the spinning frequency provides a quantitative measure of the dipolar coupling. An effective Hamiltonian for this experiment is derived, taking into account all chemical shift parameters of the spins. The length of the nbRFDR mixing time and the number of rotor cycles per π-pulse are optimized by numerical simulations for sensitive probing of the dipolar coupling strength. The zero-quantum T₂ relaxation time can easily be taken into account in the data analysis, because the overall exchange time is almost constant in these experiments. Spinning-frequency-depen-dent nbRFDR experiments near the m = 1 and m = 2 R² condition are shown for doubly ¹³C-labeled hydroxybutyric acid.

A two-dimensional (2D) experiment that correlates electron-nuclear double resonance (ENDOR) and electron spin-echo envelope modulation (ESEEM) frequencies, useful for unraveling and assigning ENDOR and ESEEM spectra from different paramagnetic centers with overlapping EPR spectra, is presented. The pulse sequence employed is similar to the Davies ENDOR experiment with the exception that the two-pulse echo detection is replaced by a stimulated echo detection in order to enhance the resolution in the ESEEM dimension. The two-dimensional data set is acquired by measuring the ENDOR spectrum as a function of the time interval T between the last two microwave pulses of the stimulated echo detection scheme. This produces a series of ENDOR spectra with amplitudes that are modulated with T. Fourier transformation (FT) with respect to T then generates a 2D spectrum with cross peaks connecting spectral lines of the ESEEM and ENDOR spectra that belong to the same paramagnetic center. Projections along the vertical and horizontal axes give the three-pulse FT-ESEEM and ENDOR spectra, respectively. The feasibility of the experiment was tested by simulating 2D ENDOR-ESEEM correlation spectra of a system consisting of an electron spin (S = 1/2) coupled to two nuclei (I₁ = I₂ = 1/2), taking into account / experimental conditions such as pulse durations and off-resonance irradiation frequencies. The experiment is demonstrated on a single crystal of Cu²⁺ doped L-histidine (Cu-His), containing two symmetrically related Cu²⁺ sites that at an arbitrary orientation exhibit overlapping ESEEM and ENDOR spectra. While the ESEEM spectrum is relatively simple and arises primarily from one weakly coupled ¹⁴N, the ENDOR spectrum is very crowded due to contributions from two nonequivalent nitrogens, two chlorides, and a relatively large number of protons. The simple ESEEM projection of the 2D ENDOR-ESEEM correlation spectrum is then used to disentangle the ENDOR spectrum and resolve two sets of lines corresponding to the different sites.

Nanoparticles of the diluted magnetic semiconductor Cd_0.991Co_0.009S, with diameters D between 3.5 and 29.5 nm, were studied by ¹¹³Cd NMR spectroscopy. Two spectral features could be discerned: (1) a strong line corresponding to cadmium atoms that are removed more than four bonds from cobalt ions and (2) a set of shifted lines resulting from transferred hyperfine (THF) interactions between the d-electrons of Co²⁺ and its next nearest (2N) neighboring cadmium atoms. Significant changes in the ¹¹³Cd spectrum were observed as a function of the size of the nanoparticles. More specifically, these changes were attributed to a structural zinc blende-to-wurtzite phase transition that occurs around D = 8 nm. The frequency spread and the fine structure of the spectra indicate that most of the Co²⁺ impurities in the crystals are located at the positions of cadmium sites. These paramagnetic ions are distributed homogeneously in the samples and the transferred hyperfine interactions between the d-electrons of cobalt and the 2N ¹¹³Cd nuclei are of the same order of magnitude as in bulk samples. Inhomogeneous broadening of the lines in the spectra can be attributed to possible distortions of the electronic polarization pathways because of surface and local disorder effects in the nanocrystals.

A new type of fast amplitude modulated pulse scheme is presented here that yields a significant sensitivity enhancement in the triple-quantum magic angle spinning NMR spectrum of a spin-5/2 nucleus. Enhancement is achieved by fast phase alternation of the triple to single-quantum conversion pulse, which transfers triple to single-quantum coherence in a direct, non-adiabatic manner. The success of this pulse relies on the difference between the quadrupolar frequency and the intensity of the rf irradiation field, during its short segments. Numerical optimizations and experimental results are presented showing the improved performance.

CdS nanoparticles precipitated from aqueous solution were studied by ¹H NMR. The nanoparticles were deliberately not capped by any surface termination agent. The samples had porous structure. Proton high spinning speed magic angle spinning (MAS) NMR spectra revealed that there are three abundant proton species in nanoparticle samples prepared with an excess of Cd, having different chemical shifts: a relatively narrow peak due to hydroxyl groups and two broader lines resulting from adsorbed water molecules with different chemical environments. The relative intensities of the lines were temperature-dependent, reflecting a complicated chemical equilibration processes. A small fraction of water molecules (∼5%) experiences anisotropic dynamic motion as deduced from the analysis of the dipolar sideband patterns. The main part of the spectrum was due to rapidly exchanging protons. The exchange between protons of the same type occurs on a time scale not much longer than 1 μs. The exchange between different lines was studied by 2D exchange MAS spectroscopy. The analysis of the proton-proton correlation spectra as a function of the mixing time led us to the conclusion that the nanocrystalline surface is covered by clusters of water. The clusters are well separated from each other and are formed by protons occupying sites with the same chemical environment. The size of the pores was also estimated to be of the order of a few nanometers.

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 ²³Na and ⁸⁷Rb nuclei as examples are presented that corroborate the usefulness of this approach.

Diluted magnetic semiconductor samples Cd_0.99Fe_0.01S and Cd_0.994Co_0.006S were investigated by ¹¹³Cd magic angle spinning NMR spectroscopy in the temperature range of 180400 K. These alloys were prepared by mixing Cd_0.97M_0.03S (M=Co, Fe) and the binary compound CdS in the appropriate molar ratios and maintaining the mixtures at about 1000 °C for seven days. The macroscopic homogeneity of the samples was determined by energy dispersive spectroscopy. The microscopic homogeneity of the paramagnetic ion distribution in these samples can be studied by analyzing their ¹¹³Cd NMR spectra. These spectra contain a set of Cd* bands (the* sign indicates the observed cadmium atoms) that are shifted by the transferred hyperfine (THF) interaction between the cadmium nuclei and their neighboring paramagnetic ions. Using the temperature dependence of the positions, the relaxation times, and anisotropies of these bands, we assigned each band to a well-defined next-nearest neighbor M(2)−S−Cd(1)−S−Cd* conformation, and correlated the THF interaction constants of all conformations to the M(2)−Cd* distances. All cadmium bands in the spectra comprise a set of lines that correspond to Cd* atoms in conformations of the type M(3)−S−Cd(2)−S−Cd(1)−Cd*−S−Cd(1)−S−M(2). The relative intensities of the lines can be calculated for given x values, when we assume a random magnetic ion impurity distribution. For the Cd_0.994Co_0.006S sample, we found that the calculated line intensities were not consistent with the experimental intensities. To explain this deviation and to simulate a spectrum that fits the experimental data, we assumed that this sample consists of clusters with different concentrations of the impurity. Good agreement was obtained when about half of the cadmium atoms do not interact with the paramagnetic ions, and the other half interacts with ions that are randomly distributed in an alloy composed of Cd_0.987Co_0.013S.

The spin dynamics of an S(1/2)I_N system during the CP mixing time of continuous wave and variable amplitude cross-polarization magic angle spinning (CWCPMAS and VACPMAS) experiments is discussed. The signal enhancement of a low abundant S spin, coupled to a set of N = 6 coupled spins with I = 1/2, is evaluated as a function of the length of the mixing time. For CWCPMAS this signal is first evaluated in the frequency domain and then transformed to the time domain. These calculations provide some additional insight into the CP spin dynamics and enable a practical approach toward the evaluation of CP signals of large spin systems. In addition the adiabatic character of the ramped VACPMAS experiments is discussed and S-spin signals of a spin system with N = 6 are simulated. Estimates of the upper bounds of the CP signals as a function of the number of I spins in an S(1/2)I_N system are given and compared with the calculated values.

CdS and CdS:Mn nanoparticles were studied by ¹¹³Cd and proton NMR. Nanoparticle samples were synthesized by precipitation of CdS from an aqueous solution of Na₂S and CdSO₄. The nanoparticles were not deliberately capped by any surface-termination agent. The NMR spectra of CdS nanoparticles prepared with an excess of Cd consist of three frequency bands: a bulk line corresponding to the inner Cd atoms with full sulfur coordination, a broad band due to surface Cd atoms, and a sharp line of CdSO₄ in solution. The assignment of these lines is accomplished by experiments on S-rich samples, by the study of the temperature dependence of the spectra, and by comparing the chemical shift values of the lines with tabulated chemical shift values of different cadmium compounds. A significant amount of water was found in the samples. This water is trapped in microscopic pores resulting in a lowering of the water-ice phase transition and a significant shortening of the proton T₁ and T₂ relaxation times. The NMR spectra of CdS:Mn do not show any additional spectral structure. Mn²⁺ ions remain in the included water and/or are located at the nanocrystallite surface and do not appear to be incorporated inside the nanoparticles.

We have investigated the reorientational mobility of n-hexane and n- pentanol guest molecules in Dianin's compound and in zeolite 5A by molecular mechanics/dynamics calculations (MM/MD) and temperature-dependent solid- state ²H NMR. To choose the proper motional models for the different host- guest systems, MM calculations were first performed and minimum-energy structures for the compounds were established. The calculations were performed on a crystallographic unit cell, with periodic boundary conditions to minimize edge effects. MD methods were then applied to the minimized structures and provided an insight into the different dynamic modes experienced by the guest molecules in their host cages. Several structural parameters of the host-guest systems were monitored for a total simulation period of up to 100 ps both at low temperature (77 K) and high temperature (300 K). ²H NMR spectra of perdeuterated and specifically deuterated guest molecules in their inclusion compounds were acquired as a function of temperature. After detection the observed line Shapes were analyzed in terms of motional models, taking into account experimental parameters and the results of the MD calculations. The solid-state ²H NMR showed a very high degree of agreement with the results of the molecular modeling calculations.

Solid extradants for metal ions have been prepared by chemical bonding of jojoba wax to a polystyrene backbone, followed by phosphonation or sulfur-chlorination of the jojoba moiety. In this study, the intermediates and final solid products of the reactions were characterized by solid-state ¹³C and ³¹P nuclear magnetic resonance spectroscopy. The spectra showed the expected chemical shifts of the atoms involved in the chemical reactions, as well as other parts of the reacting molecules. Thus, the carbonyl carbon of the jojoba chain appears at 175 ppm, the methyl carbons at 15 ppm, the polystyrene backbone at 40-42 ppm (aliphatic carbons) and 128, 137, 143-147 (aromatic carbons). Carbons adjacent to N, S, and P appear at 45-55, 60, and 48 ppm, respectively.

A structural study of glass-ionomer cement (GIC) dental restoratives has been completed. Transmission electron microscopy, selected area electron diffraction, and X-ray diffraction studies indicate domain-like microstructure in a new experimental material, whereas a featureless amorphous gel-like microstructure exists in the conventional GIC. Nuclear magnetic resonance studies were also conducted. The new experimental GIC contains domains of (i) bonelike material (apatite), (ii) mesoporous material and (iii) other framework structures (aluminium phosphate in the high cristobalite structure), with its setting chemistry a restructuring of the aluminosilicate glass around the template of poly(acrylic acid). Conventional glass-ionomer cement may set by a similar but slower process. Leaching properties of glass-ionomer cements are also explained.

The results of various ¹⁵N solid-state NMR experiments performed on solid samples of doubly ¹⁵N-Iabeled 3,5-dimethylpyrazole, 5-methyl-3-phenylpyrazole, (PMP), and 3,5-diphenylpyrazole are reported. In the solid state, these compounds form various hydrogen-bonded complexes. The principal values of the ¹⁵N chemical-shift tensors (CST) of amine and imine nitrogen atoms are derived by lineshape analysis of the ¹⁵N NMR spectra of the static powders obtained under the conditions of ¹H- ¹⁵N cross polarization and ¹H decoupling. The orientations of the ¹⁵N CST in the molecular principal axis system are obtained by taking into account the ¹⁵N- ¹⁵N dipolar interactions and the ¹⁵N-D dipolar interaction after deuteration of the mobile proton sites. The relative orientations of the amine and imine CST in PMP are independently checked by one-dimensional off-magic axis sample spinning magnetization transfer experiments. The isotropic chemical shifts, the principal elements, and the orientations of the CST of both nitrogen atoms and the ND distances depend only slightly on the chemical structure and the associated hydrogen-bonded structure. The intramolecular structure of pyrazoles, therefore, does not vary substantially when different types of hydrogen-bonded complexes are formed.

Single crystals of Dianin's inclusion compound with methyl and ring deuterated p-xylene guest molecules were grown and studied by FT deuteron NMR. The spectra from the deuterated methyl groups reveal that these groups reorient rapidly down to 12K; thereafter they enter into the tunneling regime. The rings of the p-xylene guests become motionless when T reaches 110K. By measuring the orientation dependence of the quadrupole splittings, determining from these data the quadrupole coupling tensors of the ring deuterons and relating these tensors to the C-D bond directions we infer the sites of the p-xylene guests in the cages of Dianin's inclusion compound. We find two sets of independent sites. Each contains three C₃ related individual sites. In each set the population of one of the sites is strongly depleted. The only large-anlge molecular motions are 180° rotational jumps about the long molecular axes. From measurements of T₁ we conclude that these jumps are thermally activated, τ₀ = 5·10^-14 s, ΔE=20 kJ/mol. Additional motions are rapid librations, also about the long molecular axes. Their amplitude increases with increasing temperature, at 300 K it reaches 20°. With 2D-exchange spectra we demonstrate that a p-xylene guest cannot change its site on a timescale of 100 ms and a tempering experiment suggests that this is true on a timescale of several days even at T=371 K.

Amplitude-modulated broadband and narrowband excitation pulses for spin systems with I = 1 2 are derived using Floquet theory. These pulses are defined in terms of the coefficients of their finite Fourier transforms. A methodology for the design of band-selective pulses is presented and examples are given. Two perturbation-theory approaches are exploited. In the first, normal perturbation theory about the resonance condition is used to evaluate the eigenvalues and eigenvectors of the Floquet Hamiltonian of the irradiated spins. ln the second, a simultaneous perturbation-theory calculation is performed at off-resonance positions equal to multiples of the principal frequency of the Floquet matrix. With these methods, amplitude-modulated 180° broadband excitation pulses and narrowband inversion and 90° pulses were obtained and compared with similar pulses introduced by others. In addition, the conversion of 180° broadband pulses to pulses of arbitrary flip angles is discussed by representing the spin system in its interaction representation.

Multinuclear solid-state nuclear-magnetic-resonance (NMR) experiments have been performed on a single-crystal sample of bulk composition Hg0.78Cd0.22Te. The NMR spectra of the three distinct lattice species (Hg, Cd, and Te) have been observed and assigned. Some double-resonance Hg-Te and Hg-Cd experiments clarify the assignment of Te resonance to chemical environment. These experimental results confirm our previous assignments of Te shifts to distinct chemical environments. They further suggest that in melt-grown, homogeneously distributed samples, cation distributions differ little from predictions of a statistical model.

A magic-angle spinning experiment called transferred-echo double resonance (TEDOR) has been introduced recently to measure the I-S dipolar coupling of heteronuclear I-S pairs of spin- 1 2 nuclei while eliminating unwanted background signals from uncoupled I and S spins via a coherence-transfer process. In this paper, a quantitative description of the TEDOR experiment is given in terms of the evolution of the density matrix for a pair of heteronuclear spins. The resulting equations provide a theoretical basis for evaluating the selectivity and sensitivity of TEDOR and suggest strategies for determining dipolar coupling constants directly from TEDOR data. Experimental examples illustrating these aspects of TEDOR are provided by studies performed on a range of ¹³C-¹⁵N dipolar couplings found in double-labeled asparagine, alanine, glycine, and the linear peptide antibiotic, gramicidin.

The combination of transferred-echo double resonance (TEDOR) with rotational-echo double resonance (REDOR) has been used to measure an 8-Å fluorine-carbon internuclear distance in a nine-residue fragment of the peptide antibiotic emerimicin. The fragment is ¹⁹FCH₂CO-Phe-MeA-MeA-[1-¹³C]MeA-[¹⁵N]Val-Gly-Leu-MeA-MeA-OBzl (MeA = α-methylalanine or aminoisobutyric acid). The TEDOR part of this magic-angle-spinning, solid-state NMR experiment selects the ¹³C label by its dipolar coupling to ¹⁵N and suppresses the natural-abundance carbon background. The REDOR part of the experiment measures dipolar coupling of the selected carbon to ¹⁹F. The TEDOR-REDOR combined experiment works with a variety of spin 1/2 nuclei and can be used to characterize internuclear distances and geometry in macromolecular aggregates that do not crystallize.

Expressions for the transition amplitudes of the centerband and sidebands of magic angle spinning (MAS) NMR spectra are derived by applying the Floquet theory. Signal amplitudes are defined in terms of transition amplitude operators, which are linear combinations of the Floquet operators. Two examples of the utilization of the Floquet approach for the evaluation of MAS signals are presented. In the first, the REDOR experiment on heteronuclear spin systems is discussed. The effects of finite pulse lengths on the REDOR signals are also derived. The second example deals with the MAS spectrum of a spin coupled to a heteronuclear spin that is irradiated by an rf field. Recoupled spectra are examined with the help of the Floquet theory and decoupled spectra are evaluated. In all cases the methodology of the Floquet approach is emphasized.

It has been shown previously that multiphoton resonances may be achieved by applying radiofrequency irradiation simultaneously at several frequencies with offsets from resonance related by a harmonic relationship. In practice, this is equivalent to using RF pulses whose amplitudes are time-dependent. However, it is also possible to achieve multiphoton resonances with a sequence of conventional, constant-amplitude RF pulses of varying phase. These "squared" approximations reproduce closely the results obtained using the amplitude-modulated pulses, both in computer simulations and in the experiments. A much more rapid dependence of the strength of the effective irradiation field on the amplitude of the applied RF is a feature of multiphoton experiments; this can enhance spatial and spectral selectivity considerably. The spectral characteristics of squared multiphoton composite pulses are analyzed in detail, and the influence of various parameters of the pulse sequence is considered. The results are tested in a 3'P NMR experiment in which a single spectral line is selectively inverted.

Deuterium NMR is used to study the sorption complexes formed by (methyl-deuterated) mono-, di-, and trimethylamine (MMA-d₃, DMA-d₆, and TMA-d₉) in the acid forms of the zeolites HZK-5 and HY, as well as in dehydroxylated HY and DHY, obtained by high-temperature calcination of HY. The measurements were made in the range -140 to 160°C on samples loaded up to twice the equivalent of the number of Al atoms per unit cell. For HZK-5 the uptake of MMA and DMA is rapid at room temperature, but sorption of TMA requires thermal activation. In HY and DHY all amine gases are readily absorbed upon exposure at room temperature. In all samples a variety of species are identified, roughly divided into chemi- and physisorbed. The former corresponds to sites in which the amine molecules are firmly bound to the zeolite framework but can still undergo various types of local motions. The nature of these motions is studied by analysis of the deuterium NMR line shape. In HZK-5 and HY similar species to those previously found in HRHO are observed. Their structure may be understood in terms of H-bonded complexes with the Brønsted acid site of the zeolites. In DHY other chemisorbed species are observed which appear to be formed by semipolar bonding of the amines with Lewis acid sites formed by the dehydroxylation process.

A unique method for the detection and analysis of slow molecular motions in solids is proposed and demonstrated. Where other methods require variable temperature measurements, our method of dynamic off-magic-angle sample spinning (DOMASS) NMR is performed at a single temperature, or alternatively, enables measurements in an accessible convenient temperature range. The studies of dynamic processes in a wide class of temperature-sensitive materials are possible via this method.

We describe a method suitable for the design of broadband propagators in two-level or pseudo-two-level systems via amplitude-modulated irradiation. Irradiation sequences are described in terms of a Fourier expansion. The Fourier coefficients of the expansion are used to calculate the time-independent Floquet Hamiltonian which represents the time-dependent Hamiltonian. This transformation removes the difficulty of integrating the time-dependent equations of motion. The infinite Floquet matrix is approximately diagonalized by an application of perturbation theory. A set of infinite matrix operators is introduced which assists in the diagonalization. The perturbation-theory expressions are used to derive approximate expressions for the propagator. Successive terms in the perturbation expansion can be nulled by considering additional Fourier coefficients. Broadband-irradiation sequences with low mean power or low peak power are described corresponding to coherent excitation in two-level systems through the flip angles 45°, 90°, 135°, and 180°.

The use of magic angle spinning nuclear magnetic resonance technique to examine local properties of four semiconductor alloys is presented. Cation distribution and charge transfer information were obtained for the common anion systems of Cd_{1 -x}Zn_xTe and Hg_{1 -x}Cd_xTe from chemical shift, intensity, and linewidth of the nuclear magnetic resonance (NMR) signals. Preliminary results on a common cation system, CdTe_{1 -x}Se_xand a dilute magnetic semiconductor, Cd _x _ _xMnxTe, illustrate the sensitivity of NMR to local properties. In the latter case, the predominant interaction arises from transfer hyperfine interactions.

High-resolution solid-state NMR experiments are used to study bonding in the semiconductor alloy system Hg_1-xCd_xTe over a broad range of values of x. Based on measurement of the ¹²⁵Te chemical shift and its sensitivity to coordination effects, which we demonstrate for the first time, it can be concluded that Hg and Cd do not distribute themselves randomly in the alloy lattice.

Experimentally achievable conditions where only weak off-resonant fields are used to excite coherence in a two-level system are explored. A brief review of previous theoretical results useful in treating multifrequency irradiation sequences is provided. Using an approximation method based on the Floquet formalism we derive an expression for the effective field strength as a function of the phases and amplitudes of the applied irradiation fields. Some of these results are rederived and/or explained in a simplified manner. Under conditions of four-frequency irradiation, three-photon excitation of a two-level system in NMR is experimentally demonstrated on the spin-1/2 system of the ³¹P nucleus in phosphoric acid. The behavior of the three-photon resonance is explored as a function of all important experimental parameters. The results of these tests conform closely to the theoretical predictions. Possible uses of multifrequency irradiation schemes in NMR are suggested.

Deuterium NMR spectra of the intercalation complexes of lamellar Cd₂P₂S₆ with various deuterated pyridine molecules are reported. The measurements indicate that the pyridine molecules lie within the chalcogen van der Waals gaps with their molecular planes parallel to the chalcogen layers. Between room temperature and -60°C the pyridine molecules reorient rapidly (on the NMR time scale) about an axis perpendicular to their molecular plane.

Multiple quantum effects in double frequency (df) pulsed NMR experiments on multilevel spin systems are studied. In these experiments, the spin systems are irradiated by two rf fields, applied simultaneously. A general theoretical description of these experiments is presented using the theory of Shirley for time dependent Hamiltonians. Multiphoton resonance conditions are given and time independent fictitious spin-1/2 Hamiltonians are derived using his perturbation theory treatment. With these Hamiltonians, the evolution of the spin systems during df irradiation is approximated. The example of df NMR experiments on an I=1/2 spin system is discussed. High order perturbation theory is developed to describe the time evolution of this spin system at a three photon resonance. Accurate computer calculations are performed to examine this time evolution. Df NMR experiments are performed on the single ³¹P(I=1/2) transition of phosphoric acid to check the theoretical results. The three photon resonance condition for these measurements is studied as a function of the rf irradiation intensities and of the resonance offsets of the two frequency components of df irradiation fields. Special NMR pulse cycles are used to study the dependence of the phase of the coherence created by df pulses on the initial rf phases of the two frequency components. Spin-echo type of experiments are developed to detect the spiral motion of the magnetization vector of the I=1/2 spin system at the three-photon resonance.

Triple-quantum NMR on spins with S=32 in solids can be of much help by the determination of the chemical shielding parameters. Excitation and detection of the triple-quantum coherences of S spins with small quadrupolar frequencies (Q300 sec-1), was accomplished by weak rf pulses. On spins with large quadrupolar frequencies modulated rf-pulse techniques have been explored in order to obtain their narrow-line triple-quantum spectra. In this publication cross-polarization-enhancement techniques on the single-, double-, and triple-quantum transitions of S=32 spins, in systems with abundant I=12 spins and rare S=32 spins, are developed. The theory of these experiments is an extension of the theory of double-quantum cross polarization. The S=32 spin Hamiltonian can always be divided in three commuting parts, of which two are fictitious spin-1/2 Hamiltonians. Cross polarization can occur between one of these transitions and the I spins in the system. Hartmann-Hahn conditions for these processes are derived. Nonmodulated and partially modulated rf irradiation fields are used for the enhancement of single- and triple-quantum coherences. Efficiency factors of the different cross-polarization experiments are calculated. Na23-H1 spin-lock cross-polarization measurements are performed on an oriented single crystal of sodium ammonium tartarate tetrahydrate in order to verify the different Hartmann-Hahn conditions. A full modulation cross-polarization experiment is designed to obtain large enhancements of the signal intensities of center-frequency lines of S=32 spectra from single crystals.

A quantitative analysis of the effect of spin lattice relaxation rates on pure quadrupole resonance pulse experiments for spins with I = 1 is given. A model is presented in which the three dimensional relaxation problem is reduced to a two dimensional one. In this model any possible population distribution of the energy levels corresponds to a point in a plane, the "v plane." The response of the system to spin-lattice relaxation effects and to rf pulses are described as translations of points in this plane. The experimental signal intensities are directly related to the coordinates of those points. The following cases are treated quantitatively: (i) CW saturation, (ii) CW saturation followed by a 90° pulse, (iii) two-pulse sequences, and (iv) continuous steady state pulse sequences. For each case explicit equations for the signal intensity as function of the experimental parameters are given. The analysis is made for both single crystals and powders.