Theory of covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy provides an effective way for establishing nuclear spin connectivities in molecular systems. The method, which identifies correlated spin dynamics in terms of covariances between 1D spectra, benefits from a high spectral resolution along the indirect dimension without requiring apodization and Fourier transformation along this dimension. The theoretical treatment of covariance NMR spectroscopy is given for NOESY and TOCSY experiments. It is shown that for a large class of 2D NMR experiments the covariance spectrum and the 2D Fourier transform spectrum can be related to each other by means of Parseval's theorem. A general procedure is presented for the construction of a symmetric spectrum with improved resolution along the indirect frequency domain as compared to the 2D FT spectrum.     

Theory of stochastic dipolar recoupling in solid-state nuclear magnetic resonance

Dipolar recoupling techniques in solid-state nuclear magnetic resonance (NMR) consist of radio frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create nonzero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter f(max)) increases; (2) in a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large f(max), with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) quantum mechanical interferences among noncommuting pairwise dipole-dipole couplings, which are a complicating factor in solid-state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large f(max), provided that coupled nuclei have distinct NMR chemical shifts.     

Self-consistent Perturbation Theory of 13C magnetic resonance parameters in pyridines

The ¹³C chemical shifts for pyridine and 22 of its monosubstituted derivatives, the ¹³C? ¹⁹F couplings for fluoropyridines and the ¹³C? ¹⁵N couplings for pyridine, the pyridinium cation and pyridine-N-oxide have been calculated using the SCF-INDO Finite Perturbation Theory. Experimental ¹³C chemical shifts show only modest correlation with calculated shieldings; trends and magnitudes are, however, reasonably reproduced in some cases. Theory yields a correct account of the magnitudes, signs and trends for the various couplings except for ²J(CF). Addition of an empirical correction of + 33.5 Hz to the Fermi contact term leads also to excellent reproduction of this coupling.     

Anharmonic vibrational frequencies and vibrationally averaged structures and nuclear magnetic resonance parameters of FHF-

The anharmonic vibrational frequencies of FHF(-) were computed by the vibrational self-consistent-field, configuration-interaction, and second-order perturbation methods with a multiresolution composite potential energy surface generated by the electronic coupled-cluster method with various basis sets. Anharmonic vibrational averaging was performed for the bond length and nuclear magnetic resonance indirect spin-spin coupling constants, where the latter computed by the equation-of-motion coupled-cluster method. The calculations placed the vibrational frequencies at 580 (nu(1)), 1292 (nu(2)), 1313 (nu(3)), 1837 (nu(1) + nu(3)), and 1864 cm(-1) (nu(1) + nu(2)), the zero-point H-F bond length (r(0)) at 1.1539 A, the zero-point one-bond spin-spin coupling constant [(1)J(0)(HF)] at 124 Hz, and the bond dissociation energy (D(0)) at 43.3 kcal/mol. They agreed excellently with the corresponding experimental values: nu(1) = 583 cm(-1), nu(2) = 1286 cm(-1), nu(3) = 1331 cm(-1), nu(1) + nu(3) = 1849 cm(-1), nu(1) + nu(2) = 1858 cm(-1), r(0) = 1.1522 A, (1)J(0)(HF) = 124+/-3 Hz, and D(0) = 44.4+/-1.6 kcal/mol. The vibrationally averaged bond lengths matched closely the experimental values of five excited vibrational states, furnishing a highly dependable basis for correct band assignments. An adiabatic separation of high- (nu(3)) and low-frequency (nu(1)) stretching modes was examined and found to explain semiquantitatively the appearance of a nu(1) progression on nu(3). Our calculations predicted a value of 186 Hz for experimentally inaccessible (2)J(0)(FF).     

Theory and applications of supercycled symmetry-based recoupling sequences in solid-state nuclear magnetic resonance

We present the theoretical principles of supercycled symmetry-based recoupling sequences in solid-state magic-angle-spinning NMR. We discuss the construction procedure of the SR26 pulse sequence, which is a particularly robust sequence for double-quantum homonuclear dipole-dipole recoupling. The supercycle removes destructive higher-order average Hamiltonian terms and renders the sequence robust over long time intervals. We demonstrate applications of the SR26 sequence to double-quantum spectroscopy, homonuclear spin counting, and determination of the relative orientations of chemical shift anisotropy tensors.     

Electrical and ionic conductivity effects on magic-angle spinning nuclear magnetic resonance parameters of CuI

We investigate experimentally and theoretically the effects of two different types of conductivity, electrical and ionic, upon magic-angle spinning NMR spectra. The experimental demonstration of these effects involves (63)Cu, (65)Cu, and (127)I variable temperature MAS-NMR experiments on samples of γ-CuI, a Cu(+)-ion conductor at elevated temperatures as well as a wide bandgap semiconductor. We extend previous observations that the chemical shifts depend very strongly upon the square of the spinning-speed as well as the particular sample studied and the magnetic field strength. By using the (207)Pb resonance of lead nitrate mixed with the γ-CuI as an internal chemical shift thermometer we show that frictional heating effects of the rotor do not account for the observations. Instead, we find that spinning bulk CuI, a p-type semiconductor due to Cu(+) vacancies in nonstoichiometric samples, in a magnetic field generates induced AC electric currents from the Lorentz force that can resistively heat the sample by over 200 °C. These induced currents oscillate along the rotor spinning axis at the spinning speed. Their associated heating effects are disrupted in samples containing inert filler material, indicating the existence of macroscopic current pathways between micron-sized crystallites. Accurate measurements of the temperature-dependence of the (63)Cu and (127)I chemical shifts in such diluted samples reveal that they are of similar magnitude (ca. 0.27 ppm/K) but opposite sign (being negative for (63)Cu), and appear to depend slightly upon the particular sample. This relationship is identical to the corresponding slopes of the chemical shifts versus square of the spinning speed, again consistent with sample heating as the source of the observed large shift changes. Higher drive-gas pressures are required to spin samples that have higher effective electrical conductivities, indicating the presence of a braking effect arising from the induced currents produced by rotating a conductor in a homogeneous magnetic field. We present a theoretical analysis and finite-element simulations that account for the magnitude and rapid time-scale of the resistive heating effects and the quadratic spinning speed dependence of the chemical shift observed experimentally. Known thermophysical properties are used as inputs to the model, the sole adjustable parameter being a scaling of the bulk thermal conductivity of CuI in order to account for the effective thermal conductivity of the rotating powdered sample. In addition to the dramatic consequences of electrical conductivity in the sample, ionic conductivity also influences the spectra. All three nuclei exhibit quadrupolar satellite transitions extending over several hundred kilohertz that reflect defects perturbing the cubic symmetry of the zincblende lattice. Broadening of these satellite transitions with increasing temperature arises from the onset of Cu(+) ion jumps to sites with different electric field gradients, a process that interferes with the formation of rotational echoes. This broadening has been quantitatively analyzed for the (63)Cu and (65)Cu nuclei using a simple model in the literature to yield an activation barrier of 0.64 eV (61.7 kJ/mole) for the Cu(+) ion jumping motion responsible for the ionic conductivity that agrees with earlier results based on (63)Cu NMR relaxation times of static samples.     

Methodological aspects in the calculation of parity-violating effects in nuclear magnetic resonance parameters

We examine the quantum chemical calculation of parity-violating (PV) electroweak contributions to the spectral parameters of nuclear magnetic resonance (NMR) from a methodological point of view. Nuclear magnetic shielding and indirect spin-spin coupling constants are considered and evaluated for three chiral molecules, H2O2, H2S2, and H2Se2. The effects of the choice of a one-particle basis set and the treatment of electron correlation, as well as the effects of special relativity, are studied. All of them are found to be relevant. The basis-set dependence is very pronounced, especially at the electron correlated ab initio levels of theory. Coupled-cluster and density-functional theory (DFT) results for PV contributions differ significantly from the Hartree-Fock data. DFT overestimates the PV effects, particularly with nonhybrid exchange-correlation functionals. Beginning from third-row elements, special relativity is of importance for the PV NMR properties, shown here by comparing perturbational one-component and various four-component calculations. In contrast to what is found for nuclear magnetic shielding, the choice of the model for nuclear charge distribution--point charge or extended (Gaussian)--has a significant impact on the PV contribution to the spin-spin coupling constants.     

Frequency dependence of nuclear magnetic resonance parameters in poly(methyl methacrylate)

Using 26 NMR spectrometers, the Research Group on NMR, the Society of Polymer Science, Japan observed the ¹H NMR chemical shift, resolution, and signal intensity; ¹³C NMR chemical shift, resolution, and signal intensity; the effect from initiator fragment signal; ¹H spin-lattice relaxation times; ¹³C spin-lattice relaxation times; and ¹³C nuclear Overhauser enhancement of radically polymerized poly(methyl methacrylate). Excellent reliability was found after comparison between the data from different spectrometers. Molecular motion of this polymer was analyzed with a term of 3τ model.     

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.     

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.     

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.     

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.     

Theory of long-lived nuclear spin states in solution nuclear magnetic resonance. I. Singlet states in low magnetic field

We have recently demonstrated the existence of exceptionally long-lived nuclear spin states in solution-state nuclear magnetic resonance. The lifetime of nuclear spin singlet states in systems containing coupled pairs of spins-12 may exceed the conventional relaxation time constant T1 by more than an order of magnitude. These long lifetimes may be observed if the long-lived singlet states are prevented from mixing with rapidly relaxing triplet states. In this paper we provide the detailed theory of an experiment which uses magnetic field cycling to observe slow singlet relaxation. An approximate expression is given for the magnetic field dependence of the singlet relaxation rate constant, using a model of intramolecular dipole-dipole couplings and fluctuating external random fields.     

Theoretical studies of nuclear magnetic resonance parameters for the proton-exchange pathways in porphyrin and porphycene

The nuclear magnetic resonance (NMR) parameters in porphyrin and porphycene have been calculated to investigate their changes during the process of proton exchange, using density-functional theory (DFT) for both the spin-spin coupling constants and the shielding constants. In addition, in calculations on the smaller 1,3-bis(arylimino)isoindoline molecule, we have tested the performance of our computational approach against experimental data. The calculated nuclear spin-spin coupling constants and shielding constants have been analyzed as functions of the progress of the proton transfer between two nitrogen atoms. The one-bond couplings between proton and nitrogen, dominated by the Fermi-contact term, decay steeply as the internuclear distance increases. The small changes in the intramolecular J(HH) coupling between two inner protons are mainly determined by the sum of relatively large spin-orbit terms. The isotropic shielding constant shows a strong deshielding of the nitrogen nuclei as the proton migrates away. Both the isotropic shielding of the exchanged protons and the shielding anisotropy exhibit a minimum close to the transition states.     

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.     

Towards nuclear magnetic resonance micro-spectroscopy and micro-imaging

The first successful experiments demonstrating Nuclear Magnetic Resonance (NMR) were a spin-off from the development of electromagnetic technology and its introduction into civilian life in the late forties. It was soon discovered that NMR spectra held chemically relevant information making it useful as an analytical tool. By introducing a new way of detection, moving away from continuous wave spectroscopy, Fourier Transform NMR helped to overcome sensitivity problems and subsequently opened the way for multi-dimensional spectroscopy. As a result NMR has developed into one of the most powerful analysis techniques with widespread applications. Still sensitivity is a limiting factor in the applicability of NMR. Therefore we witness a renaissance of technique development in magnetic resonance striving to improve its receptiveness. This tutorial review introduces the efforts currently made in miniaturizing inductive detection by designing optimal radio-frequency microcoils. A second approach is to introduce a new way of detecting magnetic resonance signals by means of very sensitive micromechanical force detectors. This shows that the detection limits in terms of absolute sensitivity or imaging resolution are still open to significant improvements.