The results of ab initio derivative Hartree-Fock calculations of the dipole and quadrupole shielding polarizabilities and hyperpolarizabilities of a number of small molecules are reported, together with estimates of the electric fields and field gradients present in proteins. It is argued that weak electrical interactions, mediated via these shielding polarizabilities, make major contributions to the chemical-shift nonequivalencies observed in proteins due to folding into their native conformations. The electric-field-induced shifts may be very large (≈5 ppm for 13C, ≈10 ppm for 17O and 17F), due to the low dielectric constants found in proteins, and in some cases they may dominate the experimentally observed spectral shifts.
Standard pulse sequences frequently employed in NMR studies, such as INEPT, DEPT, HETCOR, phase-sensitive HETCOR, and HETCOR with nongeminal proton decoupling in the F1 dimension, have been extended by Hahn spin echoes. This enables measurement of 15NX and long-range 15N1H couplings (together with the comparison of their relative signs) at the natural-abundance level of isotopes. The sequences were optimized and verified for X 13C, 29Si, 31P, 119Sn, 207Pb, using a wide variety of nitrogen compounds (e.g., pyrroles, nitro compounds, cyanides, cyanates, isocyanates, isothiocyanates, carbodiimides, silylamines, PN, SiN, SnN, and PbN compounds). Both positive and negative 1J(15N13C) couplings were observed. The trends were reproduced by SCF INDO FPT calculations. Reduced coupling constants 1K119Sn15N and 1K207,15Pb15N were all negative. Two-and four-bond 15N1H couplings were of either sign, whereas vicinal 3J(15N1H) couplings were always negative, showing a crude linear relationship with V 1J(15N13C) in the compounds studied. Since the intensity of the residual signal in the HEED experiments is readily adjustable, the measurement of 1514 N isotope shifts, 1Δ 1514 N(X), is straightforward. The 1|gD 15114N(13C) values determined for rather different bonding situations show a complex behavior and there is no simple relation between 1Δ values and bond order, s character, or hybridization. A previously proposed classification of 1514 (NC) isotope shifts is inadequate in the light of the present data. The 1Δ 1514 N values for 3P(III) chemical shifts are much larger than those for P(V) derivatives. The 1514 isotope effects on 13C and 29Si chemical shifts are similar in magnitude. Unexpectedly, several PbN compounds showed 1Δ1514N(207Pb) values close to zero.
A new design for a double-tuned dynamic-angle-spinning (DAS) probe that employs a RF coil wrapped directly around the stator is presented. The increased filling factor of this design and the smaller RF coil result in improved sensitivity and facilitate the incorporation of 1 H decoupling capabilities. Since the RF coil is reoriented with the spinning sample, the pulse lengths and sensitivity vary as the cosecant of the angle between the RF coil and the external magnetic field. However, this was not found to be a significant impediment to the usage of the probe. As a demonstration of the probe's performance a 1 H-decoupled 11 B DAS spectrum of boric acid is presented.
Constraints on unitary evolution derived by O. W. Sørensen (J. Magn. Reson. 86, 435 1990) are used to calculate the bounds of the region in Liouville space accessible to the spin system, given a known initial density operator. The bounds are represented graphically in two and three dimensions. A local thermodynamic interpretation of Hartmann-Hahn cross-polarization is discussed. It is found that local Zeeman thermodynamic equilibration is incompatible with the Sørensen bounds under Hartmann-Hahn mismatched conditions.
SNAPSHOT-FLASH imaging has been described as a method of fast acquisition of NMR tomograms ( I ) . It is based on a slice-selective radiofrequency pulse of small flip angle (Y and the acquisition of magnetic field gradient echoes in a 2D Fourier imaging experiment. Under these conditions, the value of TR/ T, ( TR is the repetition time) can be extremely low. A whole 128 X 12%pixel tomogram may be taken in a fraction of a second. It has been shown that a SNAPSHOT-FLASH image is mainly spin-density-weighted. Contrasts with respect to NMR parameters can be introduced by the application of RF pulses before the whole image sequence ( I ) . For T1 measurements a sequence of several SNAPSHOT-FLASH tomograms is taken after the application of a 180” pulse with negligible delay between the pictures (about one millisecond). While an image is taken the longitudinal magnetization changes steadily. The intensity of the picture depends mainly on the longitudinal magnetization, which is present at the time when the amount of the phase-encoding gradient Gp is minimal. In a 2D Fourier imaging experiment Gp is switched symmetrically from a value of -GPO to +Gpo. Thus, the intensity of picture 12 after the 180” pulse depends on the longitudinal magnetization at the time t = ( IZ 1) r t 7/2, where T is the total acquisition time of a single tomogram. For T, = 1 s, the recovery in an inversion-recovery experiment will be attained after about five seconds. Hence, the whole inversion-recovery relaxation curve may be obtained by taking a sequence of at least eight pictures with 7 = 400 ms. However, one obtains an effective relaxation time Ty which is smaller than T1 because of the constant loss of longitudinal magnetization after each application of the (Y pulse. The exact evaluation of T, must be done with respect to this effect. The following treatment regards the “relative magnetization” m (total magnetization M devided by equilibrium magnetization MO). The T2 relaxation is neglected, since echo times as low as 1.4 ms can be used in SNAPSHOT-FLASH experiments. Before the pulse sequence used to measure an arbitrary gradient echo, there is longitudinal magnetization mj . After the cr pulse it is micos( a). During the measurement, there is spin-lattice relaxation leading to m(t) = 1 + [m(O) l]exp( -t/ T,). Hence, the longitudinal magnetization before the next pulse is mi+i = 1 t [micos(cu) l]exp( -T,/ T, ). In an inversion-recovery experiment the starting value is m. = 1. These conditions are fulfilled by
The NMR relaxation behavior of the proton magnetization in adsorbed water is investigated. Longitudinal as well as transverse relaxation of the adsorbed water as a whole shows a distinct nonexponentiality and the nature of this nonexponentiality is studied. Different methods of fitting distribution of relaxation times are examined and various simulated and experimental decay curves are submitted to these fitting methods. The results of these fittings clearly indicate that both the longitudinal and the transverse relaxation of the proton magnetization in adsorbed water is related to two or three discrete components and that there is certainly no broad distribution of relaxation times present in these water-adsorbent systems.
Pulse sequences that rely on heteronuclear one-bond couplings like ‘J(H, C) and ‘J( C, C) couplings are among the most sensitive correlation experiments available in high-resolution NMR of biological macromolecules. Therefore it is desirable to extract NMR parameters such as coupling constants from such experiments. One general principle that allows the accurate measurement of coupling constants is based on an arbitrary type of transfer spectroscopy (I) between at least two spins, where a third spin remains unaffected during two adjacent evolution periods and the intermediate mixing period. This principle has been realized with nonselective small-flipangle pulses [ @COSY (2), E.COSY (3), P.E.COSY (3-5), hetero-E.COSY (6)] and selective pulses [ soft-COSY ( 7)) hetero-sofC indices of the nuclei are also used for the spin operators): After the INEPT transfer, antiphase coherence of the form
A new method was developed for 1H and 13C localization spectroscopy based on the rotating-frame-imaging technique. 1H localization was carried out using a double-concentric surface-coil probe and a pulse sequence with two radiofrequency pulses. A spatial resolution of 2 mm was attained with a phantom sample containing ethanol, benzene, and water. For suppression of the water signal in vivo, a presaturation or a 1331 semiselective excitation method was utilized. For 13C localization, the 1H localized spectra were edited by J modulation through the spin coupling between 13C and 1H. For this purpose a 13C transmitter coil was added and the measurement sequence was converted into a spin-echo sequence. Methyl protons directly attached to 13C were selectively localized when a measurement was performed with[2-13C] acetic acid.
Modulated pulses designed for NMR often suffer from imperfections arising from the pulse-shape modulator. This produces a nonideal magnetization distribution which may lead to the failure of the experiment. This paper describes how to perform quantitative analysis of the imperfections of the RF modulator by harmonic analysis of the output wave form, using the NMR spectrometer itself. From these measurements, an analytical form of the transfer function is obtained. The wave form which compensates for the distortion is then calculated by an iterative process. To demonstrate the performance of the method, it was applied to representative pulse shapes. The comparison of the experimental frequency profiles, obtained with and without correction, with the simulated profiles illustrates the reliability of the method.
The ingress of water into Nylon 6.6 has been studied over a range of temperatures by nuclear magnetic resonance imaging techniques. The results have been used to extract the translational diffusion coefficient as a function of water concentration for various temperatures. These results in turn allow the activation energies to be evaluated. Other experiments have been made to measure the spin relaxation times T 1 and T 2 . The results are interpreted using a two-phase exchange model from which good agreement for both the diffusion and relaxation-time data is obtained. High-pressure diffusion results also presented support the view that water is taken up preferentially at the amorphous amide sites in the Nylon and that pressure increases serve to force water onto sitccupied sites and/or onto occupied sites, giving up to three waters per amide site.
Following a brief description of spectral diffusion encountered in magnetic resonance, a simple but quantitative interpretation of saturation-transfer EPR spectroscopy is presented in terms of the effect of spectral diffusion induced by molecular motion on adiabatic rapid-passage (ARP) responses. Implications of Portis's method for detecting ARP signals in connection with Bloch's theoretical prediction are reexamined and assessed. Characterizations of spectral diffusion by alternative time-domain EPR techniques are discussed in light of these ideas.
A principle for self-diffusion pulse-sequence design which cancels harmful cross terms involving both imaging and sample susceptibility-induced gradients by using antisymmetric diffusion-sensitizing-gradient pulses is proposed. A water diffusion coefficient of 1.94 × 10−5 cm2 s−1 was obtained by the cross-term-free sequence, a bipolar sensitizing-gradient pulse (BGP) scheme, while the conventional method gave 2.22 and 1.60 × 10−5 cm2 s−1 with sensitizing gradient running parallel and antiparallel to the imaging gradient, respectively. A diffusion coefficient of 1.38 × 10−5 cm2 s−1 was obtained from an apple, in fair agreement with 1.56 × 10−5 cm2 s−1 for its juice, using the BGP sequence. Although the conventional technique gave similar values for apple juice, it gave only about half as large a value for the whole apple, presumably because of internal gradients from inhomogeneous susceptibility. The rms value of these local gradients in the apple was estimated as 6.0 kHz/cm in our 200 MHz instrument.
Measurements of the second-order shift of the center of gravity of the nuclear quadrupole resonance lines of CSI3 in a high magnetic field are reported. The observed shift is in excellent agreement with calculations using second-order perturbation theory, and the importance of a detailed understanding of the shift for applications in low-temperature thermometry and solid-state structural studies is discussed.
We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.
This chapter discusses dynamic NMR spectroscopy in inorganic and organometallic chemistry. The study of chemical exchange phenomena using NMR techniques rests on the measurements of the four basic NMR parameters: relative signal intensities, internal chemical shifts, nuclear spin–spin couplings, and nuclear spin relaxation times. These parameters and their temperature dependences can be measured with great precision using one- and two-dimensional techniques, thus providing chemists with almost a plethora of methods for the precise measurement of molecular dynamics. The chapter focuses on developments in measurements of intramolecular rearrangements of molecules in chemical equilibrium and also includes intermolecular processes and time-dependent studies of nonequilibrium systems. The main advances in the theory and methodology of dynamic NMR (DNMR) are described in the chapter. Inorganic coordination complexes and organometallic compounds provide the widest variety of internal dynamic or fluxional rearrangement.
The efficiencies of a number of pulse sequences designed to remove directly bonded C-H correlations from long-range C-H shift correlation maps are evaluated. A two-step J filter sequence is shown to give good suppression in 1 D experiments. Its incorporation into the long-range C-H shift correlation experiment with a BIRD sequence at the center of the refocusing period gives the BIRDTRAP sequence, which is shown to yield 2D maps with a few very weak direct correlations and no artifacts. BIRDTRAP has a sensitivity higher than that of FLOCK.
