Toshihito Nakai

Application of Floquet theory to the nuclear magnetic resonance spectra of homonuclear two‐spin systems in rotating solids

The theory for the nuclear magnetic resonance (NMR) spectra of homonuclear two‐spin systems under sample spinning has been developed. The propagator describing the time‐evolution of the systems, which is driven by the homogeneous Hamiltonian composed of the chemical‐shift difference and the flip–flop parts of the dipolar and J couplings, is treated using Floquet theory; the Floquet eigenvalues and eigenvector components determine the resonance frequencies and intensities, respectively. Nondegenerate Rayleigh–Schrodinger perturbation theory is used to solve the Floquet secular equation. Recurrence equations for the perturbation corrections have been derived, allowing us to evaluate efficiently very high‐order terms, such as 20th‐order terms. Analytical expressions for the resonance frequency obtained in the low‐order approximations provide an intuitive understanding of the main spectral features; the second‐order equations can describe the conspicuous solid‐state effects on the magic‐angle spinning (MAS) s...

J coupling in chemically equivalent spin pairs as studied by solid‐state nuclear magnetic resonance

The presence of J coupling was observed in the solid‐state nuclear magnetic resonance (NMR) spectrum of the 31P spin pair in polycrystalline 1,2‐bis (2,4,6‐tri‐tert‐butylphenyl)‐diphosphene (TBPDP) using the magic‐angle spinning (MAS) technique. This represents the first example of J coupling in a spin‐pair system with nuclei having identical isotropic chemical shifts. Average Hamiltonian theory is used to derive the time‐independent eigenstates for the system. It is shown that a second‐order perturbation term, which is dependent on the difference between the chemical‐shift tensor orientations in addition to the strength of the dipolar coupling, allows the recoupling of the J interaction for the two chemically equivalent 31P nuclei. In the absence of the perturbation term, the system is reduced to an A2 case in solution‐state NMR for which, of course, no J coupling may be observed. The magnitude of the J coupling, namely, 580±20 Hz obtained from two‐dimensional (2D) J‐resolved experiments was found to be ...

An analysis of NMR spinning sidebands of homonuclear two-spin systems using Floquet theory

NMR spinning sidebands for homonuclear two-spin systems are described using Floquet theory. The variation of asymmetry observed in J-split doublets from sideband to sideband was found to depend on ...

Spinning-frequency-dependent linewidths in 1H-decoupled 13C magic-angle spinning NMR spectra

Abstract The broadenings observed in 13 C MAS NMR spectra, which depend on the sample-spinning speed, were studied, using polycrystalline adamantane. Not only was a monotonic increase of the linewidths with the increase of the spinning frequency observed, but also a novel resonant feature was found. The phenomena were interpreted as originating from rotary-resonance 13 C 1 H recoupling.

Forbidden nuclear magnetic resonance transitions between singlet and triplet states in spin-12 pair systems in rotating solids

Abstract Forbidden transitions between singlet and triplet nuclear spin states in chemically equivalent spin- 1 2 pair systems were observed in the 31P cross-polarization magic-angle spinning (CPMAS) nuclear magnetic resonance (NMR) spectrum of 1,2-bis (2,4,6-tri-tert-butylphenyl) diphosphene (TBPDP). The fine structure of the resonance lines changed dramatically with rotor spinning frequency. Using the average Hamiltonian theory, the origin of these singular phenomena was revealed to be due to high-order anisotropic interactions in the solid state. From analysis of the spectra, the value of the J coupling between the chemically equivalent 31P nuclei in TBPDP was estimated to be 577 ± 15 Hz.

INADEQUATE NMR spectra of extremely strongly coupled spin systems

A novel product operator formalism for strongly coupled two-spin systems was developed which allows the time evolution for such systems to be estimated much more easily than using the density matrix. The newly developed theory was applied to describe the INADEQUATE (Incredible Natural Abundance DoublE QUAntum Transfer Experiment) experiments, and the condition for the efficiency of the creation of the double-quantum coherences was formulated, which is useful for setting the experimental conditions. The refocused INADEQUATE spectra of benzyl bromide, in which two one-bond 13C—13C pairs have extremely strong couplings compared with the chemical shift differences, were observed under several experimental conditions. The signals attributable to these strongly coupled spin pairs were detected with reasonably large intensities, and their coupling constants were determined by simulation of the spectral intensities; the weak and the long-range couplings in the compound were also obtained.

Residual chemical-shift effects in spin-echo NMR powder patterns of homonuclear dipolar-coupled spins

Abstract The effect of the spin-echo pulse sequence on homonuclear dipolar-coupled spins in solids has been studied. Precise analysis has revealed that the sequence may not yield simple Pake doublets but rather complicated patterns because of the imperfect refocusing of the chemical shifts. This strong-coupling effect has been verified experimentally through the measurement of the 31 P two-dimensional spin-echo powder pattern for polycrystalline tetraphenyldiphosphine; our choice of tetraphenyldiphosphine was fortunate because it transpired that the non-parallel chemical-shift tensors of the two 31 P nuclei in the compound yield the desired residual chemical-shift effects.

A fast two-dimensional switching-angle sample-spinning method for separating chemical-shift powder patterns

Some years ago, a two-dimensional NMR method incorporating the technique of switching the spinner axis direction was introduced by Terao et al. (I) and Maciel et al. (2), independently, to unravel the overlapping chemical-shift powder patterns due to inequivalent nuclei. The former named the technique switching-angle sample spinning (SASS). This type of measurement has the advantages of not requiring the skilled adjustment of the experimental parameters and of yielding lineshapes containing no serious distortions, in comparison with other methods (3-8). Today, a commercial probe for SASS measurements (9) is available, so the technique may soon be more commonly used. However, one disadvantage of the SASS method still remains; that is, it is often time-consuming because of the requirements of 2D spectroscopy. In this study, we propose a simple modification of the previous 2D chemical-shift SASS method which makes the measuring time much shorter. We report here the chemicalshift principal values for the individual carbons of 2,4-dimethoxyacetophenone separately obtained with this new method. The previous 2D SASS method yields a spectrum which reflects the anisotropic and isotropic parts of chemical-shift interactions on one axis ( W, ), and only the isotropic part on the other (02); the chemical-shift powder patterns appear on the o, cross sections, separated with respect to the isotropic shifts in the o2 dimension. The powder patterns on the w, cross sections are situated at the individual isotropic-shift positions. Since the isotropic values are spread over a wide frequency range, as is often the case with 13C NMR solid-state spectra, a large w1 spectral width is required to cover simultaneously all the powder patterns without the occurrence of confusing aliasing; in particular, this condition is critical under the high magnetic field which is necessary to obtain well-resolved resonance lines in the w2 dimension. It follows that one is often forced to perform the experiments one by one with a small tI -increment value in the 2D spectroscopy. This fact is one reason why the previous 2D SASS method is often time-consuming when we wish to obtain all the powder patterns at once. Inherently, however, only small portions of such a wide frequency range in the w1 dimension are necessary to show the individual powder patterns, because they are scaled down around the respective isotropic shifts owing to the off-magic-angle spinning (OMAS) ( 1,2, 10); the widths of the powder patterns are reduced as much as possible to achieve high sensitivity taking care that their singularities are not missed because of the lower resolution. Hence, we can employ a much smaller spectral width in the

The necessity for synchronization in DANTE experiments with rotating samples. Reclamation of the asynchronous DANTE pulse train by combination with the TOSS sequence

In recent NMR spectroscopic studies, frequency-selective excitation techniques have become increasingly important. One of their roles is the simplification of spectra by eliminating unwanted resonance lines (1, 2). Another is extracting specific slices of full multidimensional spectra such as two-dimensional exchange/spin diffusion spectra (3), 2D separation spectra (4), and imaging (5). Among such techniques, the DANTE pulse train (6) prevails widely because one can compose the pulse sequence with hard pulses which are more stable in amplitude, and more easily available, than soft pulses, and, moreover, one can readily adjust the effective field strength by altering the pulse spacing. In solid-state NMR, the DANTE pulse train is usually applied to powdered samples under magic-angle spinning (MAS) as well as to single crystals, so that it can operate on specific well-resolved lines ( I). In the MAS experiment, each pulse of the DANTE train should be irradiated synchronously with the spinning period: all the transverse magnetizations due to crystallites are individually modulated by MAS and only become in-phase after every spinning period (7). However, not only is this synchronization difficult in practice but also there are some disadvantages which ensue following a long pulse interval fixed at the spinning period. typically 250400 ps: such a long interval often renders the selective band narrower than the linewidth. Also, the magnetizations decay, in compounds with short T2 values, during the pulse train. Sample heating may occur in the cases where a heteronuclear decoupling field is applied simultaneously. Caravatti et al. ( I ) showed experimentally that synchronization is not necessary for selective saturation with the DANTE-90” pulse train. In addition, Bork and Schaefer (8) recently pointed out that the asynchronous DANTE-180” pulse train inverts an entire spinning sideband family and attempted to explain this observation qualitatively. In fact, we can confirm that the asynchronous DANTE pulse train works properly as long as the spinning frequency, UR, is large compared with chemical-shift anisotropy, AU. Figures 1 a1 c show the ‘%I spectra for polycrystalline glycine observed at vR = 4.0 kHz using the CP (cross-polarization)MAS-DANTE saturation/inversion sequence which consists of the pulse train CP-90”-DANTE-delay-90°-acquisition. ln Figs. 1 a1 C, one can see that the asynchronous pulse train almost completely saturates

Determination of spin parameters reflected in the nuclear magnetic resonance powder patterns for two equivalent 31P nuclei in Lawesson's reagent.

The nuclear magnetic resonance (NMR) powder patterns observed for the 31P spin pair in Lawessons reagent (1) were analyzed. Using an efficient procedure, wide ranges of the spin parameters were examined to determine whether they might reproduce the experimental one-dimensional (1D) spectrum of the present A2 spin system. It was demonstrated that the parameters were not uniquely determined from the 1D powder pattern only, but a significant reduction of their uncertainties was realized using the two-dimensional (2D) powder pattern. The molecular structure of 1 was discussed in terms of the refined spin parameters.