Homonuclear dipole interactions

The homonuclear dipolar recoupling technique of radio frequency-driven recoupling (RFDR) involves a hard n pulse per rotor period and its recoupling mechanism is based on the modulation of chemical shift difference [35-37]. When the delta-pulse approximation is relaxed so that the pulse width of the 7t pulse is about one-third of the rotor period, the so-called finite-pulse RFDR (fpRFDR) could selectively reintroduce the homonuclear dipole-dipole interaction under fast MAS conditions [38], Because the recoupling mechanism of fpRFDR does not require the presence of chemical shift difference, it can be applied to study samples with a singly labeled site. For the study of amyloid fibrils, the technique of fpRFDR is usually applied in a constant-time framework (see below). 

Now consider the pulse sequence in Fig. 10. Each repetition of C spans one rotor period. Between 0 and tr/2, the composite On pulse 90o360igO270o is applied. This composite pulse, which has been commonly referred to as POST, is chosen because it has been shown to compensate for effects of rf inhomogeneity [83], The mirror-image composite pulse is applied between xr/2 and xr. With this particular design of ROCSA, the homonuclear dipole-dipole interaction is considerably suppressed relative to the CSA. 

Fig. 10 ROCSA pulse sequence based on Cn symmetry. The rectangular blocks in black represent jt/2 pulses. The recoupling period (q) comprises k cycles of Cnln. Each complete cycle of Cnln spans n rotor periods (nzR). The rf phase of each Cq subcycle is set equal to 2nq/n, where q is an index running from 0 to n — 1. Within each Cq subcycle, azR and bzR indicate the position and the duration of the POST composite pulse, respectively. We find that the solution (a, b) = (0.0329,0.467) is a favorable choice for the suppression of the homonuclear dipole-dipole interaction. The bracketed and subscripted values indicate the pulse length and rf phase in radians, respectively. (Figure and caption adapted from [158], Copyright [2003], American Institute of Physics)...

In the case of pharmaceutical solids that are dominated by carbon and proton nuclei, the dipole-dipole interactions may be simplified. The carbon and proton nuclei may be perceived as dilute and abundant based upon then-isotopic natural abundance, respectively (Table 1). Homonuclear 13C—13C dipolar interactions essentially do not exist because of the low concentration of 13C nuclei (natural abundance of 1.1%). On the other hand, H—13C dipolar interactions contribute significantly to the broad resonances, but this heteronuclear interaction may be removed through simple high-power proton decoupling fields, similar to solution-phase techniques. 

For the heteronuclear dipole-dipole interaction, the spin I S whereas for the homonuclear dipolar or electric quadrupole interaction, I=S. For the anisotropic chemical shielding interaction, the spin operators are... 

In solution, dipole-dipole interactions constitute a relaxation mechanism, and the dipolar relaxation which is the basis for the well-known nuclear Overhauser effect (NOE), mostly used in the homonuclear H, H case. The 2D HOESY method between H and Li has been used to obtain structural information of many organolithium systems in solution and this field was reviewed in 1995. Li is commonly used as the relaxation is dominated by the dipole-dipole mechanism and the relaxation time is relatively long. Knowledge of the proximity of the lithium cation relative to protons in the substrate is used to derive information about the structure and aggregation of organolithium systems in solution. In a few cases quantitative investigations have been made °. An average error of the lithium position of ca 0.2 A was reported. 

The influence of the homonuclear magnetic dipole-dipole interaction on can be reduced either by an increase of the sample spinning frequency, Vjot, (Eq. (20)) or by the application of a multiple-pulse sequence causing an additional averaging of this interaction (combined rotation and multiple-pulse spectroscopy, CRAMPS 19-21 ). With today s instruments, sample spinning frequencies of up to 40 kHz can be reached using MAS NMR rotors with an outer diameter of 2.0 mm. 

The scheme of calculation we have outlined has been widely applied to diatomic molecules. In this way the authors of Ref. 107 have obtained formulas for the cross sections of excitation of rotational levels owing to the charge-dipole (for heteronuclear molecules) and the charge-quad-rupole (for homonuclear molecules) interactions. These results are in satisfactory agreement with experimental data at small velocities of the incident electron. 

To determine orientation of an adsorbed molecule relative to the mineral surface, one would need to employ dipolar recoupling techniques to extract the distance constraints between the selected spin species of the molecule and of the surface. For polypeptide-HAp systems, 13C 31P REDOR has been carried out for uniformly 13C labeled molecules, where numerical simulations show that the effect of 13C dipole-dipole interaction is relatively minor.125 For a study of bone sample, o-phospho-L-serine was taken as the model compound for the setup of the 13C 31P REDOR experiments, where the data can be well analyzed by a l3C-3lP spin-pair model with the intemuclear distance equal to 2.7 A.126 Concerning the effect of 31P homonuclear dipolar interaction on the spin dynamics, Drobny and co-workers have carried out a detailed REDOR NMR study of polycrystalline diammonium hydrogen phosphate ((NH4)2F1P04).127,128 The results show that the 15N 31P REDOR data can... 

However, preparation of partially or fully deuterated materials may not always be feasible and single crystal samples are not always available. Hence, techniques have been developed that allow high-resolution solid state H NMR spectra to be recorded for powder samples without any isotope enrichment. Homonuclear H dipole-dipole interactions are typically of the order of 50 kHz leading to very broad spectra as discussed above. In order to alleviate the effects of the homonuclear dipole-dipole interactions and obtain a H NMR spectrum that... 

Fig. 2 Timing diagram of the spin echo decay spectroscopy method devised for the measurement of homonuclear dipole-dipole interactions...

Experimental studies have shown that, in practice, the effect of second-order quadrupolar interactions can produce gross deviations from a Gaussian-type decay curve, reflecting the influence of higher moments on the time evolution behavior [ 11 ]. It has been shown, however, that dipolar information can still be obtained if the analysis is restricted to the initial curvature in the limit of short dipolar evolution times (2ti<200 ps). The validity of this approach has been tested recently for homonuclear Na- Na dipole-dipole interactions in crystalline solids, for which the M2 values are readily calculable from the known crystal structures [11]. 

Static spin echo decay spectroscopy also forms the basis for the measurement of magnetic dipole-dipole interactions between two unlike nuclei I and S. While this interaction is refocused by the Hahn spin echo, it can be recoupled by applying a 7i-pulse to the S-spins during the dipolar evolution period [12]. This manipulation inverts the sign of the heterodipolar Hamiltonian, and thereby interferes with the ability of the Hahn spin echo technique to refocus this interaction. The corresponding pulse sequence, termed SEDOR spin echo double resonance) shown in Fig. 4, compares the I-spin echo intensity as a function of dipolar evolution time (a) in the absence and (b) in the presence of the ti(S) pulses. Experiment (a) produces a decay F(2ti)/Fo, which is dominated by homonuclear dipole-dipole interactions, while experiment (b) results in an accelerated decay, reflecting the contribution from the heteronuclear I-S dipole-dipole interaction, which is now re-introduced into the spin Hamiltonian. For multi-spin systems, a Gaussian decay is expected ... 

NMR studies devoted to this issue exploit two-dimensional zero- or double quantum NMR methods to recouple homonuclear magnetic dipole-dipole interactions in MAS-spectra. The connectivity information then stems from the presence (or absence) of crosspeaks linking resolved resonances attributable to distinct sites. To date, this type of analysis has been predominantly ap-... 

Even so, there are numerous experimental and theoretical difficulties to overcome relating directly to the measurement. For example, the reliable quantification of homonuclear dipole-dipole interactions under high-resolution conditions (with MAS) in multispin systems is still an unsolved problem, in particular when quadrupolar nuclei are involved. Likewise, no rigorous strategy seems to be available at present for the REDOR measurement of heteronuclear dipolar coupling between two quadrupolar nuclear species. In this connection, it is of the utmost importance that NMR spectroscopy remains a vital and attractive research area in its own right. Assuredly, the continued influx of new solid state NMR technology into this research area will provide an... 

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