Rotary Resonance Recoupling Research Articles

Applications of Floquet–Magnus and Fer expansion approaches on rotary-resonance recoupling sequence in solid-state nuclear magnetic resonance

In this work, we used the Floquet–Magnus expansion (FME) and the Fer expansion (FE) approaches to investigate the spin dynamics during the rotary-resonance recoupling (R3) radiation experiment in solid-state nuclear magnetic resonance (SSNMR). We reformulated the two approaches and calculated their respective effective Hamiltonians and propagators. We compared the two approaches and found that the FME is more appropriate to describe the spin dynamics in the R3 experiment compared to the FE. The equations governing the spin dynamics of the first three orders of the FME look similar to the equations of the FE. Nevertheless, the FME has two additional parameters making the approach more applicable to various situations. This clearly shows that the FME will be more practical for the modifications of the R3 pulse sequence with the major corrections coming from the terms that include the additional parameters, which are not available in the FE. This work is significant and contributes theoretically and numerically in the field of spin dynamics, magnetic resonance and in particular SSNMR.

ChemInform Abstract: Nitrogen‐Proton Correlation Experiments of Organic Solids at Natural Isotopic Abundance

AbstractReview: 42 refs.

Probing proximities between different quadrupolar isotopes using multi-pulse cross-polarization

We present a novel cross-polarization MAS NMR pulse sequence to probe proximities between half-integer quadrupolar isotopes. This sequence employs a multi-pulse cross-polarization (MP-CP) transfer, instead of the previous continuous-wave CP (CW-CP) transfer. With respect to CW-CP transfers, our sequence is more robust with respect to offsets and Rotary Resonance Recoupling detrimental effects, especially when taking into account rf-inhomogeneity. Moreover, by using a frequency splitter and a single channel MAS probe, this MP-CP sequence may allow analyzing the through-space connectivities between two isotopes with half-integer spin values and close Larmor frequencies.

14N–1H Heteronuclear Multiple-Quantum Correlation Magic-Angle Spinning NMR Spectroscopy of Organic Solids

Abstract 14N–1H heteronuclear multiple-quantum correlation (HMQC) solid-state magic-angle spinning (MAS) NMR spectra recorded at a 1H Larmor frequency of 850 MHz are presented for the dipeptide β-AspAla. A modified version of the pulse sequence presented by Gan et al. (Chem. Phys. Lett. 435 (2007) 163) that utilises rotary resonance recoupling (R3) at the n = 2 condition (ν 1 = 2ν R ) is employed. Spectra recorded with a short recoupling period (under 200 μs) show two correlation peaks corresponding to the NH and NH3 moieties in the dipeptide. The quadrupolar product, P Q = C Q √ [1 + (η Q 2/3)], is determined experimentally as 3.1 MHz (NH) and 1.0 MHz (NH3) by a comparison of the 14N and 15N isotropic chemical shifts which differ due to the isotropic second-order quadrupolar shift for the spin I = 1 14N nucleus. It is shown that the peak sensitivities increase markedly upon increasing the MAS frequency from 30 to 45 to 60 kHz due to a combination of the reduced residual dipolar broadening of the 1H resonances and a lengthening of the coherence lifetimes under R 3 recoupling. Increasing the recoupling period leads to the observation of additional peaks corresponding to longer range intra- and intermolecular NH proximities. Reasonable agreement is evident upon comparing the experimental build-up of correlation peak intensity to that observed for eight-spin density-matrix simulations.

High-resolution through-space correlations between spin-1/2 and half-integer quadrupolar nuclei using the MQ-D-R-INEPT NMR experiment

The multiple-quantum dipolar refocused-INEPT (MQ-D-R-INEPT) NMR experiment is presented. This new pulse sequence allows the generation of two-dimensional through-space NMR correlation spectra between spin-½ and quadrupolar nuclei under high-resolution. Compared to the existing sequences, the MQ-D-R-INEPT sequence benefits from increased robustness, due to the reduced sensitivity to offsets and radio-frequency field inhomogeneity of the R-INEPT recoupling scheme as compared to the classical cross-polarization transfer involving a quadrupolar nucleus, and applicability to quadrupolar nuclei with any half-integer spin value. Here, the heteronuclear dipolar couplings have been reintroduced using the rotary resonance recoupling (R(3)) sequence, chosen because it is γ-encoded, and thus robust to spinning speed instabilities and to radio-frequency inhomogeneities in the case of nuclei subjected to large chemical shift anisotropy (e.g., (31)P). In the course of the article, a new definition of γ-encoding is introduced, more general and practical than the previous ones, as it does not depend on the implementation of the recoupling sequence, and is independent of the considered frame. The efficiency of the MQ-D-R-INEPT experiment is demonstrated for the observation of (31)P-(27)Al proximities. It is first tested on AlPO4-VPI-5, and then applied to a complex aluminophosphate AlPO4-(Al5P7)-DAE of incompletely established structure. For this latter sample, the high-resolution provided by the MQMAS filter allows the resolution of a large number of (31)P-(27)Al correlations, which represent an essential step towards the determination of its structural model.

Probing the quenching of rotary resonance by PISSARRO decoupling

Solid-state NMR experiments may suffer from rotary resonance recoupling ( R 3) due to the interference between sample spinning at a frequency ν rot and rf irradiation with an amplitude ν 1 H in the vicinity of harmonic relationships ν 1 H = n ν rot where n = 1 or 2. Until recently, only the use of very high rf amplitudes (e.g., ν 1 H ≫ 2 ν rot ) made it possible to avoid such interference effects. With the advent of PISSARRO decoupling, the deleterious effects of rotary resonance recoupling can be quenched, notably for ν 1 H = 2 ν rot , so that demands on the rf amplitude ν 1 H are relaxed. Here, we discuss how PISSARRO decoupling benefits from mirror symmetry and phase-shifting. We also show that PISSARRO can cope with the chemical shift anisotropy of protons and with proton–proton dipolar interactions. PISSARRO is most effective for very fast spinning at very high static fields.

Double-quantum homonuclear correlations of spin I = 5/2 nuclei

The challenges associated with acquiring double-quantum homonuclear Nuclear Magnetic Resonance correlation spectra of half-integer quadrupolar nuclei are described. In these experiments the radio-frequency irradiation amplitude is necessarily weak in order to selectively excite the central transition. In this limit only one out of the 25 double-quantum coherences possible for two coupled spin I=5/2 nuclei is excited. An investigation of all the 25 two spins double quantum transitions reveals interesting effects such as a compensation of the first-order quadrupolar interaction between the two single quantum transitions involved in the double quantum coherence. In this paper a full numerical study of a hypothetical two spin I=5/2 system is used to show what happens when the RF amplitude during recoupling is increased. In principle this is advantageous, since the required double quantum coherence should build up faster, but in practice it also induces adiabatic passage transfer of population and coherence which impedes any build up. Finally an optimized rotary resonance recoupling (oR3) sequence is introduced in order to decrease these transfers. This sequence consists of a spin locking irradiation whose amplitude is reduced four times during one rotor period, and allows higher RF powers to be used during recoupling. The sequence is used to measure 27Al DQ dipolar correlation spectra of Y3Al5O12 (YAG) and gamma alumina (γAl2O3). The results prove that aluminium vacancies in gamma alumina mainly occur in the tetrahedral sites.

Interresidue carbonyl–carbonyl polarization transfer experiments in uniformly 13C, 15N-labeled peptides and proteins

In this work, we demonstrate that Homonuclear Rotary Resonance Recoupling (HORROR) can be used to reintroduce carbonyl–carbonyl interresidue dipolar interactions and to achieve efficient polarization transfer between carbonyl atoms in uniformly 13C, 15N-labeled peptides and proteins. We show that the HORROR condition is anisotropically broadened and overall shifted to higher radio frequency intensities because of the CSA effects. These effects are analyzed theoretically using Average Hamiltonian Theory. At spinning frequencies used in this study, 22 kHz, this broadening is experimentally found to be on the order of a kilohertz at a proton field of 600 MHz. To match HORROR condition over all powder orientations, variable amplitude radio frequency (RF) fields are required, and efficient direct transfers on the order of 20–30% can be straightforwardly established. Two- and three-dimensional chemical shift correlation experiments establishing long-range interresidue connectivities (e.g., (N[i]–CO[i − 2])) are demonstrated on the model peptide N-acetyl-valine-leucine, and on the third immunoglobulin binding domain of protein G. Possible future developments are discussed.

Two-dimensional 43Ca– 1H correlation solid-state NMR spectroscopy

Calcium-43 (nuclear spin, S=7/2) is an NMR insensitive low- γ quadrupolar nucleus and up until recently only one-dimensional solid-state 43Ca NMR spectra have been reported. Through-space correlation experiments are challenging between spin- 1 2 and low- γ quadrupolar nuclei because of the intrinsically weak dipolar interaction and the often-low natural abundance of the quadrupolar nucleus. Rotary-resonance recoupling ( R 3) has recently been used to re-introduce hetero-nuclear dipolar interactions for sensitive high- γ quadrupolar nuclei, but has not yet been applied in the case of low- γ half-integer quadrupolar nuclei. Here an effective and robust 2D 1H- 43Ca NMR correlation experiment combining the R 3 dipole-recoupling scheme with 2D HMQC is presented. It is demonstrated that the weak 43Ca– 1H dipolar coupling in hydroxyapatite and oxy-hydroxyapatite can be readily re-introduced and that this recoupling scheme is more efficient than conventional cross-polarization transfer. Moreover, three 43Ca– 1H dipolar coupled calcium environments are clearly resolved in the structurally unknown oxy-hydroxyapatite. This local information is not readily available from other techniques such as powder XRD and high resolution electron microscopy. R 3-HMQC is also a desirable experiment because the set-up is simple and it can be applied using conventional multi-resonance probes.

Comparison of several hetero-nuclear dipolar recoupling NMR methods to be used in MAS HMQC/HSQC

We compare several hetero-nuclear dipolar recoupling sequences available for HMQC or HSQC experiments applied to spin-1/2 and quadrupolar nuclei. These sequences, which are applied to a single channel, are based either on the rotary resonance recoupling ( R 3) irradiation, or on two continuous rotor-synchronized modulations (SFAM 1 and SFAM 2), or on four symmetry-based sequences ( R 2 1 1 , SR 4 1 2 , R 12 3 5 , R 20 5 9 ) , or on the REDOR scheme. We analyze systems exhibiting purely hetero-nuclear dipolar interactions as well as systems where homo-nuclear dipolar interactions need to be canceled. A special attention is given to the behavior of these sequences at very fast MAS. It is shown that R 3 methods behave poorly due to the narrowness of their rf-matching curves, and that the best methods are SR 4 1 2 and SFAM (SFAM 1 or SFAM 2 if homo-nuclear interactions are not negligible). REDOR can also recouple efficiently hetero-nuclear dipolar interactions, provided the sequence is sent on the non-observed channel and homo-nuclear dipolar interactions are negligible. We anticipate that at ultra-fast spinning speed, SFAM 1 and SFAM 2 will be the most efficient methods.

Decoupling and recoupling using continuous-wave irradiation in magic-angle-spinning solid-state NMR: A unified description using bimodal Floquet theory

The application of two or more different time-dependent coherent perturbations with, in general, incommensurable frequencies occurs quite commonly in NMR experiments. Here we develop a unified description of the entire class of experiments using bimodal Floquet theory and van Vleck-Primas perturbation theory. This treatment leads to a time-independent effective Hamiltonian in Hilbert space and can be looked at as a generalization of average Hamiltonian theory to several incommensurate time dependencies. As a prototype experiment we treat the application of continuous-wave (cw) radio-frequency irradiation in combination with magic-angle sample spinning. Practically relevant examples of this type of experiments are heteronuclear spin decoupling and recoupling experiments using cw irradiation, e.g., rotary-resonance recoupling. Perturbations up to the third order must be taken into account to explain all experimentally observed resonance conditions.

Rotary resonance recoupling for half-integer quadrupolar nuclei in solid-state nuclear magnetic resonance spectroscopy

Investigations were made of rotary resonance recouplings (R3) of chemical shift anisotropy (CSA), heteronuclear dipolar (HTD), and homonuclear dipolar (HMD) couplings involving half-integer quadrupolar nuclei under magic-angle sample spinning condition. Under rotary resonance conditions provided by a low amplitude rf field and a high spinning speed, the spectrum of the central transition coherence of half-integer quadrupolar nuclei shows recouplings of CSA, HTD, and HMD interactions that depend on the ratio of the rf field to the spinning speed. These new properties can be used to extract electronic and structural information about the sample that are otherwise difficult to extract in the presence of a dominant quadrupolar interaction. An average Hamiltonian theory is used to explain the recoupling properties of various interactions. Experimental implementations of the R3 are demonstrated on model compounds with spin-3/2 systems.

Reintroducing anisotropic interactions in magic-angle-spinning NMR of half-integer quadrupolar nuclei: 3D MQMAS.

Selective reintroduction of anisotropic interactions such as the chemical shift anisotropy (CSA) and homonucler dipolar (HMD) coupling were implemented in a high-resolution NMR spectroscopy for half-integer quadrupolar nuclei. Rotary resonance recoupling (R(3)) combined with the multiple-quantum magic-angle spinning (MQMAS) in a three-dimensional (3D) experiment provides not only site-specific high-resolution spectra to yield the quadrupolar interaction parameters but also the CSA or HMD interaction parameters. This 3D experiment provides an avenue for the complete local structural information of half-integer quadrupolar nuclei. Three-dimensional MQMAS experiments incorporating R(3) of HMD and CSA interactions were demonstrated on model compounds containing (11)B, (23)Na, and (87)Rb nuclei.

Rotary resonance recoupling of [formula omitted] dipolar interactions in magic angle spinning [formula omitted] NMR of dynamic solids

Rotary resonance recoupling of heteronuclear 13 C− 1 H dipolar interactions in magic angle spinning solid state 13 C NMR spectra (recorded under conditions of 1 H decoupling at frequency ν 1 and magic angle spinning at frequency ν r) has been studied for three examples of molecular solids (adamantane, ferrocene and hexamethylbenzene) in which substantial molecular motion is known to occur. It is shown that when rotary resonance conditions are satisfied (i.e. ν 1/ ν r= n, for n=1 or 2), the recoupling can lead to motionally averaged Pake-like powder patterns from which information on 13 C− 1 H internuclear distances and/or molecular motion can be derived.

31P and 13C chemical shielding tensors in the phosphoenolpyruvate moiety from rotary resonance recoupling 13C and 31P MAS and single crystal 31P NMR

A 31P and 13C NMR study of powder and single crystal samples of two phosphoenolpyruvate (PEP) compounds, the tris-ammonium salt monohydrate (NH4)3(PEP)·H2O (1), and the mono-ammonium-salt (NH4)(H2PEP) (2) is presented. The P chemical shielding tensors in 1 are measured by 31P single crystal NMR on four minuscule samples and assigned without ambiguity by exploiting the orientation-dependent 31P-31p dipolar splittings of the resonance lines. The orientation of the 31P chemical shielding tensor is discussed in terms of the C2v — and C3-type distortions of the phosphate PO4-coordination sphere. From 13C MAS NMR experiments with 31P rotary resonance recoupling on polycrystalline powder samples the orientations of the 31P chemical shielding tensors in 1 and 2 are obtained, for 1 in very good agreement with the 31P single crystal NMR results. Only some of the orientational parameters of the three 13C chemical shielding tensors in the PEP moiety of 1 could be derived from 13C MAS NMR experiments with 31P rotary resonance recoupling.

Rotary resonance recoupling of dipolar interactions in solid-state nuclear magnetic resonance spectroscopy

A new resonance effect in solid-state nuclear magnetic resonance (NMR) is described. The effect involves a combination of magic-angle sample rotation with irradiation of a heteronuclear spin system at the Larmor frequency of one of the spin species. If the irradiation intensity is such as to establish a match between spin nutation and sample rotation, it is shown that the heteronuclear dipolar spin interaction is selectively reintroduced into the spectrum. This allows small dipolar coupling constants to be measured in the presence of large shielding anisotropies. Applications are anticipated for determination of internuclear distances in materials lacking long-range order, such as polycrystalline materials, polymers, and surfaces.

Rotary Resonance Recoupling in Heteronuclear Spin Pair Systems

AbstractIn solid state magic angle spinning experiments on a polycrystalline sample containing dilute heteronuclear spin pairs, the usual spectrum is insensitive to small heteronuclear couplings between the spins, and to the relative orientations of the various interaction tensors. Applying a radio frequency of an intensity chosen to satisfy a rotary resonance condition can restore the heteronuclear splittings in the spectrum. Theory and numerical simulations of this effect are presented. The sensitivity of the spectra to the intensity of the radio frequency field and to the relative orientations of tensors is explored. To fully explain the experimental results, it is necessary to postulate a small phase modulation induced by the motion of the sample through a radio frequency field of non‐uniform direction.