Homonuclear Recoupling Research Articles

HORRENDOUS NMR: Establishing correlations in solution-state NMR by reinstating non-secular J-coupling terms

Homonuclear isotropic mixing modules allow J-coupled spins to exchange magnetization even when separated by chemical shift offsets that exceed their couplings. This is exploited in TOtal Correlation SpectroscopY (TOCSY) experiments and its variants, which facilitate these homonuclear polarization exchanges by applying broadband RF pulses. These then establish an effective Hamiltonian in which chemical shift offsets are erased, while J-coupling terms –including flip-flop components– remain active. The polarization that these non-secular terms will transfer among systems of chemically inequivalent sites over the course of a mixing period, are widely used modules in 1D and in multidimensional liquid-state NMR. Homonuclear correlation experiments are also common in solids NMR, particularly among X = 13C or 15N nuclei. Solids NMR experiments are often challenged by high-power RF demands which have led to a family of homonuclear solid-state correlation experiments that avoid pulsing on the nuclei of interest, and focus instead on the 1Hs that are bonded to them. These solid experiments usually reintroduce/strengthen 1H-X dipolar couplings; these, in conjunction with assistance from rotational resonance effects, bring back the truncated X-X dipolar interactions and facilitate the generation of cross peaks. The present study explores whether a similar goal can be achieved for solution-state counterparts, based on the reintroduction of truncated flip-flop terms in the J-coupling Hamiltonian via the pulsing on other, heteronuclear species. A proposal to achieve this is derived, and the resulting HOmonucleaR Recoupling by hEteroNuclear DecOUplingS (HORRENDOUS) approach to provide correlations between like nuclei without pulsing on them, is demonstrated.

Theory of frequency-selective homonuclear dipolar recoupling in solid-state NMR.

In solid-state nuclear magnetic resonance, frequency-selective homonuclear dipolar recoupling is key to quantitative distance measurement or selective enhancement of correlations between atoms of interest in multiple-spin systems, which are not amenable to band-selective or broadband recoupling. Previous frequency-selective recoupling is mostly based on the so-called rotational resonance (R2) condition that restricts the application to spin pairs with resonance frequencies differing in integral multiples of the magic-angle spinning (MAS) frequency. Recently, we have proposed a series of frequency-selective homonuclear recoupling sequences called SPR (short for Selective Phase-optimized Recoupling), which have been successfully applied for selective 1H-1H or 13C-13C recoupling under from moderate (∼10kHz) to ultra-fast (150kHz) MAS frequencies. In this study, we fully analyze the average Hamiltonian theory of SPR sequences and reveal the origin of frequency selectivity in recoupling. The theoretical description, as well as numerical simulations and experiments, demonstrates that the frequency selectivity can be easily controlled by the flip angle (p) in the (p)ϕk(p)ϕk+π unit in the pSPR-Nn sequences. Small flip angles lead to frequency-selective recoupling, while large flip angles may lead to broadband recoupling in principle. The result shall shed new light on the designof homonuclear recoupling sequences with arbitrary frequency bandwidths.

On the use of radio-frequency offsets for improving double-quantum homonuclear dipolar recoupling of half-integer-spin quadrupolar nuclei.

Detecting proximities between nuclei is crucial for atomic-scale structure determination with nuclear magnetic resonance (NMR) spectroscopy. Different from spin-1/2 nuclei, the methodology for quadrupolar nuclei is limited for solids due to the complex spin dynamics under simultaneous magic-angle spinning (MAS) and radio-frequency irradiation. Herein, the performances of several homonuclear rotary recoupling (HORROR)-based homonuclear dipolar recoupling sequences are evaluated for 27 Al (spin-5/2). It is shown numerically and experimentally on mesoporous alumina that outperforms the supercycled S3 sequence and its pure double-quantum (DQ) (bracketed) version, [S3 ], both in terms of DQ transfer efficiency and bandwidth. This result is surprising since the S3 sequence is among the best low-power recoupling schemes for spin-1/2. The superiority of is thoroughly explained, and the crucial role of radio-frequency offsets during its spin dynamics is highlighted. The analytical approximation of , derived in an offset-toggling frame, clarifies the interplay between offset and DQ efficiency, namely, the benefits of off-resonance irradiation and the trough in DQ efficiency for when the irradiation is central between two resonances, both for spin-1/2 and half-integer-spin quadrupolar nuclei. Additionally, density matrix propagations show that the sequence, applied to quadrupolar nuclei subject to quadrupolar interaction much larger than radio-frequency frequency field, can create single- and multiple-quantum coherences for near on-resonance irradiation. This significantly perturbs the creation of DQ coherences between central transitions of neighboring quadrupolar nuclei. This effect explains the DQ efficiency trough for near on-resonance irradiation, in the case of both cross-correlation and autocorrelation peaks. Overall, this work aids experimental acquisition of homonuclear dipolar correlation spectra of half-integer-spin quadrupolar nuclei and provides theoretical insights towards improving recoupling schemes at high magnetic field and fast MAS.

Spectral editing of alanine, serine, and threonine in uniformly labeled proteins based on frequency-selective homonuclear recoupling in solid-state NMR.

Spectral editing is crucial to simplify the crowded solid-state NMR spectra of proteins. New techniques are introduced to edit 13C-13C correlations of uniformly labeled proteins under moderate magic-angle spinning (MAS), based on our recent frequency-selective homonuclear recoupling sequences [Zhang et al., J. Phys. Chem. Lett. 2020, 11, 8077-8083]. The signals of alanine, serine, or threonine residues are selected out by selective 13Cα-13Cβ double-quantum filtering (DQF). The 13Cα-13Cβ correlations of alanine residues are selectively established with efficiency up to ~ 1.8 times that by dipolar-assisted rotational resonance (DARR). The techniques are shown in 2D/3D NCCX experiments and applied to the uniformly 13C, 15N labeled Aquaporin Z (AqpZ) membrane protein, demonstrating their potential to simplify spectral analyses in biological solid-state NMR.

Homonuclear dipolar recoupling of arbitrary pairs in multi-spin systems under magic angle spinning: A double-frequency-selective ZQ-SEASHORE experiment

We describe a useful method for measuring the internuclear distances within arbitrarily selected pairs of like nuclei in dipolar-coupled multi-spin systems. The method uses a combination of the zero-quantum shift-evolution-assisted selective homonuclear recoupling (ZQ-SEASHORE) technique developed by Hu and Tycko [J. Chem. Phys. 2009, 131, 045101] and double-frequency-selective radio-frequency pulse. The double-frequency-selective pulse inverts polarizations of two spins simultaneously, and thus applications of the method presented here are only limited by the spectral resolution, and not by the number of interacting spins. Our experiments demonstrate the validity of the method and present analytical expressions for the dephasing curve.

Transient effects in π-pulse sequences in MAS solid-state NMR

Dipolar recoupling techniques that use isolated rotor-synchronized π pulses are commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological molecules. These sequences excel through their simplicity, stability towards radio-frequency (rf) inhomogeneity, and low rf requirements. For a theoretical understanding of such sequences, we present a Floquet treatment based on an interaction-frame transformation including the chemical-shift offset dependence. This approach is applied to the homonuclear dipolar-recoupling sequence Radio-Frequency Driven Recoupling (RFDR) and the heteronuclear recoupling sequence Rotational Echo Double Resonance (REDOR). Based on the Floquet approach, we show the influence of effective fields caused by pulse transients and discuss the advantages of pulse-transient compensation. We demonstrate experimentally that the transfer efficiency for homonuclear recoupling can be doubled in some cases in model compounds as well as in simple peptides if pulse-transient compensation is applied to the π pulses. Additionally, we discuss the influence of various phase cycles on the recoupling efficiency in order to reduce the magnitude of effective fields. Based on the findings from RFDR, we are able to explain why the REDOR sequence does not suffer in the recoupling efficiency despite the presence of effective fields.

Two pulse recoupling

The paper describes a family of novel recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, called two pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block (π)ϕ(π)-ϕ where ϕ=π4n, and n is number of blocks in a rotor period. The recoupling block is made robust to rf-inhomogeneity by extending it to (π)ϕ(π)-ϕ(π)π+ϕ(π)π-ϕ. The heteronuclear recoupling pulse sequence consists of a building block (π)ϕ1(π)-ϕ1 and (π)ϕ2(π)-ϕ2 on channel I and S, where ϕ1=3π8n,ϕ2=π8n and n is number of blocks in a rotor period. The recoupling block is made robust to rf-inhomogeneity by extending it to (π)ϕ1(π)-ϕ1(π)π+ϕ1(π)π-ϕ1 and (π)ϕ2(π)-ϕ2(π)π+ϕ2(π)π-ϕ2 on two channels respectively. The recoupling pulse sequences mix the z magnetization. Experimental quantification of this method is shown for13Cα-13CO homonuclear recoupling in a sample of Glycine and 15N-13Cα heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-13C,15N]-Met-Leu-Phe-OH (MLF). Compared to R-sequences (Levitt, 2002), these sequences are more robust to rf-inhomogeneity and give better sensitivity, as shown in Fig. 3.

Four pulse recoupling

The paper describes a family of novel recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, called four pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block π20°3π2ϕ°π2180°+ϕ°3π2180° where ϕ=πnϕ°=180°n, and n is number of blocks in a two rotor period. The heteronuclear recoupling pulse sequence consists of a building block π20°3π2ϕ1°π2180°+ϕ1°3π2180° and π20°3π2ϕ2°π2180°+ϕ2°3π2180°on channel I and S, where ϕ1=3π2n,ϕ2=π2n and n is number of blocks in a two rotor period. The recoupling pulse sequences mix the y magnetization. We show that four pulse recoupling is more broadband compared to three pulse recoupling [1]. Experimental quantification of this method is shown for 13Cα-13CO, homonuclear recoupling in a sample of Glycine and 15N-13Cα, heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-13C,15N]-Met-Leu-Phe-OH (MLF).

Recoupling pulse sequences with constant phase increments

The paper studies a family of recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, that are characterized by constant phase increments at regular intervals. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block (2π)ϕp, where ϕp=p(n-1)πn, where n is number of blocks in a rotor period and p=0,1,2,…. The pulse sequence repeats itself every rotor period when n is odd and every two rotor period when n is even. The heteronuclear recoupling pulse sequence consists of a building block (2π)ϕ1p and (2π)ϕ2p on channel I and S, where ϕ1p=p(2n-3)π2n,ϕ2p=p(2n-1)π2n and n is number of blocks in a rotor period. The recoupling pulse sequences mix the z magnetization. Experimental quantification of this method is shown for 13Cα-13CO, homonuclear recoupling in a sample of Glycine and 15N-13Cα, heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-13C,15N]- Met-Leu-Phe-OH (MLF).

A Floquet description of phase alternated sequences for efficient homonuclear recoupling in solid perdeuterated systems

A Floquet description of a phase alternated homonuclear recoupling scheme for perdeuterated systems is presented. As a result, we demonstrate improvements in the recoupling efficiency of the DOuble Nucleus Enhanced Recoupling [DONER; J. Am. Chem. Soc. 131 (2009) 17054] technique by utilizing Phase Alternated Recoupling Irradiation Schemes [PARIS; Chem. Phys. Lett. 469 (2009) 342]. The effect of proton and deuterium radio frequency irradiation during recoupling has been systematically studied and theoretical observations have been verified experimentally using a deuterated model compound, l-Alanine, at 10 and 20kHz magic angle spinning frequency. Experimental results are well in agreement with theoretical observations, thereby significantly increasing the recoupling efficiency of conventional DONER in perdeuterated systems.

13C-13C Homonuclear Recoupling in Solid-State Nuclear Magnetic Resonance at a Moderately High Magic-Angle-Spinning Frequency

Two-dimensional 13C-13C correlation experiments are widely employed in structure determination of protein assemblies using solid-state nuclear magnetic resonance. Here, we investigate the process of 13C-13C magnetisation transfer at a moderate magic-angle-spinning frequency of 30 kHz using some of the prominent second-order dipolar recoupling schemes. The effect of isotropic chemical-shift difference and spatial distance between two carbons and amplitude of radio frequency on 1H channel on the magnetisation transfer efficiency of these schemes is discussed in detail.

Radio frequency assisted homonuclear recoupling – A Floquet description of homonuclear recoupling via surrounding heteronuclei in fully protonated to fully deuterated systems

We present a Floquet theory approach for the analysis of homonuclear recoupling assisted by radio frequency (RF) irradiation of surrounding heteronuclear spins. This description covers a broad range of systems from fully protonated to deuterated proteins, focusing in detail on recoupling via protons and deuterons separately as well as simultaneously by the double nucleus enhanced recoupling (DONER) scheme. The theoretical description, supported by numerical simulations and compared to experimental results from a partially deuterated model compound, indicates that in perdeuterated systems setting the RF amplitude equal to the magic angle spinning (MAS) frequency is not necessarily optimal for recoupling via 1H and/or 2H nuclei and modified recoupling conditions are identified.

Zero-quantum frequency-selective recoupling of homonuclear dipole-dipole interactions in solid state nuclear magnetic resonance

We describe a method for measuring magnetic dipole-dipole interactions, and hence distances, between pairs of like nuclear spins in a many-spin system under magic-angle spinning (MAS). This method employs a homonuclear dipolar recoupling sequence that creates an average dipole-dipole coupling Hamiltonian under MAS with full zero-quantum symmetry, including both secular and flip-flop terms. Flip-flop terms are then attenuated by inserting rotor-synchronized periods of chemical shift evolution between recoupling blocks, leaving an effective Hamiltonian that contains only secular terms to a good approximation. Couplings between specific pairs of nuclear spins can then be selected with frequency-selective pi pulses. We demonstrate this technique, which we call zero-quantum shift evolution assisted homonuclear recoupling, in a series of one-dimensional and two-dimensional (13)C NMR experiments at 17.6 T and 40.00 kHz MAS frequency on uniformly (13)C-labeled L-threonine powder and on the helix-forming peptide MB(i+4)EK, synthesized with a pair of uniformly (13)C-labeled L-alanine residues. Experimental demonstrations include measurements of distances between (13)C sites that are separated by three bonds, placing quantitative constraints on both sidechain and backbone torsion angles in polypeptides.

High-resolution 1H homonuclear dipolar recoupling NMR spectra of biological solids at MAS rates up to 67 kHz

Two-dimensional 1H homonuclear correlation NMR spectra of solids of biological interest have been recorded at high magnetic fields (14.1 and 18.8 T) and MAS rates up to 67 kHz, using RN n ν symmetry-based homonuclear recoupling and CRAMPS decoupling; this method affords exceptional spectral resolution and is well suited to probe 1H– 1H proximities in powdered solids.

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.

Characterization of microporous aluminophosphate IST-1 using 1H Lee–Goldburg techniques

The presence of two independent methylamine species in microporous aluminophosphate IST-1 (|(CH 3NH 2) 4(CH 3NH + 3) 4(OH −) 4|[Al 12P 12O 48]) has been shown previously by synchrotron powder X-ray diffraction. One of these species, [N(1)–C(1)], links to a six-coordinated framework Al-atom [Al (1)], while the other methylamine [N(2)–C(2)] is protonated and hydrogen-bonded to three O-atoms [O (1), O (2) and O (12)]. We revisit the structure of IST-1 and report the complete assignment of the 1H NMR spectra by combining X-ray data and high-resolution heteronuclear/homonuclear solid-state NMR techniques based on frequency-switched Lee–Goldburg homonuclear decoupling and 31P– 31P homonuclear recoupling. Careful analysis of the 2D 1H–X homonuclear correlation (X = 1H) and 2D heteronuclear correlation (X = 13C, 31P and 27Al) spectra allowed the distinction of both methylamine species and the assignment of all 31P and 13C resonances. For the first time at a relatively high (9.4 T) magnetic field, symmetric doublet patterns have been observed in the 13C spectra, caused by the influence of the 14N second-order quadrupolar interaction.

Broadband Homonuclear Correlation Spectroscopy at High Magnetic Fields and MAS Frequencies

We present a new homonuclear recoupling sequence, CMAR, that allows observation of 2D 13C-13C correlation spectra at high magnetic fields and MAS frequencies (10-30 kHz). The main advantages of the sequence are that it provides efficient, broadband dipolar recoupling and concurrently decouples the 1H spins from the 13C's. Thus, no additional 1H decoupling is required during the mixing period, thereby significantly reducing the radio frequency power requirements for the experiment. Thus, CMAR significantly extends the range of applicability of the usual homonuclear recoupling techniques and should be of major interest for structure determinations of biomolecules at high magnetic fields.

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.

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.

Triple-quantum dynamics in multiple-spin systems undergoing magic-angle spinning: application to 13C homonuclear correlation spectroscopy

We analyze the multiple-quantum dynamics governed by a new homonuclear recoupling strategy effecting an average dipolar Hamiltonian comprising three-spin triple-quantum operators (e.g., S p + S q + S r + ) under magic-angle spinning conditions. Analytical expressions are presented for polarization transfer processes in systems of three and four coupled spins-1/2 subject to triple-quantum filtration (3QF), and high-order multiple-quantum excitation is investigated numerically in moderately large clusters, comprising up to seven spins. This recoupling approach gives highly efficient excitation of triple-quantum coherences: ideally, up to 67% of the initial polarization may be recovered by 3QF in three-spin systems in polycrystalline powders. Two homonuclear 2D correlation strategies are demonstrated experimentally on powders of uniformly 13C-labeled alanine and tyrosine: the first correlates the single-quantum spectrum in the first dimension with the corresponding 3QF spectrum along the other. The second protocol correlates triple-quantum coherences with their corresponding single-quantum coherences within triplets of coupled spins.