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Heteronuclear spin decoupling is a highly important component of solid-state NMR experiments to remove undesired coupling interactions between unlike spins for spectral resolution. Recently, experiments using a unification strategy of standard decoupling schemes were presented for high radio-frequency (RF) amplitudes and slow-intermediate magic-angle-spinning (MAS) frequencies, in the pursuit of deeper understanding of spin decoupling under phase-modulated RF irradiation [A. Equbal et al., J. Chem. Phys. 142, 184201 (2015)]. The approach, unified two-pulse heteronuclear decoupling (UTPD), incorporates the simultaneous time- and phase-modulation strategies, commonly used in solid-state NMR. Here, the UTPD based decoupling scheme is extended to the experimentally increasingly important regime of low RF amplitudes and fast MAS frequencies. The unified decoupling approach becomes increasingly effective in identifying the deleterious dipole-dipole and, in particular, J recoupling conditions which become critical for the low-amplitude RF regime. This is because J coupling is isotropic and therefore not averaged out by sample spinning unlike the anisotropic dipole-dipole coupling. Numerical simulations and analytic theory are used to understand the effects of various nuclear spin interactions on the decoupling performance of UTPD, in particular, the crucial difference between the low-phase and high-phase UTPD conditions with respect to J coupling. In the UTPD scheme, when the cycle-frequency of the pulse-sequence is comparable to the RF nutation frequency, the existence of a non-zero effective rotation in the basic two-pulse scheme becomes an essential feature for the efficient and robust averaging out of the scalar J coupling. This broad viewpoint is expected to bring different optimum low-power decoupling pulse schemes under a common footing. [ABSTRACT FROM AUTHOR]

We present a general theoretical description that allows us to describe the influence of isotropic chemical shift in homonuclear and heteronuclear dipolar recoupling experiments in magic-angle-spinning solid-state NMR. Through a transformation of the Hamiltonian into an interaction frame with the combined radio-frequency irradiation and the isotropic chemical shift, we determine an effective Hamiltonian to first order with respect to the relevant internal nuclear spin interactions. This unravels the essential resonance conditions for efficient dipolar recoupling. Furthermore, we propose how to handle situations where the resonance conditions are not exactly fulfilled. To verify the general theoretical description, we compare numerical simulations using a time-sliced time-dependent Hamiltonian with simulations using the calculated effective Hamiltonian for propagation. The comparisons are exemplified for the homonuclear dipolar recoupling experiments C72¹ and POST-C72¹. [ABSTRACT FROM AUTHOR]

Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient 1H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the ¹H-¹H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of ¹H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme. [ABSTRACT FROM AUTHOR]

We present a theoretical analysis of the influence of chemical shifts on amplitude-modulated heteronuclear dipolar recoupling experiments in solid-state NMR spectroscopy. The method is demonstrated using the Rotor Echo Short Pulse IRrAdiaTION mediated Cross-Polarization (RESPIRATIONCP) experiment as an example. By going into the pulse sequence rf interaction frame and employing a quintuple-mode operator-based Floquet approach, we describe how chemical shift offset and anisotropic chemical shift affect the efficiency of heteronuclear polarization transfer. In this description, it becomes transparent that the main attribute leading to non-ideal performance is a fictitious field along the rf field axis, which is generated from second-order cross terms arising mainly between chemical shift tensors and themselves. This insight is useful for the development of improved recoupling experiments. We discuss the validity of this approach and present quaternion calculations to determine the effective resonance conditions in a combined rf field and chemical shift offset interaction frame transformation. Based on this, we derive a broad-banded version of the RESPIRATIONCP experiment. The new sequence is experimentally verified using SNNFGAILSS amyloid fibrils where simultaneous 15N→ 13CO and 15N→ 13Cα coherence transfer is demonstrated on high-field NMR instrumentation, requiring great offset stability. [ABSTRACT FROM AUTHOR]

The homonuclear radio-frequency driven recoupling (RFDR) experiment is commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological samples due to its ease of implementation, stability towards fluctuations/missetting of radio-frequency (rf) field strength, and in general low rf requirements. A theoretical operator-based Floquet description is presented to appreciate the effect of having a temporal displacement of the π-pulses in the RFDR experiment. From this description, we demonstrate improved transfer efficiency for the RFDR experiment by generating an adiabatic passage through the zero-quantum recoupling condition. We have compared the performances of RFDR and the improved sequence to mediate efficient 13CO to 13Cα polarization transfer for uniformly 13C,15N-labeled glycine and for the fibril forming peptide SNNFGAILSS (one-letter amino acid codes) uniformly 13C,15N-labeled at the FGAIL residues. Using numerically optimized sweeps, we get experimental gains of approximately 20% for glycine where numerical simulations predict an improvement of 25% relative to the standard implementation. For the fibril forming peptide, using the same sweep parameters as found for glycine, we have gains in the order of 10%-20% depending on the spectral regions of interest. [ABSTRACT FROM AUTHOR]

A unified strategy of two-pulse based heteronuclear decoupling for solid-state magic-angle spinning nuclear magnetic resonance is presented. The analysis presented here shows that different decoupling sequences like two-pulse phase-modulation (TPPM), X-inverse-X (XiX), and finite pulse refocused continuous wave (rCWA) are basically specific solutions of a more generalized decoupling scheme which incorporates the concept of time-modulation along with phase-modulation. A plethora of other good decoupling conditions apart from the standard, TPPM, XiX, and rCWA decoupling conditions are available from the unified decoupling approach. The importance of combined time- and phasemodulation in order to achieve the best decoupling conditions is delineated. The consequences of different indirect dipolar interactions arising from cross terms comprising of heteronuclear and homonuclear dipolar coupling terms and also those between heteronuclear dipolar coupling and chemicalshift anisotropy terms are presented in order to unfold the effects of anisotropic interactions under different decoupling conditions. Extensive numerical simulation results are corroborated with experiments on standard amino acids. [ABSTRACT FROM AUTHOR]

Application of sets of 13C-13C internuclear distance restraints constitutes a typical key element in determining the structure of peptides and proteins by magic-angle-spinning solid-state NMR spectroscopy. Accurate measurements of the structurally highly important 13C-13C distances in uniformly 13C-labeled peptides and proteins, however, pose a big challenge due to the problem of dipolar truncation. Here, we present novel two-dimensional (2D) solid-state NMR experiments capable of extracting distances between carbonyl (13C′) and aliphatic (13Caliphatic) spins with high accuracy. The method is based on an improved version of the four-oscillating field (FOLD) technique [L. A. Straasø, M. Bjerring, N. Khaneja, and N. C. Nielsen, J. Chem. Phys.130, 225103 (2009)] which circumvents the problem of dipolar truncation, thereby offering a base for accurate extraction of internuclear distances in many-spin systems. The ability to extract reliable accurate distances is demonstrated using one- and two-dimensional variants of the FOLD experiment on uniformly 13C,15N-labeled-L-isoleucine. In a more challenging biological application, FOLD 2D experiments are used to determine a large number of 13C′-13Caliphatic distances in amyloid fibrils formed by the SNNFGAILSS fibrillating core of the human islet amyloid polypeptide with uniform 13C,15N-labeling on the FGAIL fragment. [ABSTRACT FROM AUTHOR]

A novel strategy for heteronuclear dipolar decoupling in magic-angle spinning solid-state nuclear magnetic resonance (NMR) spectroscopy is presented, which eliminates residual static high-order terms in the effective Hamiltonian originating from interactions between oscillating dipolar and anisotropic shielding tensors. The method, called refocused continuous-wave (rCW) decoupling, is systematically established by interleaving continuous wave decoupling with appropriately inserted rotor-synchronized high-power π refocusing pulses of alternating phases. The effect of the refocusing pulses in eliminating residual effects from dipolar coupling in heteronuclear spin systems is rationalized by effective Hamiltonian calculations to third order. In some variants the π pulse refocusing is supplemented by insertion of rotor-synchronized π/2 purging pulses to further reduce the residual dipolar coupling effects. Five different rCW decoupling sequences are presented and their performance is compared to state-of-the-art decoupling methods. The rCW decoupling sequences benefit from extreme broadbandedness, tolerance towards rf inhomogeneity, and improved potential for decoupling at relatively low average rf field strengths. In numerical simulations, the rCW schemes clearly reveal superior characteristics relative to the best decoupling schemes presented so far, which we to some extent also are capable of demonstrating experimentally. A major advantage of the rCW decoupling methods is that they are easy to set up and optimize experimentally. [ABSTRACT FROM AUTHOR]

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B0) and rf field (B1) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters 'JCP' in a water phantom. [ABSTRACT FROM AUTHOR]

Strongly enhanced spin polarization in the form of longitudinal spin order can be generated on target molecules by using parahydrogen in a catalyzed hydrogenation reaction. An optimal control algorithm was used to generate radiofrequency pulse sequences which convert the arising longitudinal two-spin order into single-spin Zeeman order with high efficiency and distribute it evenly between three coupled spins within the same molecule. The pulses are designed to be very robust towards variations in the B0 and B1 fields. Furthermore, this strategy is applied to enhance the NMR signal in an ultrafast gradient assisted single excitation two-dimensional spectroscopy experiment. [ABSTRACT FROM AUTHOR]

A new solid-state NMR method, the double-oscillating field technique (DUO), that under magic-angle-spinning conditions produces an effective Hamiltonian proportional to the native high-field homonuclear dipole-dipole coupling operator is presented. The method exploits one part of the radio frequency (rf) field to recouple the dipolar coupling interaction with a relatively high scaling factor and to eliminate offset effects over a reasonable bandwidth while in the recoupling frame, the other part gives rise to a sufficiently large longitudinal component of the residual rf field that averages nonsecular terms and in addition ensures stability toward rf inhomogeneity and rf miscalibration. The capability of the DUO experiment to mediate transfer of polarization is described theoretically and compared numerically and experimentally with finite pulse rf driven recoupling and experimentally with dipolar-assisted rotational resonance. Two-dimensional recoupling experiments were performed on antiparallel amyloid fibrils of the decapeptide SNNFGAILSS with the FGAIL fragment uniformly labeled with 13C and 15N. [ABSTRACT FROM AUTHOR]

The past decade has demonstrated increasing interests in using optimal control based methods within coherent quantum controllable systems. The versatility of such methods has been demonstrated with particular elegance within nuclear magnetic resonance (NMR) where natural separation between coherent and dissipative spin dynamics processes has enabled coherent quantum control over long periods of time to shape the experiment to almost ideal adoption to the spin system and external manipulations. This has led to new design principles as well as powerful new experimental methods within magnetic resonance imaging, liquid-state and solid-state NMR spectroscopy. For this development to continue and expand, it is crucially important to constantly improve the underlying numerical algorithms to provide numerical solutions which are optimally compatible with implementation on current instrumentation and at same time are numerically stable and offer fast monotonic convergence toward the target. Addressing such aims, we here present a smoothing monotonically convergent algorithm for pulse sequence design in magnetic resonance which with improved optimization stability lead to smooth pulse sequence easier to implement experimentally and potentially understand within the analytical framework of modern NMR spectroscopy. [ABSTRACT FROM AUTHOR]

We present design of novel low-power homonuclear dipolar recoupling experiments for magic-angle-spinning solid-state NMR studies of proteins. The pulse sequences are developed by combining principles of symmetry-based dipolar recoupling and optimal control-based pulse sequence design. The scaffold of the pulse sequences is formed by known CN-type recoupling sequences, while the intrinsic sequence elements are designed using optimal control. This procedure allows for the development of high-performance pulse sequences demanding significantly weaker rf fields than previous symmetry-based pulse sequences while compensating for rf inhomogeneity and providing excitation over relevant ranges of chemical shifts for biological applications. The new recoupling experiments, referred to as optimal control CN (OCCN), are demonstrated numerically and experimentally by two-dimensional (2D) 13C–13C and three-dimensional (3D) 15N–13C–13C chemical shift correlation experiments on uniformly 13C, 15N-labeled ubiquitin. Exploiting the double-quantum, band-selective dipolar recoupling properties of the OCCN experiments, we demonstrate significant sensitivity enhancement for 2D and 3D correlation spectra showing exclusively one- or two-bond correlations. [ABSTRACT FROM AUTHOR]

Dipolar truncation prevents accurate measurement of long-range internuclear distances between nuclei of the same spin species, e.g., within 13C–13C spin pairs in uniformly 13C-isotope-labeled proteins, using magic-angle spinning solid-state NMR spectroscopy. Accordingly, one of the richest sources of accurate structure information is at present not exploited fully, leaving the bulk part of the experimentally derived structural constraints to less accurate long-range 13C–13C dipolar couplings estimated from methods based on spin diffusion through proton spins in the close environment. In this paper, we extend our previous triple-oscillating field technique [N. Khaneja and N. C. Nielsen, J. Chem. Phys. 128, 015103 (2008)] for dipolar recoupling without dipolar truncation in homonuclear spin systems to a more advanced rf modulation with four independent oscillations and rotations involving nonorthogonal axes. This provides important new degrees of freedom, which are used to improve the scaling factor of the recoupled dipole-dipole couplings by a factor of 2.5 relative to the triple-oscillating field approach. This significant improvement, obtained by refocusing of otherwise defocused parts of the residual dipolar coupling Hamiltonian, may be exploited to measure much weaker 13C–13C dipolar couplings (and thereby longer distances) with much higher accuracy. We present a detailed theoretical description of multiple-field oscillating recoupling experiments, along with numerical simulations and experimental results on U–13C, 15N-L-threonine and U–13C,15N-ubiquitin. [ABSTRACT FROM AUTHOR]

Optimal control theory has recently been introduced to nuclear magnetic resonance (NMR) spectroscopy as a means to systematically design and optimize pulse sequences for liquid- and solid-state applications. This has so far primarily involved numerical optimization using gradient-based methods, which allow for the optimization of a large number of pulse sequence parameters in a concerted way to maximize the efficiency of transfer between given spin states or shape the nuclear spin Hamiltonian to a particular form, both within a given period of time. Using such tools, a variety of new pulse sequences with improved performance have been developed, and the NMR spin engineers have been challenged to consider alternative routes for analytical experiment design to meet similar performance. In addition, it has lead to increasing demands to the numerical procedures used in the optimization process in terms of computational speed and fast convergence. With the latter aspect in mind, here we introduce an alternative approach to numerical experiment design based on the Krotov formulation of optimal control theory. For practical reasons, the overall radio frequency power delivered to the sample should be minimized to facilitate experimental implementation and avoid excessive sample heating. The presented algorithm makes explicit use of this requirement and iteratively solves the stationary conditions making sure that the maximum of the objective is reached. It is shown that this method is faster per iteration and takes different paths within a control space than gradient-based methods. In the present work, the Krotov approach is demonstrated by the optimization of NMR and dynamic nuclear polarization experiments for various spin systems and using different constraints with respect to radio frequency and microwave power consumption. [ABSTRACT FROM AUTHOR]

We present a new concept for homonuclear dipolar recoupling in magic-angle-spinning (MAS) solid-state NMR experiments which avoids the problem of dipolar truncation. This is accomplished through the introduction of a new NMR pulse sequence design principle: the triple oscillating field technique. We demonstrate this technique as an efficient means to accomplish broadband dipolar recoupling of homonuclear spins, while decoupling heteronuclear dipolar couplings and anisotropic chemicals shifts and retaining influence from isotropic chemical shifts. In this manner, it is possible to synthesize Ising interaction (2IzSz) Hamiltonians in homonuclear spin networks and thereby avoid dipolar truncation—a serious problem essentially all previous homonuclear dipolar recoupling experiments suffer from. Combination of this recoupling concept with rotor assisted dipolar refocusing enables easy readout of internuclear distances through comparison with analytical Fresnel curves. This forms the basis for a new class of solid-state NMR experiments with potential for structure analysis of uniformly 13C labeled proteins through accurate measurement of 13C–13C internuclear distances. The concept is demonstrated experimentally by measurement of Cα–C′, Cβ–C′, and Cγ–C′ internuclear distances in powder samples of the amino acids L-alanine and L-threonine. [ABSTRACT FROM AUTHOR]

We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all Ix, Iy, and Iz polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of √2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of 13Cα, 13Cβ-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments. [ABSTRACT FROM AUTHOR]

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state nuclear magnetic resonance (NMR) spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiments. [ABSTRACT FROM AUTHOR]

Our recent exact effective Hamiltonian theory (EEHT) for exact analysis of nuclear magnetic resonance (NMR) experiments relied on a novel entanglement of unitary exponential operators via finite expansion of the logarithmic mapping function. In the present study, we introduce simple alternant quotient expressions for the coefficients of the polynomial matrix expansion of these entangled operators. These expressions facilitate an extension of our previous closed solution to the Baker–Campbell–Hausdorff problem for SU(N) systems from N≤4 to any N, and thereby the potential application of EEHT to more complex NMR spin systems. Similarity matrix transformations of the EEHT expansion are used to develop alternant quotient expressions, which are fully general and prove useful for evaluation of any smooth matrix function. The general applicability of these expressions is demonstrated by several examples with relevance for NMR spectroscopy. The specific form of the alternant quotients is also used to demonstrate the fundamentally important equivalence of Sylvester’s theorem (also known as the spectral theorem) and the EEHT expansion. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A novel type of solid-state nuclear magnetic resonance experiment for efficient transfer of coherence between different nuclear spin I=1/2 species under magic-angle spinning conditions is introduced. The method combines the attractive features of γ-encoded dipolar recoupling [Nielsen et al., J. Chem. Phys. 101, 1805 (1995)] with coherence transfer mediated by a longitudinal spin-order operator in a transferred echo experiment. Using two-channel rotary resonance recoupling with different phase and amplitude modulation schemes, the transferred echo sequence can be tuned to achieve dipolar recoupling and coherence transfer over a well-defined range of chemical shifts while keeping the ratio between the rf field strength and the sample spinning frequency relatively low. The method, referred to as gamma-encoded transfer echo, is described analytically, by numerical simulations for various different spin systems, and experimentally by [sup 15]N to [sup 13]C coherence transfers in a powder sample of [sup 13]C, [sup 15]N-labeled glycine. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Composite spin-state-selective rotations are introduced. They are devised to remedy the following problem: When determining scalar plus residual dipolar couplings by conventional NMR experiments in partially aligned molecules, a considerable variation in the effective coupling constant often entails systematic errors compromising the accuracy of the measurements. The concept of composite pulses is extended in order to design spin-state-selective composite rotations (S[sup 3]CR) robust to variation in effective coupling constants. With the S[sup 3]CR approach the broadband performance of spin-state-selective excitation improves significantly as is demonstrated both numerically and experimentally. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report analytical solutions to the unitary bound problem for coherence/polarization transfer in IS two-spin-[FRACTION SHAPE="CASE"][NUM]1[/NUM][DEN]2[/DEN][/FRACTION] systems by means of unitary operations. Theoretical upper bounds for the transfer efficiency along with the associated optimum transformation operators are obtained analytically by decomposing the unitary operator as a product of exponentials in the special unitary Lie group SU(4). Addressing NMR spectroscopy as a specific example, the method is demonstrated for the non-Hermitian transfers I[sup -]→S[sup -] and 2I[sup -]S[sub z]→S[sup -] being relevant for heteronuclear single-quantum coherence (HSQC) experiments as well as the double- to single-quantum transfer I[sup -]S[sup -]→I[sup -]S[sup β]+I[sup β]S[sup -] being representative for coherence-order and spin-state-selective transfer in INADEQUATE CR experiments. Furthermore, using a Lagrangian function approach it is demonstrated how the method enables analytical description of two-dimensional bounds for I[sub z]→S[sub z] cross polarization. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Major advances have recently been made in the field of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance (NMR). These developments have improved the resolution and sensitivity of the NMR spectrum of spins coupled to protons. One such new scheme, denoted as rCW ApA , has proven to be robust with practically no need for parameter optimization [A. Equbal et al. Chem. Phys. Lett., 635, 339 (2015)]. Most of the experiments with rCW ApA have been carried out in the regimes of slow to moderate magic-angle spinning while simultaneously applying high decoupling radio-frequency amplitudes. Here, we explore the performance of the rCW ApA sequence and its predecessor rCW A in the regime of low-power radio-frequency irradiation and fast magic-angle spinning. The robustness of the refocused continuous-wave (rCW) schemes to experimental parameters such as pulse lengths and offset irradiation is demonstrated. Numerical simulations and analytical theory have been used to understand the effects of various nuclear spin interactions on the decoupling performance of the low-power rCW decoupling scheme relative to other decoupling methods. This has lead to the design of an "optimum low-power decoupling sequence" that can be used without parameter optimization. This result is particularly important in the context of samples with low signal to noise.

Application of sets of (13)C-(13)C internuclear distance restraints constitutes a typical key element in determining the structure of peptides and proteins by magic-angle-spinning solid-state NMR spectroscopy. Accurate measurements of the structurally highly important (13)C-(13)C distances in uniformly (13)C-labeled peptides and proteins, however, pose a big challenge due to the problem of dipolar truncation. Here, we present novel two-dimensional (2D) solid-state NMR experiments capable of extracting distances between carbonyl ((13)C') and aliphatic ((13)C(aliphatic)) spins with high accuracy. The method is based on an improved version of the four-oscillating field (FOLD) technique [L. A. Straasø, M. Bjerring, N. Khaneja, and N. C. Nielsen, J. Chem. Phys. 130, 225103 (2009)] which circumvents the problem of dipolar truncation, thereby offering a base for accurate extraction of internuclear distances in many-spin systems. The ability to extract reliable accurate distances is demonstrated using one- and two-dimensional variants of the FOLD experiment on uniformly (13)C,(15)N-labeled-L-isoleucine. In a more challenging biological application, FOLD 2D experiments are used to determine a large number of (13)C'-(13)C(aliphatic) distances in amyloid fibrils formed by the SNNFGAILSS fibrillating core of the human islet amyloid polypeptide with uniform (13)C,(15)N-labeling on the FGAIL fragment.

We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.