Selection Rules for Multiple Quantum NMR Excitation in Solids: Derivation from Time-Reversal Symmetry and Comparison with Simulations and C NMR Experiments

New derivations of selection rules for excitation and detection of multiple quantum coherences in coupled spin-1/2 systems are presented. The selection rules apply to experiments in which the effective coupling Hamiltonian used for multiple quantum excitation is both time-reversal invariant and time-reversible by a phase shift of the radiofrequency pulse sequence that generates the effective couplings. The selection rules are shown to be consequences of time-reversal invariance and time-reversibility and otherwise independent of the specific form of the effective coupling Hamiltonian. Numerical simulations of multiple quantum NMR signal amplitudes and experimental multiple quantum excitation spectra are presented for the case of a multiply ¹³C-labeled helical polypeptide. The simulations and experiments confirm the selection rules and demonstrate their impact on multiple quantum ¹³C NMR spectra in this biochemically relevant case.     

Geometry of kinked protein helices from NMR data

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.     

Discerning the degenerate transitions of scalar coupled H NMR spectra: Correlation and resolved techniques at higher quantum

The blend of spin topological filtering and the spin state selective detection of single quantum transitions by the two dimensional multiple quantum-single quantum correlation and higher quantum resolved techniques have been employed for simplifying the complexity of scalar coupled ¹H NMR spectra. The conventional two dimensional COSY and TOCSY experiments, though identify the coupled spin networks, fail to differentiate them due to severe overlap of transitions. Non-selective excitation of homonuclear higher quantum of protons results in filtering of spin systems irrespective of their spin topologies. The spin state selection by passive ¹⁹F spins provides fewer transitions in each cross section of the single quantum dimension simplifying the analyses of the complex spectra. The degenerate single quantum transitions are further discerned by spin selective double and/or triple quantum resolved experiments that mimic simultaneous heteronuclear and selective homonuclear decoupling in the higher quantum dimension. The techniques aided the determination of precise values of spectral parameters and relative signs of the couplings.     

C-13 and H-1 NMR Assignments of the Chamigrenes Prepacifenol and Dehydroxyprepacifenol Epoxioes

A complete assignment of the signals in the ¹H and ¹³C NMR spectra and the stereostructural analysis of the compounds prepacifenol epoxide and the new dehydroxyprepacifenol epoxide are presented. These compounds were extracted from the marine mollusc Aplysia dactylomela and represent the first occurrence of chamigrenes found in Brazilian waters. The NMR analyses are supported by NOE difference and COSY experiments and also by gradient selected HMBC, HSQC-TOCSY and HSQC-DE. ¹H spectra simulations were done for the final fitting of the chemical shifts and coupling constants.     

Selective NMR excitation in strongly inhomogeneous magnetic fields

The NMR-MOUSE is a unilateral and mobile NMR sensor which operates with highly inhomogeneous magnetic fields. To produce a mobile NMR unit, RF excitation is sought, which can be produced with the most simple equipment, in particular nonlinear, low-power amplifiers, and to observe a free induction decay in strongly inhomogeneous fields, the excitation needs to be selective. The possibility to produce selective excitation by sequences of hard low-power radiofrequency pulses in the strongly inhomogeneous magnetic fields of the NMR-MOUSE is explored. The use of the DANTE sequence for selection of magnetization from parts of the sensitive volume was investigated for longitudinal and transverse magnetization by computer simulations and experiments. The spectra of the recorded FIDs and echo signals are in good agreement with those simulated for the excitation, which verifies the concept of the DANTE excitation. The results obtained are an important step towards a low-power operation of the NMR-MOUSE to improve its mobility.     

Effects of experimental imperfections on a spin counting experiment

Spin counting NMR is an experimental technique that allows a determination of the size and time evolution of networks of dipolar coupled nuclear spins. This work reports on an average Hamiltonian treatment of two spin counting sequences and compares the efficiency of the two cycles in the presence of flip errors, RF inhomogeneity, phase transients, phase errors, and offset interactions commonly present in NMR experiments. Simulations on small quantum systems performed using the two cycles reveal the effects of pulse imperfections on the resulting multiple quantum spectra, in qualitative agreement with the average Hamiltonian calculations. Experimental results on adamantane are presented, demonstrating differences in the two sequences in the presence of pulse errors.     

Coulomb effects in artificial molecules

We study the capacitance spectra of artificial molecules consisting of two and three coupled quantum dots from an extended Hubbard Hamiltonian model that takes into account quantum confinement, intra- and inter-dot Coulomb interaction and tunneling coupling between all single particle states in nearest neighbor dots. We find that, for weak coupling, the interdot Coulomb interaction dominates the formation of a collective molecular state. We also calculate the effects of correlations on the tunneling probability through the evaluation of the spectral weights, and corroborate the importance of selection rules for understanding experimental conductance spectra.     

Exact results on spin dynamics and multiple quantum NMR dynamics in alternating spin-1/2 chains with <Emphasis Type="Italic">XY</Emphasis> Hamiltonian at high temperatures

We extend the picture of a transfer of nuclear spin-1/2 polarization along a homogeneous one-dimensional chain with the XY Hamiltonian to the inhomogeneous chain with alternating nearest neighbor couplings and alternating Larmor frequencies. To this end, we exactly calculate the spectrum of the spin-1/2 XY Hamiltonian of the alternating chain with an odd number of sites. The exact spectrum of the XY Hamiltonian is also applied to study the multiple quantum (MQ) NMR dynamics of the alternating spin-1/2 chain. MQ NMR spectra are shown to have the MQ coherences of zero and ± second orders just as in the case of a homogeneous chain. The intensities of the MQ coherences are calculated.     

A suite of 3D NMR methods for characterizing complex hydrocarbon structure fragments

A suite of triple resonance 3D NMR experiments is presented for the complete connectivity assignment of the hydrocarbon network in complex macromolecular and supramolecular organic structures. These new 3D NMR methods rely only on the presence of a unique set of (13)C resonances (from (13)C(X)) which are separated from the rest of the (13)C NMR spectrum. These experiments take the advantage of region selective excitation and selective inversion by composite pulses to provide correlations among H(A), (13)C(A); H(B), (13)C(B) and neighboring (13)C(X) resonances along three frequency dimensions. These methods include: gHC(A)C(X), gHC(A)C(X)-HH-TOCSY and gHC(A)C(X)-CC-TOCSY experiments. The utility of this approach is illustrated with spectra of selected structure fragments in poly(ethylene-co-n-butyl acrylate-co-carbon monoxide) (polyEBC) prepared from 1,2,3-(13)C(3)-n-butyl acrylate.     

卡泊三醇的核磁共振谱解析

利用核磁共振氢谱（¹H NMR）、碳谱（¹³C NMR）、同核位移相关谱（¹H-¹H COSY）、异核单量子相干谱（HSQC）和异核多键相关谱（HMBC）等多种核磁研究方法对抗银屑病药物卡泊三醇的¹H、¹³C信号进行完全归属.     

Numerical simulation of NQR/NMR: Applications in quantum computing

A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php.     

Separation of 47Ti and 49Ti solid-state NMR lineshapes by static QCPMG experiments at multiple fields

Experimental procedures are proposed and demonstrated that separate the spectroscopic contribution from both (47)Ti and (49)Ti in solid-state nuclear magnetic resonance spectra. These take advantage of the different nuclear spin quantum numbers of these isotopes that lead to different "effective" radiofrequency fields for the central transition nutation frequencies when these nuclei occur in sites with a significant electric field gradient. Numerical simulations and solid-state NMR experiments were performed on the TiO(2) polymorphs anatase and rutile. For anatase, the separation of the two isotopes at high field (21.1T) facilitated accurate determination of the electric field gradient (EFG) and chemical shift anisotropy (CSA) tensors. This was accomplished by taking advantage of the quadrupolar interaction between the EFG at the titanium site and the different magnitudes of the nuclear quadrupole moments (Q) of the two isotopes. Rutile, having a larger quadrupolar coupling constant (C(Q)), was examined by (49)Ti-selective experiments at different magnetic fields to obtain spectra with different scalings of the two anisotropic tensors. A small chemical shielding anisotropy (CSA) of -30 ppm was determined.     

Specification and visualization of anisotropic interaction tensors in polypeptides and numerical simulations in biological solid-state NMR

Software facilitating numerical simulation of solid-state NMR experiments on polypeptides is presented. The Tcl-controlled SIMMOL program reads in atomic coordinates in the PDB format from which it generates typical or user-defined parameters for the chemical shift, J coupling, quadrupolar coupling, and dipolar coupling tensors. The output is a spin system file for numerical simulations, e.g., using SIMPSON (Bak, Rasmussen, and Nielsen, J. Magn. Reson. 147, 296 (2000)), as well as a 3D visualization of the molecular structure, or selected parts of this, with user-controlled representation of relevant tensors, bonds, atoms, peptide planes, and coordinate systems. The combination of SIMPSON and SIMMOL allows straightforward simulation of the response of advanced solid-state NMR experiments on typical nuclear spin interactions present in polypeptides. Thus, SIMMOL may be considered a "sample changer" to the SIMPSON "computer spectrometer" and proves to be very useful for the design and optimization of pulse sequences for application on uniformly or extensively isotope-labeled peptides where multiple-spin interactions need to be considered. These aspects are demonstrated by optimization and simulation of novel DCP and C7 based 2D N(CO)CA, N(CA)CB, and N(CA)CX MAS correlation experiments for multiple-spin clusters in ubiquitin and by simulation of PISA wheels from PISEMA spectra of uniaxially oriented bacteriorhodopsin and rhodopsin under conditions of finite RF pulses and multiple spin interactions.     

高分辨核磁共振谱计算机解析方法

本文应用哈密顿矩阵范数逼近方法,利用计算机计算了三自旋、四自旋系统高分辨核磁共振谱的化学位移和偶合常数。与一般迭代程序相比,简化了计算过程,提高了计算精度,并保证了解的唯一性。选择实验能级值作为哈密顿矩阵零级近似,避免了选取初始δ,J值的麻烦。本方法在图谱定量分析中取得了较好效果。     

Line shapes of multiple quantum NMR coherences in one-dimensional quantum spin chains in solids

General formulae for intensities of multiple quantum (MQ) NMR coherences in systems of nuclear spins coupled by the dipole-dipole interactions are derived. The second moments of the MQ coherences of zero- and second orders are calculated for infinite linear chains in the approximation of the nearest neighbor interactions. Supercomputer simulations of intensities of MQ coherences of linear chains are performed at different times of preparation and evolution periods of MQ NMR experiments. The second moments obtained from the developed theory are compared with the results of the supercomputer analysis of MQ NMR dynamics. The linewidth information in MQ NMR experiments is discussed.     

Theoretical and experimental assessment of single- and multiple-quantum cross-polarization in solid state NMR

Continuous wave cross-polarization (CP) NMR experiments with magic angle spinning (MAS) are reviewed for the case of isolated spin pairs I-S, with spin quantum numbers I = ½ and S ½ (1/2, 3/2, …). For two spin-1/2 nuclei, the Hartmann-Hahn matching conditions are examined at various sample rotation rates ν_R, especially with regard to off-resonance behaviour. In addition to signal enhancement, the CPMAS experiment can be used for the selective determination of inter-nuclear distances between spin-1/2 nuclei. Theoretical examination of the CP transfers to single-quantum (1Q-CPMAS) and multiple-quantum (MQ-CPMAS) levels of quadrupolar nuclei is presented. Simple analytical formulae describing the Hartmann-Hahn matching under various experimental conditions are verified using computer simulations of the spin density matrix under MAS, and the experimental data. The strategies for the most efficient acquisition of 1Q-CPMAS and MQ-CPMAS spectra are extensively discussed.     

迭代软阈值法压缩感知重建谱峰较宽的二维固体谱

压缩感知技术可以打破传统奈奎斯特采样定理的限制,利用优化算法对欠采数据进行重建,并获得高质量的结果,因此在核磁共振领域得到了广泛的关注．但是当核磁共振谱的谱峰很宽时,基于共轭梯度方法的压缩感知重建却难以得到令人满意的谱图．因此,该文采用凸优化非线性重建算法,使用基于谱图域软阈值的压缩感知算法重建固体二维宽谱（¹H双量子-单量子谱或MQMAS谱）,有效地解决了宽峰在重建时变弱的问题．     

Dipolar 31P NMR spectroscopy of crystalline inorganic phosphorus compounds.

The ability of the 90 degrees-t1-180 degrees pulse sequence to produce accurate dipole-dipole coupling information in solids is investigated. To this end, the experimental 31P spin echo decays are measured for eighteen crystalline phosphides and phosphorus chalcogenides and compared with simulations, based on the known internuclear distances in these compounds. The experimental results are generally found accurate in compounds where the dominant contribution to the dipole-dipole coupling arises from nuclei in structurally inequivalent sites with large chemical shift anisotropies. For this situation, the quantum mechanical "flip-flop" term in the dipolar Hamiltonian is suppressed and the dipole-dipole coupling is entirely heteronuclear in character. All of those compounds that do not obey this condition show accelerated spin echo decays due to a fractional contribution of the flip-flop term and possibly incomplete refocusing of chemical shift terms on the time scale of the experiment. The results confirm on an empirical basis that the spin echo NMR technique can provide accurate dipole-dipole coupling information (and thus distance distributions) in disordered solids and glasses.     

Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR

Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.