An ensemble of paired spin(-1/2) nuclei in a rotating solid: Polarization evolution and NMR spectrum in a wobbling frame

The evolution of the magnetic polarization of an ensemble of paired spin(-1/2) nuclei in an MAS NMR (nuclear magnetic resonance) experiment and the induced spectrum are described theoretically by means of a Liouville-von Neumann equation representation in a wobbling rotating frame in combination with the averaged Hamiltonian theory. In this method, the effect of a high-intensity external static magnetic field and the effects of the leftover interaction components of the Hamiltonian that commute with the approximate Hamiltonian are taken into account simultaneously and equivalently. This method reproduces details that really exist in the recorded spectra, caused by secular terms in the Hamiltonian, which might otherwise be smoothed out owing to the approximate treatment of the effects of the secular terms. Complete analytical expressions, which describe the whole NMR spectrum including the rotational sideband sets, and which consider all the relevant intermolecular interactions, are obtained.     

超强磁场中核磁共振信号与屏蔽效应的理论研究

研究了超强磁场对于核磁共振样品中双原子分子中电子系统的哈密顿量的影响,并且给出了磁共振信号中由于外磁场与氢原子电子系统相互作用所产生的含有B02的修正项.基于核磁共振原理,获得了利用氢的NMR谱对超强磁场进行精确测量的理论依据,推导出了一种基于核磁共振技术的超强磁场测量公式,从而在理论上证明了对超强磁场进行精确测量是可行的.     

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.     

里德堡钠原子抗磁谱的模型势计算

用B样条基组展开方法结合模型势计算了里德堡钠原子抗磁谱和相应的振子强度谱.径向和角向均采用高阶B样条基组.计算结果与已有的R-矩阵和多通道量子亏损理论相结合(R-matrix MQDT)法及其他理论计算结果作了比较,几种理论结果在我们所研究的能区内符合得非常好.本文方法较R-ma-trix MQDT法简单,易于推广到交叉电磁场中里德堡原子的精确谱的计算中.     

Controlling coherence using the internal structure of hard pi pulses

The tiny difference between hard pi pulses and their delta-function approximation can be exploited to control coherence. Variants on the magic echo that work despite a large spread in resonance offsets are demonstrated using the zeroth- and first-order average Hamiltonian terms, for 13C NMR in 60C. The 29Si NMR linewidth of silicon has been reduced by a factor of about 70,00 using this approach, which also has potential applications in magnetic resonance microscopy and imaging of solids.     

Hardware modification of a 7 mm MAS NMR probe to a single-crystal goniometer

Tensorial terms of the Hamiltonian can be measured by solid-state single-crystal nuclear magnetic resonance (NMR) spectroscopy which requires a goniometer NMR probehead. Goniometer probes; however, are not standard parts of solid NMR spectrometers and are available only at a much higher price than magic-angle spinning (MAS) probeheads widely used in research. Due to requirements of MAS experiments, modern probeheads are designed for small ceramic rotors, which are 1-4 mm in diameter, to reach very high angular frequencies, so there are several older 7 mm MAS probeheads used rarely todays in NMR laboratories. In this paper, a simple method is presented how to rebuild step-by-step a 7 mm Bruker MAS probehead to be suitable for single-crystal spectroscopy. In the second part (31)P chemical shift tensors of Na(4)P(2)O(7) x 10H(2)O are determined to demonstrate the functionality of the rebuilt probehead.     

Influence of the anisotropic hyperfine interaction on the 14N ENDOR and the ESEEM orientation-disordered spectra

The influence of the anisotropic hyperfine interaction on the 14N electron-nuclear double resonance/electron spin echo envelope modulation spectra is studied by approximate analytical and graphical methods for the case of the isotropic g-factor. The suggested determination of the modified characteristic directions of the magnetic field due to anisotropy enhances the insight in the structural details of the system and analytical solutions of the secular equation for these conditions are derived. The graphical method, previously used for the analysis of the orientation dependence of the 14N nuclear-transition frequencies in orientation-disordered samples for isotropic hyperfine interaction is extended to the case of arbitrary anisotropic hyperfine tensor. The above analytical and graphical methods are illustrated and tested against exact simulations in two practically important cases: (i) isotropic hyperfine interaction (hfi) exceeding other nuclear interactions in nuclear spin Hamiltonian. (ii) Cancellation of the isotropic part of the hfi.     

Entanglement assisted metrology

We propose a new approach to the measurement of a single spin state, based on nuclear magnetic resonance (NMR) techniques and inspired by the coherent control over many-body systems envisaged by quantum information processing. A single target spin is coupled via the magnetic dipolar interaction to a large ensemble of spins. Applying radio frequency pulses, we can control the evolution so that the spin ensemble reaches one of two orthogonal states whose collective properties differ depending on the state of the target spin and are easily measured. We first describe this measurement process using quantum gates; then we show how equivalent schemes can be defined in terms of the Hamiltonian and thus implemented under conditions of real control, using well established NMR techniques. We demonstrate this method with a proof of principle experiment in ensemble liquid state NMR and simulations for small spin systems.     

High resolution NMR spectroscopy of rat brain in vivo through indirect zero-quantum-coherence detection

The time evolution of zero-quantum-coherences (ZQCs) is insensitive to magnetic field inhomogeneity. Using a 2D indirect ZQC detection method it is shown that high-resolution (1)H NMR spectra can be obtained from rat brain in vivo at 11.74T that are immune to magnetic field inhomogeneity. Simulations based on the density matrix formalism, as well as in vitro measurements are used to demonstrate the features of 2D ZQC NMR spectra. Unique spectral information which is normally not directly available from regular (1)H NMR spectra can be extracted and used for compound identification or improved prior knowledge during spectral fitting.     

A quantum field theory of lattice dynamics at finite temperature

A quantum field theoretical treatment of three-dimensional cubic crystals at finite temperature is presented from the view-point of the spontaneous breakdown of the spatial translational invariance using thermo field theory. The effective interaction Hamiltonian is constructed by taking into account the dynamical map of the molecular density operator which is obtained from the Ward-Takahashi relations. The acoustic phonons are expected to be the excitation of particle-hole pairs. The conventional secular equation for the lattice vibrations is obtained by neglecting some quantum effects in the Bethe-Salpeter equation for the molecular density fluctuations. The phonon spectra, the phonon propagators and the dynamical map of the molecular density operator are calculated at finite temperature.     

Semiclassical Calculation of Recurrence Spectra of He Rydberg Atom in Strong External Fields

Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.     

Local spin moment distribution in antiferromagnetic molecular rings probed by NMR

The NMR spectra of 19F and 53Cr have been obtained at low temperatures in a heterometallic substituted antiferromagnetic (AF) ring Cr7Cd with an S=3/2 ground state and compared with the spectra in a homometallic Cr8 AF ring with an S=0 ground state. From the analysis of the spectra one can derive directly model independent values of the staggered nonuniform distribution of the local moment in the heterometallic ring Cr7Cd. The experimental values are found to be in excellent agreement with the theoretical values calculated on the basis of an effective spin Hamiltonian which includes crystal field effects.     

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。     

非厄米哈密顿量的物理意义

分析了一个脉冲激光与原子相互作用的四能级系统，并考虑最上层能级的自电离过程，从而引入非厄米哈密顿量.在缀饰原子模型下，通过直接求解此哈密顿量的本征值与本征函数，得到系统布居的演化函数.与数值方法所得演化函数的对比表明二者相当符合，从而肯定了非厄米哈密顿量在量子力学框架中的地位，并得到其本征值虚部的物理意义.这将使传统量子力学中力学量的定义得以拓展. 关键词： 非厄米哈密顿量 缀饰原子模型     

Statics and dynamics of the modulation in incommensurate Rb2ZnBr4 as detected by NMR

The dynamics of the incommensurate modulation of Rb₂ZnBr₄ is investigated near the transition to the normal high-temperature phase using first-order quadrupole effects in nuclear magnetic resonance (NMR).⁸⁷Rb NMR spectra and two-dimensional⁸⁷Rb NMR exchange spectra are reported. All results can be described consistently in terms of a static modulation in the incommensurate phase without any indication for “floating” or large-scale fluctuations of the modulation wave. The spectra taken about 135 K below T_i in the lower incommensurate phase well above the soliton regime show no indication for the existence of a higher-order commensurate modulation in Rb₂ZnBr₄.     

Time-dependence of nuclear magnetic resonance quadrupole interactions for polymers under shear

We consider the problem of performing NMR spectroscopy under conditions of flow, a central issue in Rheo-NMR. By way of example, the effects of rotational motion on the deuterium NMR spectrum are considered for Couette cell experiments involving deformation of polymers under shearing conditions. The polymer was modelled as a power law fluid and for each streamline, the spin Hamiltonian evolved to allow for flow reorientation. The gap-integral spectra are compared with the 'ideal' spectra for a polymer under shear, but without reorientation. It is found that flow does affect the shape of the deuterium spectra, as well as slightly perturbing the splittings.     

Selection rules for multiple quantum NMR excitation in solids: derivation from time-reversal symmetry and comparison with simulations and (13)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 (13)C-labeled helical polypeptide. The simulations and experiments confirm the selection rules and demonstrate their impact on multiple quantum (13)C NMR spectra in this biochemically relevant case.     

1-D and 2-D NMR of broad-line solids: an application to quasicrystals

Nuclear magnetic resonance (NMR) techniques for measuring one-dimensional absorption spectra and two-dimensional exchange spectra of solids with extremely inhomogeneously broadened lines are discussed. Among various “broad-line” solids, quasicrystals represent alloys of metallic elements, the structures of which include “forbidden” symmetry elements. NMR absorption lines of quasicrystals exhibit a strong electric-quadrupole-induced inhomogeneous broadening that originates from the lack of translational periodicity of the otherwise perfectly long-range-ordered quasiperiodic lattice. Recording an NMR spectrum of a quasicrystalline sample requires a magnetic field-sweep technique. The two-dimensional exchange experiment on quasicrystals can be performed on selectively excited portions of the NMR spectrum only. Due to the off-resonance effects in a selective excitation, the use of a simple three-pulse stimulated-echo exchange sequence is preferred. The²⁷Al spectra of the Al-Pd-Mn and Al-Pd-Re families show interesting features like temperature-dependent frequency shifts and exchange effects due to atomic motion.     

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.     

魔角旋转核磁共振波谱学

样品绕与外加恒定磁场方向成魔角β_M=cos^-1(1)/√3的轴向快速旋转(MAS)可以消除固体NMR的多种谱增宽。本文首先介绍了固体中的几种主要的各向异性相互作用,即偶极-偶极,核四极,自旋-自旋或称间接偶极-偶极以及化学位移相互作用。然后用平均哈密顿理论阐述了MAS对这些相互作用的影响。现今的固体高分辨方法有四种,即多脉冲(MP),多量子(MQ),交叉极化和大功率异核去耦合(CP)以及MAS,在这些方法中MAS方法是唯一可以获得各向同性化学位移的。因而要得到类似于液体谱的固体高分辨,MAS往往是最后的手段。以上这些方法的联合运用以及极为广泛的应用研究使得固体高分辨NMR兴旺发达起来了。本文引述了大量原始和最新的文献,力图概述当前该领域中的大部分成就。评论这一领域的理论和实验技术的发展。