The virtual NMR spectrometer: a computer program for efficient simulation of NMR experiments involving pulsed field gradients

This paper presents a software program, the Virtual NMR Spectrometer, for computer simulation of multichannel, multidimensional NMR experiments on user-defined spin systems. The program is capable of reproducing most features of the modern NMR experiment, including homo- and heteronuclear pulse sequences, phase cycling, pulsed field gradients, and shaped pulses. Two different approaches are implemented to simulate the effect of pulsed field gradients on coherence selection, an explicit calculation of all coherence transfer pathways, and an effective approximate method using integration over multiple positions in the sample. The applications of the Virtual NMR Spectrometer are illustrated using homonuclear COSY and DQF COSY experiments with gradient selection, heteronuclear HSQC, and TROSY. The program uses an intuitive graphical user interface, which resembles the appearance and operation of a real spectrometer. A translator is used to allow the user to design pulse sequences with the same programming language used in the actual experiment on a real spectrometer. The Virtual NMR Spectrometer is designed as a useful tool for developing new NMR experiments and for tuning and adjusting the experimental setup for existing ones prior to running costly NMR experiments, in order to reduce the setup time on a real spectrometer. It will also be a useful aid for learning the general principles of magnetic resonance and contemporary innovations in NMR pulse sequence design.     

Entanglement, phase correlation and dephasing of two-qubit states

The relation between entanglement and phase correlation of two-qubit states is studied. Decoherence of entanglement and phase correlation caused by correlated classical noises is also investigated. It is found that the decay of the phase correlation is quite different from that of the entanglement when the finite-time disentanglement occurs.     

非均匀磁场和杂质磁场对自旋1系统量子关联的影响

通过负值度和测量诱导的扰动, 研究了非均匀磁场和杂质磁场对自旋为1的Heisenberg系统量子关联的影响. 研究发现非均匀磁场的增加会降低纠缠, 但也可用来产生纠缠, 并且会提高临界非线性作用K_c的值, 测量诱导的扰动的临界磁场要高于负值度的临界磁场, 而且测量诱导的扰动不会随着非线性作用|K| 的减小而消失, 它能全面反映量子关联的存在. 研究还发现, 不同杂质磁场对测量诱导的扰动的影响彼此间无交叉. 杂质磁场下, 相互作用|J| 必须小于非线性作用|K| 才会有纠缠存在, 但是测量诱导的扰动却可以在相互作用|J| 大于非线性作用|K| 时依然存在, |J| 与|K| 相同时只是测量诱导的扰动的最小取值点. 此外, 系统粒子数目对量子关联也具有重要影响.     

Diffusion exchange NMR spectroscopy in inhomogeneous magnetic fields

Two-dimensional diffusion exchange experiments in the presence of a strong, static magnetic field gradient are presented. The experiments are performed in the stray field of a single sided NMR sensor with a proton Larmor frequency of 11.7 MHz. As a consequence of the strong and static magnetic field gradient the magnetization has contributions from different coherence pathways. In order to select the desired coherence pathways, a suitable phase cycling scheme is introduced. The pulse sequence is applied to study diffusion as well as the molecular exchange properties of organic solvents embedded in a mesoporous matrix consisting of a sieve of zeolites with a pore size of 0.8 nm and grain size of 2 μm. This pulse sequence extends the possibilities of the study of transport properties in porous media, with satisfying sensitivity in measurement times of a few hours, in a new generation of relatively inexpensive low-field NMR mobile devices.     

空间非均匀场下核间距对不对称分子谐波发射的影响

数值研究了空间非均匀场下核间距离对于不对称分子HeH2+发射高次谐波以及阿秒脉冲的影响。计算结果表明,通过适当调节HeH2+分子离子的核间距离以及空间非均匀参数,不仅谐波发射的截止能量得到了延伸,而且单一的短量子路径也被选择出来对谐波发射起作用。随后适当引入第二束控制激光场,谐波截止能量得到了进一步扩展,形成了两个带宽分别在431eV和372eV的连续平台区。 最后,通过适当的叠加谐波,可获得脉宽为31as-65as的一系列阿秒X射线光源。     

Probing four orders of magnitude of the diffusion time in porous silica glass with unconventional NMR techniques

The combined use of two unconventional NMR diffusometry techniques permits measurements of the self-diffusion coefficient of fluids confined in porous media in the time range from 100 microseconds to seconds. The fringe field stimulated echo technique (FFStE) exploits the strong steady gradient in the fringe field of a superconducting magnet. Using a standard 9.4 T (400 MHz) wide-bore magnet, for example, the gradient is 22 T/m at 375 MHz proton resonance and reaches 60 T/m at 200 MHz. Extremely short diffusion times can be probed on this basis. The magnetization grid rotating frame imaging technique (MAGROFI) is based on gradients of the radio frequency (RF) field. The RF gradients not necessarily need be constant since the data are acquired with spatial resolution along the RF gradient direction. MAGROFI is also well suited for unilateral NMR applications where all fields are intrinsically inhomogeneous. The RF gradients reached depend largely on the RF coil diameter and geometry. Using a conic shape, a value of at least 0.3 T/m can be reached which is suitable for long-time diffusion measurements. Both techniques do not require any special hardware and can be implemented on standard high RF power NMR spectrometers. As an application, the influence of the tortuosity increasing with the diffusion time is examined in a saturated porous silica glass.     

非均匀流体介质内部散射声场重建的逐层计算方法*

入射声波激励下非均匀流体介质内部散射声场的重建方法对超声层析成像具有重要意义。以往采用矩量法求解,但该方法全域离散形成的复数满秩矩阵规模随着分辨率与计算精度的提高而急剧增大,对算力具有很高的要求,一定程度上限制了其在实际中的应用。为克服上述缺陷,本文以逐层离散、逐层计算为核心思想,以声散射基本公式与近场声全息理论为基础,推导出逐层计算非均匀流体介质内部散射声场的理论公式并给出对应的几何离散模型。为验证该方法的可行性,以矩量法为参照,对同样的介质模型进行介质内部声场重构仿真。结果表明,逐层算法不仅可以有效地重建非均匀流体介质内部散射声场,且大幅度减小了求解规模。     

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.     

Electric field gradients in niobium pentachloride dimer

Electric field gradient tensors at the bridging chlorine sites in niobium pentachloride dimer have been evaluated using point-charge model with de Wette’s planewise summation method for rapid convergence of the lattice sums. The results are discussed based on the experimental results and the existing theory on dimeric molecules.     

不均匀场中氢分子离子高次谐波产生的理论研究

在非Born-Oppenheimer近似下,通过求解含时薛定谔方程的方法,对氢分子离子在不均匀场中高次谐波的产生进行了理论研究.计算结果显示,同均匀场相比,电离的电子在不均匀场中加速会获得更多的能量,从而更有利于得到宽频谱.此外,通过优化不均匀场中的空间不均匀度,长量子路径被明显的抑制,最终通过叠加110阶到150阶谐波,获得一个60as的孤立阿秒脉冲.同时,通过库仑势和激光场的相互作用势以及时频分布图解释了其中的物理机制.     

不均匀场中氢分子离子高次谐波产生的理论研究

在非Born-Oppenheimer近似下,通过求解含时薛定谔方程的方法,对氢分子离子在不均匀场中高次谐波的产生进行了理论研究.计算结果显示,同均匀场相比,电离的电子在不均匀场中加速会获得更多的能量,从而更有利于得到宽频谱.此外,通过优化不均匀场中的空间不均匀度,长量子路径被明显的抑制,最终通过叠加110阶到150阶谐波,获得一个60as的孤立阿秒脉冲.同时,通过库仑势和激光场的相互作用势以及时频分布图解释了其中的物理机制.     

Electric field gradients in fluoride crystalline powders: correlation of NMR measurements with ab initio calculations

Electric field gradients (EFG) of ²³Na and ²⁷Al in three model fluoride crystalline powders AlF₃, Na₃AlF₆ and Na₅Al₃F₁₄ were computed using the density functional based electronic structure code WIEN97 and compared to values derived from nuclear magnetic resonance (NMR). First, results of measurements of ²³Na and ²⁷Al quadrupolar parameters in AlF₃, Na₃AlF₆ and Na₅Al₃F₁₄ were revisited by using high-resolution solid-state NMR. To determine chemical shifts and quadrupolar parameters with a high precision, the experimental procedure involved magic angle spinning, satellite transition spectroscopy and multi-quanta techniques applied to the quadrupolar nuclei together with a computed reconstruction of the NMR spectra. The large discrepancies which appear between previously published results in some cases, justify the use of ab initio calculations of the corresponding EFG using the WIEN97 code based on the known structural data of the crystalline phases. The agreement obtained between these calculations and the experimental results which is better than 10% in almost all cases supports the reliability of the present NMR investigations and of the crystallographic data.     

非均匀磁场中等离子体射流质量色散强度

研究了非均匀磁场中多质量射流的运动轨迹,推导出质量色散强度表达式。考虑到不同入射方式及羽流角度的情况下,应用MATLAB模拟射流的运动轨迹,计算出质量色散强度,并同均匀磁场中的质量色散强度大小相比较,以确定该种磁场中射流质量分离的效果。模拟结果表明:非均匀磁场中多质量射流的质量色散强度大于均匀磁场的情况,可实现等离子体射流的高效质量分离。     

Theoretical exploration of asymmetric molecular harmonic emission and attosecond pulse generation in the presence of spatially inhomogeneous plasmon-enhanced field

Asymmetric molecular harmonic generation from HeH²⁺ ion in the presence of the spatially inhomogeneous plasmon-enhanced field has been theoretically investigated by solving the two-dimensional non-Born–Oppenheimer time-dependent Schrödinger equation (both the electron and nuclear motions are considered only along the laser polarisation axis). It shows that (1) for the normal homogeneous field, the harmonic cut-off from the asymmetric molecule is beyond the classical harmonic cut-off energy from the atom (I_p + 3.17 U_p). Further analyses show that the multi-channels ionisation–recombination process is responsible for the harmonic extension. (2) For the spatially inhomogeneous plasmon-enhanced field, the harmonic cut-off can be further enhanced, and an optimal 3.0 dB enhanced field with a 482 eV supercontinuum has been obtained. Quantum time-frequency harmonic analyses have been shown to explain the harmonic characteristics and the harmonic extension process. (3) Initial vibrational state and isotopic effects show that intense harmonics can be generated from higher initial vibrational state and the heavier molecule. Finally, by properly superposing the harmonics, a series of sub-30 as attosecond pulses can be obtained.     

Electric field gradients in Hf2Fe

Perturbed Angular Correlations (PAC) technique was applied to measure the electric field gradients (EFG) at ¹⁸¹Ta sites in Hf₂Fe. The compound has the cubic structure of the Ti₂Ni prototype with two non‐equivalent crystallographic sites for Hf atoms. EFGs for the two sites were measured as a function of the temperature. In addition, one more EFG was observed, which was assigned to the presence of defects in the lattice. The ratio of the measured EFG at the regular lattice sites has been used to assign charges to the ions through a simple calculation using the point charge model and it is shown that the lattice symmetry can explain the very different EFG at both sites. This revised version was published online in August 2006 with corrections to the Cover Date.     

Al quadrupole interaction in zeolites loaded with probe molecules—a quantum-chemical study of trends in electric field gradients and chemical bonds in clusters

The electric field gradient (EFG) has been calculated in zeolite clusters at the aluminium site surrounded by four SiO₄ tetrahedra. Density functional theory (DFT) with the 6-31G^{* *} basis set has been employed. Formation of a Brønsted acid site by protonation of one oxygen atom of the A1O₄ tetrahedron perturbs the coordination of aluminium, i.e., the corresponding Al-O bond is considerably weaker than in the unprotonated case. This leads to a large EFG, and the calculated quadrupole coupling constant (QCC) for ²⁷Al is 18.2 MHz. Different probe molecules were adsorbed on the Brønsted site. The hydrogen bond formed between the acid proton and the probe molecule weakens the zeolitic O---H bond. For conservation of the overall bond order of the oxygen atom, its bonds to the neighboring tetrahedral atoms (Si, Al) become stronger. As a consequence, the perturbation of the AlO₄ tetrahedron and the EFG at the aluminium position decrease depending on the strength of the hydrogen bond. Perturbation of an oxygen atom of the AlO₄ tetrahedron by accepting a hydrogen bond from the base molecule also affects the corresponding AlO---O bond order. A linear correlation is found between the calculated QCC constants for ²⁷Al and the AlO---O bond orders of the oxygen atoms which are perturbed by protonation or by hydrogen bonds. A geometrical shear strain parameter and a simple electrostatic point charge model are less successful at predicting the trends in EFG which clearly shows the importance of the chemical bonds. Published by Elsevier Science B.V.     

NMR tomography in an unstable and inhomogeneous polarizing magnetic field

A method of NMR imaging and elimination of image distortions in an inhomogeneous and unstable polarizing magnetic field is developed. An algorithm is given to determine the plane shifts of signals caused by a change in the magnetic field. Institute of Applied Physics of the National Academy of Sciences of Belarus, 16, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Priklanoi Spektroskopii, Vol. 66, No. 2, pp. 270–274, March–April, 1999.     

The internal magnetic field distribution, and single exponential magnetic resonance free induction decay, in rocks

When fluid saturated porous media are subjected to an applied uniform magnetic field, an internal magnetic field, inside the pore space, is induced due to magnetic susceptibility differences between the pore-filling fluid and the solid matrix. The microscopic distribution of the internal magnetic field, and its gradients, was simulated based on the thin-section pore structure of a sedimentary rock. The simulation results were verified experimentally. We show that the 'decay due to diffusion in internal field' magnetic resonance technique may be applied to measure the pore size distribution in partially saturated porous media. For the first time, we have observed that the internal magnetic field and its gradients in porous rocks have a Lorentzian distribution, with an average gradient value of zero. The Lorentzian distribution of internal magnetic field arises from the large susceptibility contrast and an intrinsic disordered pore structure in these porous media. We confirm that the single exponential magnetic resonance free induction decay commonly observed in fluid saturated porous media arises from a Lorentzian internal field distribution. A linear relationship between the magnetic resonance linewidth, and the product of the susceptibility difference in the porous media and the applied magnetic field, is observed through simulation and experiment.     

Synchronization of spiral waves in a two-layer coupled inhomogeneous excitable system

We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.     

Electric field gradients in simple tetragonal lattice at interstitial site

Electric field gradient (efg) is calculated at the centre of the cell in the simple tetragonal crystal. The method uses Euler-Maclaurin summation formula and makes the planewise summation in the direct crystal space without any special regrouping of charges in point charge model. The results are in fair agreement with previous results of de Wette on the same system using Fourier transform to reciprocal space.