New methodologies for computer simulation of paramagnetic resonance spectra

A new software package, SOPHE, for computer simulation of randomly oriented EPR spectra is described. A central feature of SOPHE is that all interactions associated with the electronic spins and major nuclear spins are treated equally through full matrix diagonalisation. In order to make this approach “workable”, several new methodologies have been developed, which include a novel partition scheme for partitioning the unit sphere, an interpolation scheme involving a combination of cubic spline and linear interpolations, and a segmentation method for handling multiple resonances between a given pair of energy levels. As a result, these new developments have led to a significant reduction in computational times. The SOPHE package can be used to simulate a variety of EPR spectra arising from isotropic organic radicals to complex coupled spin systems. It also incorporates the major linewidth models developed previously for the simulation of randomly oriented EPR spectra from magnetically isolated spin systems.     

EPR谱图模拟软件EasySpin的图形用户界面设计

EasySpin是一款较为流行的电子顺磁共振（EPR）谱图模拟和拟合软件,LabVIEW是一种图形化编程语言开发环境．本文介绍了一款使用LabVIEW为EasySpin设计的图形用户界面LV-EasySpin．LV-EasySpin提供了一种直观的操作方法来实现连续波EPR多组分波谱的可视化模拟和拟合．本文辅以各种模式下的实例进行说明,阐述了LV-EasySpin的设计思路与实现方案,最终希望具有简洁、易操作界面的LV-EasySpin可以降低用户使用EasySpin分析EPR谱图的难度．     

EasySpin, a comprehensive software package for spectral simulation and analysis in EPR

EasySpin, a computational package for spectral simulation and analysis in EPR, is described. It is based on Matlab, a commercial technical computation software. EasySpin provides extensive EPR-related functionality, ranging from elementary spin physics to data analysis. In addition, it provides routines for the simulation of liquid- and solid-state EPR and ENDOR spectra. These simulation functions are built on a series of novel algorithms that enhance scope, speed and accuracy of spectral simulations. Spin systems with an arbitrary number of electron and nuclear spins are supported. The structure of the toolbox as well as the theoretical background underlying its simulation functionality are presented, and some illustrative examples are given.     

一种EPR谱图模拟软件的研制

采用Microsoft Visual BASIC 4.0 for Windows 95编写了一个EPR谱图模拟软件.此软件采用鼠标控制命令按键进行程序过程.得到的图象分辨率和色彩优于用其他早期开发的BASIC语言编写的程序,打印的黑白图象质量也很好.运算时间小于20秒.这种软件可用于多种EPR模拟应用,包括自由基EPR谱图的模拟、过渡金属离子E PR谱图的模拟和二维EPR成像的模拟.EPR成像可以彩色强度图、等高线图或三维俯视图来表示.所有的模拟图象均可用激光打印机打印成黑白图片.自由基模拟程序的数据组有2560点.EPR成像的像素一般为128×128点.     

Simulation of Magnetic Resonance Static Powder Lineshapes: A Quantitative Assessment of Spherical Codes

Simulation of magnetic resonance static powder spectra is performed by a (possibly weighted) summation of single-crystal spectra computed for different orientations of the external field with respect to the principal axes of the magnetic interactions. The many available methods differ in the choice of the integration points (i.e., orientations) and weights, the set of which is called spherical code. There is continuing interest in minimizing the number of integration points necessary to a good simulation. Neglecting the possible interpolation of transition frequencies and intensities between integration points, we turn our attention to the efficiency of spherical codes themselves. To this end, an unbiased quantitative procedure to assess their efficiency in simulating magnetic resonance static powder spectra is proposed. To achieve an impartial judgement, the procedure has been designed by carefully taking into consideration the following points: choice of exact reference spectra; accurate definition of the merit figures; extended range of number of integration points; orientation dependence of the efficiency. The proposed procedure has been applied to an inclusive set of 23 spherical codes. It was found that most codes perform rather similarly. SPIRAL is the most efficient code, whereas Monte Carlo and “repulsive” codes show the best rotational invariance of the simulated lineshape with respect to the orientation of the spherical code.     

A three-dimensional electrostatic particle-in-cell methodology on unstructured Delaunay–Voronoi grids

The mathematical formulation and computational implementation of a three-dimensional particle-in-cell methodology on unstructured Delaunay–Voronoi tetrahedral grids is presented. The method allows simulation of plasmas in complex domains and incorporates the duality of the Delaunay–Voronoi in all aspects of the particle-in-cell cycle. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints. Electric potential and fields are derived from a finite-volume formulation of Gauss’ law using the Voronoi–Delaunay dual. Boundary conditions and the algorithms for injection, particle loading, particle motion, and particle tracking are implemented for unstructured Delaunay grids. Error and sensitivity analysis examines the effects of particles/cell, grid scaling, and timestep on the numerical heating, the slowing-down time, and the deflection times. The problem of current collection by cylindrical Langmuir probes in collisionless plasmas is used for validation. Numerical results compare favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. The versatility of the methodology is demonstrated with the simulation of a complex plasma microsensor, a directional micro-retarding potential analyzer that includes a low transparency micro-grid.     

Comparison of Continuous Wave, Spin Echo, and Rapid Scan EPR of Irradiated Fused Quartz

The E' defect in irradiated fused quartz has spin lattice relaxation times (T(1)) about 100 to 300 μs and spin-spin relaxation times (T(2)) up to about 200 μs, depending on the concentration of defects and other species in the sample. These long relaxation times make it difficult to record an unsaturated continuous wave (CW) electron paramagnetic resonance (EPR) signal that is free of passage effects. Signals measured at X-band (~9.5 GHz) by three EPR methods: conventional slow-scan field modulated EPR, rapid scan EPR, and pulsed EPR, were compared. To acquire spectra with comparable signal-to-noise, both pulsed and rapid scan EPR require less time than conventional CW EPR. Rapid scan spectroscopy does not require the high power amplifiers that are needed for pulsed EPR. The pulsed spectra, and rapid scan spectra obtained by deconvolution of the experimental data, are free of passage effects.     

Impact of High-Dielectric-Loss Materials on the Microwave Field in EPR Experiments

A dielectric material distorts the microwave field inside an EPR resonator, which results in distortion of the EPR signal from spins inside the material. In this paper, the effects of a spherical bulb filled with a dielectric liquid such as water or a water–ethanol mixture were examined. EPR spectra were recorded for small samples inside and outside of the sphere. The studies include CW and ESE experiments at two microwave frequencies, X band (9.2 GHz) and L band (1.03 GHz). The double integral (area) of an EPR signal depends on[formula]at the position of the sample, causing a large difference in EPR signal intensities between samples in regions of different dielectrics. The phase of the EPR signal also is affected by the presence of the dielectric. These results were compared with three methods of calculating electromagnetic fields (quasi-static method, plane-wave-superposition method, and numerical analysis). Good agreement was found between experimental and calculated results.     

Electron paramagnetic resonance imaging using magnetic-field-gradient spinning

A novel X-band CW EPR imaging has been developed using magnetic-field-gradient (MFG) spinning to obtain spatial distributions of electron paramagnetic species. Spinning MFG EPR imaging for 65 projection spectra required just 55 s while conventional imaging took 11 min 40 s, that is, the acquisition time for the new system is one order of magnitude shorter than that for conventional EPR imaging. Spinning MFG EPR imaging allows one to measure reconstructed images in an interactive manner where resolution and condition can be changed quickly.     

EPR and Optical Absorption Study of VO2+ Ions Doped Potassium Hexaaquazinc (II) Sulfate Single Crystals

X-band single-crystal electron paramagnetic resonance (EPR) studies are done on VO²⁺ ions doped in potassium hexaaquazinc (II) sulfate, K₂[Zn (H₂O)₆] (SO₄)₂ (PHZS) at room temperature. The spin Hamiltonian parameters, i.e., g and A tensors and their direction cosines, are evaluated by the standard diagonalization procedure using angular variation of the EPR spectra in three planes (ab, bc* and c*a), with the help of a computer program. The EPR spectrum is simulated using the EasySpin program to verify the calculations. The detailed EPR analysis indicates the presence of two magnetically inequivalent VO²⁺ sites. Both the vanadyl complexes are found to take up the substitutional position in the host lattice. The optical absorption spectrum of VO²⁺ ions doped in PHZS single crystal at room temperature is also recorded and four main d–d transfer bands in the visible region are assigned. The theoretical band positions are obtained using energy expressions and a good agreement is found with the experimental values. With the help of assigned bands the crystal-field parameters (Dq, Ds and Dt) are evaluated. Finally, with the optical and EPR data, the nature of bonding in the complex is discussed.     

用于全电磁粒子模拟的复杂建模及网格生成技术

 基于Open CASCADE开源的计算机辅助几何设计类库,给出了全电磁粒子模拟中复杂模型构建技术及网格生成技术。介绍了Open CASCADE软件的基本特点;给出了基于Open CASCADE进行自主研发的用于全电磁粒子模拟的复杂模型构建软件EasyEMModeling的设计思想、程序框架及已具备的功能;基于Open CASCADE中的射线与几何体的求交算法,给出了Yee网格中共形描述3维复杂模型的共形网格生成技术;最后,给出了验证实例,证实了共形网格生成方法的正确性及有效性。     

Fullerene C<Subscript>70</Subscript> Triplet Zero-Field Splitting Parameters Revisited by Light-Induced EPR at Thermal Equilibrium

Continuous-wave (CW) electron paramagnetic resonance (EPR) and echo-detected (ED) EPR spectra of triplet state of fullerene C₇₀ in molecular glasses of decalin, o-terphenyl and toluene, and in polymethylmethacrylate polymer were obtained under continuous light illumination. Temperature was high enough so that the EPR spectra corresponded to thermal equilibrium between the spin sublevels. The comparison of CW EPR and ED EPR data has shown that pseudorotation in the ³C₇₀ frame does not remarkably affect deriving the zero-field splitting (ZFS) D and E parameters from the EPR spectra. ³C₇₀ EPR spectra were simulated at 77 K fairly well using the distribution of the ZFS D and E parameters. These distributions may be caused by the inhomogeneity of the glassy matrix surrounding, which affects the Jahn–Teller distortions of ³C₇₀ molecules (D-strain and E-strain).     

X-band rapid-scan EPR of nitroxyl radicals

X-band rapid-scan EPR spectra were obtained for dilute aqueous solutions of nitroxyl radicals (15)N-mHCTPO (4-hydro-3-carbamoyl-2,2,5,5-tetra-perdeuteromethyl-pyrrolin-1-(15)N-oxyl-d(12)) and (15)N-PDT (4-oxo-2,2,6,6-tetra-perdeuteromethyl-piperidinyl-(15)N-oxyl-d(16)). Simulations of spectra for (15)N-mHCTPO and (15)N-PDT agreed well with the experimental spectra. As the scan rate is increased in the rapid scan regime, the region in which signal amplitude increases linearly with B(1) extends to higher power and the maximum signal amplitude increases. In the rapid scan regime, the signal-to-noise for rapid-scan spectra was about a factor of 2 higher than for unbroadened CW EPR, even when the rapid scan spectra were obtained in a mode that had only 4% duty cycle for data acquisition. Further improvement in signal-to-noise per unit time is expected for higher duty cycles. Rapid scan spectra have higher bandwidth than CW spectra and therefore require higher detection bandwidths at faster scan rates. However, when the scan rate is increased by increasing the scan frequency, the increase in noise from the detection bandwidth is compensated by the decrease in noise due to increased number of averages per unit time. Because of the higher signal bandwidth, lower resonator Q is needed for rapid scan than for CW, so the rapid scan method is advantageous for lossy samples that inherently lower resonator Q.     

Nonequivalent spectra of unpaired electrons in field and frequency modulation

We report a difference in the spectral lineshapes of continuous-wave (CW) electron paramagnetic resonance (EPR) spectroscopy between field and frequency modulation. This finding addresses the long-standing question of the effect of modulation in EPR absorption. We compared the first-derivative EPR spectra at 1.1 GHz for lithium phthalocyanine crystals, which have a single narrow linewidth in the EPR absorption spectrum, using field and frequency modulation. The experimental findings suggest that unpaired electrons have different behaviors under perturbation due to field and frequency modulation.     

Electron spin relaxation studies of La@C82 in the solid state by EPR

The temperature dependence of EPR spectrum of La@C₈₂ in the powder of empty C₆₀ and C₇₀ mixed crystals was studied by EPR spectroscopy employing X- and Q-band microwave frequencies. The rigid limit spectra (at 4.2 K for the X-band and at 132 K for the Q-band) could be analyzed by static spectral simulation which yielded the EPR parameters,g _‖=2.0021,g _⊥=1.9970,^La A _⊥=7.8 MHz,^La A _‖～0 MHz and an isotropic¹³C coupling value of about 3 MHz. For higher temperatures an appreciable motional averaging effect was observed and the spectra were analyzed by using dynamic spectral simulation based on the stochastic Liouville equation, where we assumed an isotropic rotational motion with the Brownian diffusion. The calculated spectra reproduced the dominant feature of the temperature dependence of the spectra almost satisfactorily for both the X-and Q-band frequencies with the appropriate rotational correlation times. The Arrhenius plots of the correlation time gave two activation energies of 0.9 kcal/mol and 2.9–3.8 kcal/mol for the temperatures below and above 200 K, respectively.     

EPR studies of the X-ray irradiated dithiophosphate salts

The powder EPR spectra of some ammonium and potassium salts of dithiophosphoric acid, (RO)₂P(S)SH, irradiated with X-rays at 77 K have been recorded and analyzed in respect to their distinguishable EPR-active components. In general each EPR spectrum is a superposition of isotropic and anisotropic features from a number of carbon- and phosphorus-centered radicals. Whereas carbon-centered radicals are practically isotropic the phosphorus-centered species exhibit threefold anisotropy with a large (700–800 G) isotropic³¹P hyperfine splitting. The identification of the latter is based on the magnitudes of the³¹P splitting as well as on the phosphorous 3p/3s spin densities ratio. The experimentally obtained EPR parameters of the studied radicals are refined using computer simulation procedure.     

Voronoi-cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids

We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schrödinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.     

EPR of Yb3+ ions in Ba1−xLaxF2+x mixed crystals

Electron paramagnetic resonance (EPR) spectra of impurity Yb³⁺ ions (about 0.1 at.%) in mixed crystals BaF₂(1-x) plus LaF₃(x) have been investigated for different values of the concentrationx at a frequency of about 9.5 GHz by both continuous-wave (CW) EPR and electron spin echo methods. A spectrum of trigonal symmetry with a complex hyperfine structure is observed in “pure” BaF₂:Yb³⁺ (x=0). Upon admixture of small amounts of LaF₃ (x=0.001), additional EPR lines arise with intensities increasing with the increase ofx up to 0.005. These lines are attributed to trigonal centers including two rare-earth ions and two compensating fluorine ions. A further increase ofx results in a decrease of the total EPR spectrum intensity, and atx≥0.05 the CW resonance becomes practically unobservable. This may be due to the formation of rare-earth ion clusters with paramagnetic Yb³⁺ ions occurring in domains with a disordered structure of surroundings resulting in very broad EPR lines, which cannot be registered by CW EPR. Indeed, very broad (not less than 1 KG) EPR lines were observed by the electron spin echo method for concentrationsx<-0.02.     

Models for the modern power grid

This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation.     

Generalized Pseudospectral Method for Solving the Time-Dependent Schrödinger Equation Involving the Coulomb Potential

We present an accurate and efficient generalized pseudospectral method for solving the time-dependent Schrödinger equation for atomic systems interacting with intense laser fields. In this method, the time propagation of the wave function is calculated using the well-known second-order split-operator method implemented by the numerically exact, fast transform between the grid and spectral representations. In the grid representation, the radial coordinate is discretized using the Coulomb wave discrete variable representation (CWDVR), and the angular dependence of the wave function is expanded in the Gauss-Legendre-Fourier grid. In the spectral representation, the wave function is expanded in terms of the eigenfunctions of the field-free zero-order Hamiltonian. Calculations on the high order harmonic generation and ionization dynamics of hydrogen atom in strong laser pulses are presented to demonstrate the accuracy and efficiency of the present method. This new algorithm will be found more computationally attractive than the close-coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.