Error matrices in gas-electron diffraction: I. Effects of systematic errors in intensities

Error matrices in gas-electron diffraction: II. Influence of weight matrix

1. Introduction 3721.1 Residual dipolar couplings as a route to structure and dynamics 3721.2 A brief history of oriented phase high resolution NMR 3742. Theoretical treatment of dipolar interactions 3762.1 Anisotropic interactions as probes of macromolecular structure and dynamics 3762.1.1 The dipolar interaction 3762.1.2 Averaging in the solution state 3772.2 Ordering of a rigid body 3772.2.1 The Saupe order tensor 3782.2.2 Orientational probability distribution function 3802.2.3 The generalized degree of order 3802.3 Molecular structure and internal dynamics 3813. Inducing molecular order in high resolution NMR 3833.1 Tensorial interactions between the magnetic field and anisotropic magnetic susceptibilities 3833.2 Dilute liquid crystal media: a tunable source of order 3843.2.1 Bicelles : from membrane mimics to aligning media 3853.2.2 Filamentous phage 3873.2.3 Transfer of alignment from ordered media to macromolecules 3883.3 Magnetic field alignment 3893.3.1 Paramagnetic assisted alignment 3893.3.2 Advantages of using magnetic alignment 3894. The measurement of residual dipolar couplings 3914.1 Introduction 3914.2 Frequency based methods 3924.2.1 Coupling enhanced pulse schemes 3924.2.2 In phase anti-phase methods (IPAP): 1DNH couplings in proteins 3934.2.3 Exclusive correlated spectroscopy (E-COSY): 1DNH, 1DNC′ and 2DHNC′ 3954.2.4 Extraction of splitting values from the frequency domain 3964.3 Intensity based experiments 3974.3.1 J-Modulated experiments: the measurement of 1DCαHα in proteins 3974.3.2 Phase modulated methods 3994.3.3 Constant time COSY – the measurement of DHH couplings 3994.3.4 Systematic errors in intensity based experiments 4005. Interpretation of residual dipolar coupling data 4015.1 Structure determination protocols utilizing orientational constraints 4015.1.1 The simulated annealing approach 4015.1.2 Order matrix analysis of dipolar couplings 4025.1.3 A discussion of the two approaches 4025.2 Reducing orientational degeneracy 4035.2.1 Multiple alignment media in the simulated annealing approach 4045.2.2 Multiple alignment media in the order matrix approach 4055.3 Simplifying effects arising due to molecular symmetry 4065.4 Database approaches for determining protein structure 4076. Applications to the characterization of macromolecular systems 4086.1 Protein structure refinement 4086.2 Protein domain orientation 4096.3 Oligosaccharides 4136.4 Biomolecular complexes 4156.5 Exchanging systems 4167. Acknowledgements 4188. References 419Within its relatively short history, nuclear magnetic resonance (NMR) spectroscopy has managed to play an important role in the characterization of biomolecular structure. However, the methods on which most of this characterization has been based, Nuclear Overhauser Effect (NOE) measurements for short-range distance constraints and scalar couplings measurements for torsional constraints, have limitations (Wüthrich, 1986). For extended structures, such as DNA helices, for example, propagation of errors in the short distance constraints derived from NOEs leaves the relative orientation of remote parts of the structures poorly defined. Also, the low density of observable protons in contact regions of molecules held together by factors other than hydrophobic packing, leads to poorly defined structures. This is especially true in carbohydrate containing complexes where hydrogen bonds often mediate contacts, and in multi-domain proteins where the area involved in domain–domain contact can also be small. Moreover, most NMR based structural applications are concerned with the characterization of a single, rigid conformer for the final structure. This can leave out important mechanistic information that depends on dynamic aspects and, when motion is present, this can lead to incorrect structural representations. This review focuses on one approach to alleviating some of the existing limitations in NMR based structure determination: the use of constraints derived from the measurement of residual dipolar couplings (D).

The Jiangmen Underground Neutrino Observatory has critical requirements on quality of the liquid scintillator, one of which is long attenuation length. A system with a height of 3 m is used to precisely measure the attenuation length of the liquid scintillators. The light generated by a LED is transmitted through an optical fiber. After being focused, filtered and collimated, the light enters the test tube with the liquid scintillator and is detected by the PMT. The stepping motor is controlled by the Labview program to adjust the level of the liquid scintillator, and the emitted light intensity of different liquid levels can be obtained to fit the attenuation length. In addition, the systematic errors have been studied, which includes the measurement error of the emitted light intensity and the error caused by the movement of light spot, and the latter is responded to the non-uniformity of the PMT photocathode. Meanwhile, analytical methods were improved. The system can measure the attenuation length stably and a small error was obtained, including statistical error and systematic error (0.69–23.70 m).

The molecular structure of trimethylphosphine–boron tribromide (CH3)3P·BBr3 has been determined from gas electron-diffraction and vibrational-spectroscopic data. The molecular parameters and their uncertainties were rg(B–Br)=2.010±0.009 Å, rg(P–B)=1.946±0.029 Å, rg(C–P)=1.804±0.004 Å, rg(C–H)=1.098±0.010 Å, ∠BrBBr=111.7±0.7°, and ∠CPC=108.0±0.7°. The potential barrier around the P–B bond was also estimated to be about 10 kcal mol−1 (1 cal=4.184 J).

This paper reports on the dosimetric effects of random and systematic modulator errors in delivery of dynamic intensity modulated beams. A sliding-widow type delivery that utilizes a combination of multileaf collimators (MLCs) and backup diaphragms was examined. Gaussian functions with standard deviations ranging from 0.5 to 1.5 mm were used to simulate random positioning errors. A clinical example involving a clival meningioma was chosen with optic chiasm and brain stem as limiting critical structures in the vicinity of the tumour. Dose calculations for different modulator fluctuations were performed, and a quantitative analysis was carried out based on cumulative and differential dose volume histograms for the gross target volume and surrounding critical structures. The study indicated that random modulator errors have a strong tendency to reduce minimum target dose and homogeneity. Furthermore, it was shown that random perturbation of both MLCs and backup diaphragms in the order of σ = 1 mm can lead to 5% errors in prescribed dose. In comparison, when MLCs or backup diaphragms alone was perturbed, the system was more robust and modulator errors of at least σ = 1.5 mm were required to cause dose discrepancies greater than 5%. For systematic perturbation, even errors in the order of ±0.5 mm were shown to result in significant dosimetric deviations.

The effect of fluorination in trimethylamine: gas-phase structures of CF3N(CH3)2 and (CF3)2NCH3

IntroductionT2 relaxometry has become an important tool in quantitative MRI. Little focus has been put on the effect of the refocusing flip angle upon the offset parameter, which was introduced to account for a signal floor due to noise or to long T2 components. The aim of this study was to show that B1 imperfections contribute significantly to the offset. We further introduce a simple method to reduce the systematic error in T2 by discarding the first echo and using the offset fitting approach.Materials and MethodsSignal curves of T2 relaxometry were simulated based on extended phase graph theory and evaluated for 4 different methods (inclusion and exclusion of the first echo, while fitting with and without the offset). We further performed T2 relaxometry in a phantom at 9.4T magnetic resonance imaging scanner and used the same methods for post-processing as in the extended phase graph simulated data. Single spin echo sequences were used to determine the correct T2 time.ResultsThe simulation data showed that the systematic error in T2 and the offset depends on the refocusing pulse, the echo spacing and the echo train length. The systematic error could be reduced by discarding the first echo. Further reduction of the systematic T2 error was reached by using the offset as fitting parameter. The phantom experiments confirmed these findings.ConclusionThe fitted offset parameter in T2 relaxometry is influenced by imperfect refocusing pulses. Using the offset as a fitting parameter and discarding the first echo is a fast and easy method to minimize the error in T2, particularly for low to intermediate echo train length.

The molecular structure of tungsten oxide tetrachloride was determined by the sector-microphotometer method of gas electron diffraction. The molecule was found to have a square-pyramidal structure, and the following molecular parameters were obtained by a least-squares method; rg(W–Cl)=2.281±0.003 Å, rg(W–O)=1.686±0.011 Å, and rg(Cl···Cl(s))=3.151±0.015 Å. The OWCl angle, 102.4±1.3°, is much larger than the corresponding angles found in other square-pyramidal molecules such as XeOF4 and IF5.

The cumulant analysis (CA) method was expanded to tetrahedrally symmetric molecules. In conjunction with real time gas electron diffraction (GED/RT), the method was applied to study the molecular structural parameters of CF 4 over the temperature range from 298 to 673K. The molecular parameters of CF 4 by the cumulant analysis method were compared with those from the simplified cumulant analysis (SCA) and traditional method. The value of the equilibrium distance (r e ) for bonded distance C-F was used as a criterion for the accuracy of anharmonic force fields obtained from high resolution spectroscopy. The accuracies of five different anharmonic forces fields have been tested by using CA. The equilibrium structural parameters of CF 4 were obtained by CA and SCA. The equilibrium distances (r e ) were 131.51(4) pm by SCA for C-F of CF 4 at 298K.

Nuclear magnetic resonance spectroscopy of molecules aligned in nematic liquid crystalline media provides information on the molecular structure and order parameters. The partial alignment of the molecules in the liquid crystalline phases gives rise to residual intramolecular dipolar couplings which are dependent on internuclear distances, and therefore yield information on the structure of molecules. The dipolar couplings are in general large compared to chemical shifts, and the spectra become rapidly complex with the increase in the number of interacting spins and decrease of symmetry of molecules. In this article, the procedure for the analyses of such spectra is outlined in a pedagogical manner. The concept of the order parameter is illustrated in a phenomenological way. The utility of the technique and obtainable information is demonstrated using practical examples. ©1998 John Wiley & Sons, Inc. Concepts Magn Reson 10: 167–192, 1998

Nuclear Magnetic Resonance (NMR) spectroscopy of molecules aligned in liquid crystalline media provides information on molecular structure and order parameters. The partial alignment of the molecules in the anisotropic phase of the liquid crystals gives rise to residual intramolecular dipolar couplings which are dependent on the internuclear distances and therefore yield information on the geometry of molecules. The spectra of these aligned molecules become rapidly complex with the increase in the number of interacting spins and with decrease in the symmetry of the molecules. The spectra of these molecules are generally strongly coupled and are complex. Thus the first order analysis of the spectra as applicable to liquid state is generally not applicable and one should resort to numerical analysis using computers. In this report problems associated with the analyses of such complex spectra, methods developed to aid such analyses and the precision of the structural parameters derived are discussed. Use of mixed liquid crystals of opposite diamagnetic susceptibility anisotropies to extract information which is otherwise not possible to derive using single liquid crystals is highlighted. Current developments in the field with special emphasis on the discovery of a novel liquid crystal with low order parameter and the use of natural abundance deuterium NMR spectra of the probe molecules for the analyses of complex spectra are discussed.

The distance between the host and guest molecular components of the supramolecular inclusion compound p-tert-butylcalix[4]arene–fluorobenzene is examined by solid-state rotational-echo double resonance (REDOR) NMR and single-crystal X-ray diffraction (XRD) techniques. Unlike many compounds studied with REDOR, no isotopic enrichment is required for either interacting nuclei. The 13C NMR signal of the host methyl group is modulated by heteronuclear dipolar interactions with the 19F-containing guest in REDOR NMR experiments. REDOR curves using internuclear distances derived directly from the XRD structural unit cell fail to match those determined experimentally. This discrepancy arises from two limitations: (1) consideration of only a single C–F internuclear distance, and (2) use of a static structural model, which neglects the effect of motional averaging on the heteronuclear dipolar interaction. Dipolar interactions between the guest fluorine and both the host methyl group of the immediate host cavity and the crystallographically-equivalent methyl carbon of the adjacent host cavity must be considered in this SI2-spin system. Additionally, rapid t-butyl methyl group reorientation reduces the effective C–F dipolar interaction. When a structural model incorporating both multiple spin interactions and molecular reorientation is used, the REDOR curve approaches the experimental curve within experimental error. A mathematical treatment of the angular and distance dependence of a generalized SIn system of n-spins under motional conditions is developed. These results extend the scope of distance-determining NMR techniques such as REDOR to systems complicated by disorder, molecular reorientation and multiple-spin interactions.

We report the results of a precise test of charge symmetry in the scattering of polarized neutrons from polarized protons at a laboratory bombarding energy of 183 MeV. The observable sensitive to charge symmetry is the difference between the analyzing powers associated with the neutron spin [${\mathit{A}}_{\mathit{n}}$(\ensuremath{\theta})] and with the proton spin [${\mathit{A}}_{\mathit{p}}$(\ensuremath{\theta})]. Systematic errors and experimental ambiguities in the measurement of this difference are extensively discussed. Our result for \ensuremath{\Delta}A\ensuremath{\equiv}${\mathit{A}}_{\mathit{n}}$-${\mathit{A}}_{\mathit{p}}$, averaged over the angular range 82.2\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\mathrm{\ensuremath{\theta}}}_{\mathrm{c}.\mathrm{m}.}$\ensuremath{\le}116.1\ifmmode^\circ\else\textdegree\fi{}, is (33.1\ifmmode\pm\else\textpm\fi{}5.9\ifmmode\pm\else\textpm\fi{}4.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$. With the statistical and systematic errors added in quadrature, this value is 3.4 standard deviations larger than the effect expected from pure photon exchange (the electromagnetic spin-orbit interaction) between the neutron and proton, and thus represents clear evidence of charge symmetry breaking in the strong interaction. We also extract information about the angular dependence of \ensuremath{\Delta}A(\ensuremath{\theta}), within limitations imposed by uncertainties in the measured beam and target polarizations. Both the angle-averaged value and the angular dependence measured for \ensuremath{\Delta}A are in excellent agreement with predictions from meson-exchange theory, when these include both the effect of the n-p mass difference on one-pion exchange and the isospin mixing of ${\mathrm{\ensuremath{\rho}}}^{0}$ and ${\mathrm{\ensuremath{\omega}}}^{0}$ mesons. In particular, the Bonn nucleon-nucleon (NN) potential model accounts for the present results utilizing \ensuremath{\rho}NN and \ensuremath{\omega}NN coupling constant values deduced previously for this potential from fits to more conventional NN scattering data.

The wave plate is a basic device for transforming and measuring the polarization states of light.It is known that the transformation of light by means of two wave plates makes it possible to measure the state of polarization in an arbitrary basis.The finite spectral width of the light, however, leads to a chromatic aberration of the polarization quantum transformation caused by the parasitic dispersion of the birefringence of the plate material.This causes systematic errors in the tomography of quantum polarization states and significantly reduces its accuracy.This study is a development of our work 1 , in which an adequate model for quantum measurements of polarization qubits under chromatic aberration was first formulated.This work includes a generalization of the results obtained earlier for the cases of two-qubit states.Along with examples of random states those uniformly distributed over the Haar measure are considered.Using a matrix of complete information, it is quantitatively traced how the presence of chromatic aberrations under conditions of a finite spectral width of light leads to the loss of information in quantum measurements.It is shown that the use of the developed model of fuzzy measurements instead of the model of standard projection measurements makes it possible to suppress systematic errors of quantum tomography even when using high-order wave plates.It turns out that the fuzzy measurement model can give a significant increase in the reconstruction accuracy compared to the standard measurement model.

Rotation and displacement errors between sensors and the Inertial Navigation System have significant effects on the accuracy of measured point clouds. In ship-borne mobile surveying systems, over and underwater targets are measured by a laser scanner and multibeam echo sounder, respectively. A simple calibration method and a universal calibration field are urgently needed to address both rotation errors and displacement problems for over and underwater sensors. First, a systematic error analytic function is established through the path that the geolocation expression of measured data is derived and substituted into the expression of known calibration planes. Then, the calibration expression that can calibrate both rotation errors and displacement is derived based on the least-squares criteria using a designed calibration pool. The calibrating results showed that for both over and underwater sensors, the accuracies of rotation errors and displacement estimation are better than 0.015° and 1.2 mm, respectively. After this calibration, the geolocation accuracy of measured points is better than 5 cm within a range of 30 m. The method can effectively calibrate systematic errors and serve as guidance to address the calibration problem for mobile surveying systems.