High-order data

As discussed in chapter 3, the valence electrons scatter mainly in the low-order region. Consequently, refinement of high-order data, first proposed by Jeffrey and Cruickshank (1953), yields parameters less biased by bonding effects. The X-X deformation density is calculated with the high-order X-ray parameters, and is defined as... 

The function C(u), plotted in Fig. 5.15, is a measure for the correlation between points A and B. As u is proportional to Hmax for a given value of Ir — r , the correlation between adjacent points decreases with Hmax, a manifestation of the increased resolution on adding high-order data. The correlation between adjacent points is generally positive, but it becomes slightly negative at u 5.8. 

Whereas there has been a huge interest in multimode calibration in the theoretical chemometrics literature, there are important limitations to the applicability of such techniques. Good, very high order, data are rare in analytical chemistry. Even three-way calibration, such as in DAD-HPLC, has to be used cautiously as there are frequent experimental difficulties with exact alignments of chromatograms in addition to interpretation of the numerical results. However, there have been some significant successes in areas such as sensory research and psychometrics. 

An excellent example in which the information obtained from X-X/,0 studies of deformation density maps has been compared with that from theoretical calculations is given by tetrafluoroterephthalonitrile. This compound is ideal for these studies because it contains no hydrogen atoms, and all the atoms have similar scattering power (6 to 9 electrons for C, N, and F). The molecule has high symmetry which simplifies the number of parameters to be refined. A very precise set of X-ray Bragg reflections were measured at a low temperature (98 K) and to sin0/A = 1.15 Least-squares refinement based on the high-order data... 

High-order data Bragg reflections with values of sin0/A greater than a value at which scattering due to valence electrons is judged to be small (around 0.8 A ). 

The larger the value of n, the more uniform is the size distribution. Other types of distribution functions can be found in Reference 1. Distribution functions based on two parameters sometimes do not accurately match the actual distributions. In these cases a high order polynomial fit, using multiple parameters, must be considered to obtain a better representation of the raw data. 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

As judged by vacuum stability test data (see below), Explosive D is of a very high order of stability. The material has been found to withstand storage at ordinary temps for a period of twenty years with no evidence of deterioration, and at 50° for more than five years without marked deterioration... 

Our results indicate that dispersion coefficients obtained from fits of pointwise given frequency-dependent hyperpolarizabilities to low order polynomials can be strongly affected by the inclusion of high-order terms. A and B coefficients derived from a least square fit of experimental frequency-dependent hyperpolarizibility data to a quadratic function in ijf are therefore not strictly comparable to dispersion coefficients calculated by analytical differentiation or from fits to higher-order polynomials. Ab initio calculated dispersion curves should therefore be compared with the original frequency-dependent experimental data. 

Preliminary room temperature x-ray data of 0.65 Me4C00-PECH indicates that the sample presents a highly ordered smectic mesophase which was not yet completely assigned. The textures seen by polarized optical microscopy are also typical of smectic phases. Due to the very high molecular weights involved, textures specific to mesophase in thermodynamic equilibrium could not be developed within a reasonable amount of time by annealing. 

Two new insect toxicants, aldrin and dieldrin, provide new halogenated insect toxicants with an extremely high order of toxicity toward insects, combined, for the first time, with complete stability to alkalies. Under all the usual conditions of use these new toxicants are also stable to acids. Data illustrate the order of magnitude of the insecticidal activity of these materials and their utility. Aldrin is a relatively nonresidual material, in contrast to dieldrin which, because of its high persistence, exhibits prolonged residual activity. 

Difference density maps from the current data and the SC [11] data after high order refinements are shown in Figure 1(a) and (b). The main features of the maps agree... 

Figure 1. Difference map after high order refinement - data cutoff at sin 0/k = 0.9A1 for reflections with F2 > (a) this work (b) SC. Model map after multipole refinement - data cutoff at... 

With data averaged in point group m, the first refinements were carried out to estimate the atomic coordinates and anisotropic thermal motion parameters IP s. We have started with the atomic coordinates and equivalent isotropic thermal parameters of Joswig et al. [14] determined by neutron diffraction at room temperature. The high order X-ray data (0.9 < s < 1.28A-1) were used in this case in order not to alter these parameters by the valence electron density contributing to low order structure factors. Hydrogen atoms of the water molecules were refined isotropically with all data and the distance O-H were kept fixed at 0.95 A until the end of the multipolar refinement. The inspection of the residual Fourier maps has revealed anharmonic thermal motion features around the Ca2+ cation. Therefore, the coefficients up to order 6 of the Gram-Charlier expansion [15] were refined for the calcium cation in the scolecite. 

Tm data 2-D NMR CD fluorescence propose rigid oxidant in highly-ordered environment... 

Fourth, kinetic data of the sulfur extrusion reaction of thiepin will provide direct evidence for the transition state of the process. Data on the conversion of the thiepin 34 into its corresponding naphthalene derivative are available 2SK The substantially large negative activation entropy (AS si —24 cal mol-1 deg-1) points to the existence of a highly ordered transition state, namely a thianorcaradiene, in the reaction. 3,4-Bis(methoxycarbonyl)-5-hydroxybenzo[/>]thiepin 33 thermally... 

Transition matrix estimators have received less attention than the multicanonical and Wang-Landau methods, but have been applied to a small collection of informative examples. Smith and Bruce [111, 112] applied the transition probability approach to the determination of solid-solid phase coexistence in a square-well model of colloids. Erring ton and coworkers [113, 114] have also used the method to determine liquid-vapor and solid-liquid [115] equilibria in the Lennard-Jones system. Transition matrices have also been used to generate high-quality data for the evaluation of surface tension [114, 116] and for the estimation of order parameter weights in phase-switch simulations [117]. 

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