Scattering model

RHEED intensities cannot be explained using the kinematic theory. Dynamical scattering models of RHEED intensities are being developed. With them one will be able to obtain positions of the surface atoms within the surface unit cell. At this writing, such modeling has been done primarily for LEED. 

All of the studies published so far have been aiming at the reconstruction of the total electron density in the crystal by redistribution of all electrons, under the constraints imposed by the MaxEnt requirement and the experimental data. After the acceptance of this paper, the authors became aware of valence-only MaxEnt reconstructions contained in the doctoral thesis of Garry Smith [58], The authors usually invoke the MaxEnt principle of Jaynes [23-26], although the underlying connection with the structural model, known under the name of random scatterer model, is seldom explicitly mentioned. 

When it is employed to specify an ensemble of random structures, in the sense mentioned above, the MaxEnt distribution of scatterers is the one which rules out the smallest number of structures, while at the same time reproducing the experimental observations for the structure factor amplitudes as expectation values over the ensemble. Thus, provided that the random scatterer model is adequate, deviations from the prior prejudice (see below) are enforced by the fit to the experimental data, while the MaxEnt principle ensures that no unwarranted detail is introduced. 

The error-free likelihood gain, V,( /i Z2) gives the probability distribution for the structure factor amplitude as calculated from the random scatterer model (and from the model error estimates for any known substructure). To collect values of the likelihood gain from all values of R around Rohs, A, is weighted with P(R) ... 

An interesting aspect of the present arrangement arises in connection with the poor quality of the data set and at the same time the reliability of H-atom positions. These are included in the scattering model with a fair amount of ambiguity in their positions, more than usual in X-ray experiments. Certain abnormalities in the geometry of the carboxyl groups may be understood as a result of conformational... 

Contact resistance values calculated by the diffuse scattering model are higher than those obtained experimentally in the case that the two materials are similar (in density and... 

In mesoscopic physics, because the geometries can be controlled so well, and because the measurements are very accurate, current under different conditions can be appropriately measured and calculated. The models used for mesoscopic transport are the so-called Landauer/Imry/Buttiker elastic scattering model for current, correlated electronic structure schemes to deal with Coulomb blockade limit and Kondo regime transport, and charging algorithms to characterize the effects of electron populations on the quantum dots. These are often based on capacitance analyses (this is a matter of thinking style - most chemists do not consider capacitances when discussing molecular transport junctions). 

The scattering models employed in data processing invariably involve the assumption of particle sphericity. Size data obtained from the analysis of suspensions of asymmetrical particles using laser diffraction tend to be somewhat more ambiguous than those obtained by electronic particle counting, where the solid volumes of the particles are detected. 

Figure 26. Three-dimensional electron scattering model for a resist on a thick substrate with a scanning electron beam of zero diameter.

The use of more sophisticated scattering models, in which bonding effects on the charge density are taken into account, discussed in chapter 3, leads to a significant improvement in the results of the rigid-bond test. An example, based on a low-temperature analysis of p-nitropyridine-N-oxide, is given in Table 2.3. 

Since the scale factor is considered an unknown in the least-squares procedure, its estimate is dependent on the adequacy of the scattering model. Other parameters that correlate with k may be similarly affected. In particular, the temperature factors are positively correlated with k, the correlation being more pronounced the smaller the sin 0//. range of the data set, as for a small range the scale factor k and the temperature factor exp ( —fl sin 02ft.2) affect the structure factors in identical ways. 

As discussed in the previous section, a residual density calculated after least-squares refinement will have minimal features. This is confirmed by experience (Dawson 1964, O Connell et al. 1966, Ruysink and Vos 1974). Least-biased structural parameters are needed if the adequacy of a charge density model is to be investigated. Such parameters can be obtained by neutron diffraction, from high-order X-ray data, or by using the modified scattering models discussed in chapter 3. 

The X-N technique is sensitive to systematic errors in either data set. As discussed in chapter 4, thermal parameters from X-ray and neutron diffraction frequently differ by more than can be accounted for by inadequacies in the X-ray scattering model. In particular, in room-temperature studies of molecular crystals, differences in thermal diffuse scattering can lead to artificial discrepancies between the X-ray and neutron temperature parameters. Since the neutron parameters tend to be systematically lower, lack of correction for the effect leads to sharper atoms being subtracted, and therefore to larger holes at the atoms, but increases in peak height elsewhere in the X-N deformation maps (Scheringer et al. 1978). 

The main purpose of the method is to define molecular shapes through isodensity surfaces. Tests on a number of small molecules show that this aim is achieved with a great efficiency in computer time. Discrepancies between MEDLA densities and theoretical distributions, averaged over the grid points, are typically below 10% of the total density. While this does not correspond to an adequate accuracy for an X-ray scattering model, the results do provide important information on the shapes of macromolecules. 

In the cellular multiple scattering model , finite clusters of atoms are subjected to condensed matter boundary conditions in such a manner that a continuous spectrum is allowed. They are therefore not molecular calculations. An X type of exchange was used to create a local potential and different potentials for up and down spin-states could be constructed. For uranium pnictides and chalcogenides compounds the clusters were of 8 atoms (4 metal, 4 non-metal). The local density of states was calculated directly from the imaginary part of the Green function. The major features of the results are ... 

I would like to ask Prof. J. Troe whether he could discuss some typical situations where the SAC approximation may fail. For example, consider the F + HBr — FHBr — HF(u) + Br reaction with energy E just above the potential barrier V41. In this situation, the adiabatic channels in the transition state ( ) should be populated only in the vibrational ground state, and they should, therefore, yield products HF(u = 0) + Br, according to the assumption of adiabatic channels. This is in contrast with population inversion in the experimental results that is, the preferred product channels are HF(i/) + Br, where v = 3, 4 [1] see also the quantum scattering model simulations in Ref. [2]. The fact that dynamics cannot be rigorously adiabatic (as in the most literal interpretation of SAC) has been discussed by Green et al. [3], and the most recent results (for the case of ketene) are in Ref. 4. 

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