Polarization effects structure functions

The distance of each reflection from the center of the pattern is a function of the fiber-to-film distance, as well as the unit-cell dimensions. Therefore, by measuring the positions of the reflections, it is possible to determine the unit-cell dimensions and, subsequently, index (or assign Miller indices to) all the reflections. Their intensities are measured with a microdensitometer or digitized with a scanner and then processed.8-10 After applying appropriate geometrical corrections for Lorentz and polarization effects, the observed structure amplitudes are computed. This experimental X-ray data set is crucial for the determination and refinement of molecular and packing models, and also for the adjudication of alternatives. 

For interfacial systems, potential functions should ideally be transferrable from the gas-phase to the condensed phase. Aqueous-mineral interfaces are not in the gas phase (although they may be close, see (7)), but both the water molecules and the atoms/ions in the substrate are in contact with an environment that is very different from their bulk environment. The easiest different environment to test, especially when comparing with electronic structure calculations, is a vacuum, so there is likely to be a great deal of information available on either the surface of the solid or the gas-phase polynuclear ion or the gas-phase aquo complex (i.e., Fe(H20)63+, C03(H20)62-). The gas-phase transfer-ability requirements on potential functions are challenging, but it is difficult to imagine constructing effective potential functions for such systems without using gas-phase systems in the construction process. This means that any water molecules used on these complexes must also transfer from the gas phase to the condensed phase. A fundamental aspect of this transferability is polarization. 

In general, for each acid HA, the HA-(H20) -Wm model reaction system (MRS) comprises a HA (H20) core reaction system (CRS), described quantum chemically, embedded in a cluster of Wm classical, polarizable waters of fixed internal structure (effective fragment potentials, EFPs) [27]. The CRS is treated at the Hartree-Fock (HF) level of theory, with the SBK [28] effective core potential basis set complemented by appropriate polarization and diffused functions. The W-waters not only provide solvation at a low computational cost they also prevent the unwanted collapse of the CRS towards structures typical of small gas phase clusters by enforcing natural constraints representative of the H-bonded network of a surface environment. In particular, the structure of the Wm cluster equilibrates to the CRS structure along the whole reaction path, without any constraints on its shape other than those resulting from the fixed internal structure of the W-waters. 

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