Inner region

In order to determine the energy it would thus seem that it is necessary merely to minimise E with respect to the positions x and the displacements y. However, a complication arises due to the fact that the displacements in the outer region are themselves a function of the inner-region coordinates. The solution to this problem is to require that the forces on the ions in region 1 are zero, rather than that the energy should be at a minimum (for simple problems the two are synonymous, but in practice there rnay still be some non-zero forces present when the energy minimum is considered to have been located). An additional requirement is that the ions in region 2 need to be at equilibrium. 

The summation is over the different types of ion in the unit cell. The summation ca written as an analytical expression, depending upon the lattice structure (the orij Mott-Littleton paper considered the alkali halides, which form simple cubic lattices) evaluated in a manner similar to the Ewald summation this typically involves a summc over the complete lattice from which the explicit sum for the inner region is subtractec... 

One disadvantage is that the lower levels of theory must be able to describe all atoms in the inner regions of the molecule. Thus, this method cannot be used to incorporate a metal atom into a force field that is not parameterized for it. The effect of one region of the molecule causing polarization of the electron density in the other region of the molecule is incorporated only to the extent that the lower levels of theory describe polarization. This method requires more CPU time than most of the others mentioned. However, the extra time should be minimal since it is due to lower-level calculations on smaller sections of the system. 

In fine wool such as that obtained from merino sheep, the cuticle is normally one cell thick (20 x 30 x 0.5 mm, approximate dimensions) and usually constitutes about 10% by weight of the total fiber. Sections of cuticle cells show an internal series of laminations (Figs. 1 and 2) comprising outer sulfur-rich bands known as the exocuticle and inner regions of lower sulfur content called the endocuticle (13). On the exposed surface of cuticle cells, a membrane-like proteinaceous band (epicuticle) and a unique hpid component form a hydrophobic resistant barrier (14). These hpid and protein components are the functional moieties of the fiber surface and are important in fiber protection and textile processing (15). 

The sulphide usually forms an interconnected network of particles within a matrix of oxide and thus provides paths for rapid diffusion of nickel to the interface with the gas. At high temperatures, when the liquid Ni-S phase is stable, a duplex scale forms with an inner region of sulphide and an outer porous NiO layer. The temperature dependence of the reaction is complex and is a function of gas pressure as indicated in Fig. 7.40 . A strong dependence on gas pressure is observed and, at the higher partial pressures, a maximum in the rate occurs at about 600°C corresponding to the point at which NiS04 becomes unstable. Further increases in temperature lead to the exclusive formation of NiO and a large decrease in the rate of the reaction, due to the fact that NijSj becomes unstable above about 806°C. 

The values of all of the sites contained within the B x T) dotted inner region of this figure are completely determined by the values in the outer lined region. Since this surrounding area contains B- -2r T — 1)) sites (where V is, as usual, the range of the given CA rule), we have that... 

The nature of spheron-spheron interactions is such that maximum stability is achieved when each spheron ligates about itself the maximum number of neighbors, to produce a nucleus with a closest-packed structure. A simple argument (12) leads to the conclusion that the spherons in a nucleus are arranged in concentric layers. The packing radius of a spheron varies from 1.28 f for the dineutron to 1.62 f for the helion. The radius (to nucleon density half that of the inner region) of the largest nucleus is 6.8 f... 

Combustion is generally confined to fhe inner regions of the combustion chamber during stratified combustion. This is mainly because the late fuel injection does... 

It is seen that in the inner region (positive values of the abscissae), the atomic orbital is close neither to the optimal orbital nore to the un-optimised orbital. On the contrary, the atomic orbital is very close of the un-optimised orbital but not of the optimised one in the outer region (negative values of the abscissae). The inverse con-... 

The dielectric effect on the interactions among inner region atoms is represented... 

Although the formulation of GSBP is self-consistent, the validity of the approach depends on many factors especially the size of the inner region and the choice of the dielectric constant for the outer region. Therefore, for any specific application, the simulation protocol has to be carefully tested using relevant benchmarks such as pKa of key residues (see examples below in Sections 7.3.1 and 7.3.2). 

His residues at configurations sampled using the popular link-host-atom exclusion scheme changes the free energy derivatives by 8-9 kcal/mol despite that the QM/MM frontiers are far from the zinc-bound water. With this effect taken into account, the calculated pKa value for the zinc-bound water in the WT CAII is in encouraging agreement with experiment the value is 7.1 (5.4) for the 20 (25) A-inner-region simulations, as compared to the experimental value of around 7 [86],... 

So far we have considered the shape of the electron density of a limited inner region of each atom but not of the complete atom. How do we find the shape of the complete atom In other words, how do we find the interatomic surfaces that separate one atom from another and define the size and shape of each atom The atoms in molecules (AIM) theory developed by Bader and coworkers (4) provides a method for doing this. 

The vasa recta are modified peritubular capillaries. As with the peritubular capillaries, the vasa recta arise from efferent arterioles. However, these vessels are associated only with the juxtamedullary nephrons and are found only in the medullary region of the kidney. The vasa recta pass straight through to the inner region of the medulla, form a hairpin loop, and return straight toward the cortex. This structure allows these vessels to lie parallel to the Loop of Henle and collecting ducts. 

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