Coordination number calculation

Fig. 5. The MES f-factors versus site coordination numbers calculated for cub-octahedral Auj3 and AUjs as well as several larger magic-number and non-magic-number cuboctahedral cluster sizes. The symbols are defined as follows ...

At the same conditions of density and temperature, the smallest cation (Na" ") has larger dynamic hydration number than K" " and Rb", as found experimentally from correlations of conductance measurements. The trend holds at all subcritical conditions. This behavior is opposite to that of static coordination numbers calculated from time-averaged radial distribution functions, which give increasing coordination numbers when the ionic radius increases. Another interesting feature of the hydration numbers is given by their temperature dependence. For all ions at 573 K, dynamic hydration numbers (even when lower than their corresponding coordination numbers) are approximately the same as they are at ambient conditions. The same characteristic is observed at supercritical conditions, as illustrated in Table 12. 

Equation 5.1 gives an appropriate approximation of coordination numbers for ideal agglomerate structures. Table 5.1 lists coordination numbers calculated from Equation 5.1 and compares them with coordination numbers of ideal structures, like some illustrated in Figure 5.2. 

Coordination Number The coordination number Cnn, as discussed before, is calculated by integrating the g(r) till its first minimum (rc) using the equation Cm, = pg r)dr. Hence, the most important inputs that goes in to the calculation of the Cnn is the rc and the density of the liquid. Hence, the differences in the g(r) (both from experiments and simulations) and the difference in the densities measured and calculated by experiments and simulations, will reflect in the differences we find in the calculated coordination numbers as it can seen in the Fig. 6. To evaluate how much the coordination numbers calculated by SW potential are affected by the underestimation of the density, we have shown in the Fig. 6 the coordination numbers calculated using both the densities obtained in the simulations and the experimental density values [50]. 

The coordination numbers calculated are very sensitive to the location of the first minima of g(r) and the density. There is a large spread in the coordination numbers reported by different experimental groups, between 5 and 6.5. 

Donor strengths, taken from ref. 207b, based upon the solvent effect on the symmetric stretching frequency of the soft Lewis acid HgBr2. Gutmann s donor number taken from ref 207b, based upon AHr for the process of coordination of an isolated solvent molecule to the moderately hard SbCL molecule in dichioroethane. ° Bulk donor number calculated as described in ref 209 from the solvent effect on the adsorption spectrum of VO(acac)2. Taken from ref 58, based on the NMR chemical shift of triethylphosphine oxide in the respective pure solvent. Taken from ref 61, based on the solvatochromic shift of a pyridinium-A-phenoxide betaine dye. 

The reaction coordinate is calculated in a number of steps. If too few steps are used, then the points that are computed will follow the reaction coordinate less closely. Usually, the default number of points computed by software packages will give reasonable results. More points may be required for complex mechanisms. This algorithm is sometimes called the IRC algorithm, thus creating confusion over the definition of IRC. 

The ratio between the anionic and cationic radii leads to coordination numbers, the lowest of which is 6, which correspond to a octahedral polyhedron of anions around a central cation [135]. In this case, the compound structure type depends on the ratio of total number of anions and cations. The total number of anions (X) is calculated by summing up the number of oxygen (O) ions and of fluorine (F) ions X=0+F, while the total number of cations (Me) is the number of tantalum ions, niobium ions and other similar cations. 

Three conceptual steps can be discerned in the definition of the ionic structure of fluoride melts containing tantalum or niobium. Based on the very first thermodynamic calculations and melting diagram analysis, it was initially believed that the coordination numbers of tantalum and niobium, in a molten system containing alkali metal fluorides, increase up to 8. 

The radii av a2 and coordination numbers zv z2 follow from x-ray analysis (cf. Section I.B), and aQ/2 — 1.25 A corresponds to Pauling s van der Waals radius of 1.40 A for a covalently bound oxygen atom.25 The value of eQlk — 166.9°K was chosen to obtain agreement between calculated and experimental values of the equilibrium vapor pressure of argon hydrate at 0°C. 

The best way to determine the type of unit cell adopted by a metal is x-ray diffraction, which gives a characteristic diffraction pattern for each type of unit cell (see Major Technique 3 following his chapter). However, a simpler procedure that can be used to distinguish between close-packed and other structures is to measure the density of the metal we then calculate the densities of the candidate unit cells and decide which structure accounts for the observed density. Density is an intensive property, which means that it does not depend on the size of the sample (Section A). Therefore, it is the same for a unit cell and a bulk sample. Hexagonal and cubic close packing cannot be distinguished in this way, because they have the same coordination numbers and therefore the same densities (for a given element). 

Calculate the number of cations, anions, and formula units per unit cell in each of the following solids (a) the rock-salt unit cell shown in Fig. 5.39 (h) the fluorite (CaF2) unit cell shown here, (c) What are the coordination numbers of the ions in fluorite ... 

Fig. 1.—The correction AR = i (CN12) — R(A2) from the A2 structure to coordination number 12. The dashed curve and its extension are calculated by equation 3 the full line passes through the experimental values.

In applying the metallic radii in the discussion of the structure of a metal or intermetallic compound either the observed distances may be used with the single-bond radii to calculate the bond numbers, the sums of which may then be compared with the expected valences, or the distances may be compared with the sums of radii for suitable coordination numbers, such as CN12. The correction to be added to i (CN12) to give the radius for another coordination number, the va-... 

By CNDO calculation BE is an increasing function of cluster size for Ag clusters and for Ni clusters [54]. The calculations for Ni clusters showed that the contribution an atom makes to the total BE is proportional to its coordination number [54]. The orbital energies of Ni follow a smooth function of cluster size. As size increases, LUMO decreases and HOMO increases. This represents a convergence of IP and electron affinity values with increase in size. 

The effects of adsorbate coverage (film thickness) on the Pd 3d5/2 XPS peak positions of the Pd/W(l 1 0), Pd/ Re(0001), and Pd/Mo(l 10) systems were systematically investigated [63]. The peak positions reported for Pd coverage in excess of 1 ML represent a product of electrons emitted from surface and subsurface atoms. For the case of Pd(lOO), theoretical calculation suggest that the Pd 3d5/2 XPS BE of the surface atoms is 0.4 eV lower than that of bulk Pd. A similar difference has been observed experimentally for Ni and Pt surfaces. These shifts in BE are a consequence of variations in the coordination number of the surface atoms compared to bulk atom. If we reference the combined peak of bulk and surface atoms in 40 ML of Pd on W(1 1 0) to that of Pd(l 00) a difference of —0.8 eV is obtained between the Pd 3ds/2 BE of a pseudomorphic monolayer of Pd on W(110) and that of the surface atoms of Pd(l 00). The corresponding shifts... 

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