Numbers coordination

Definition of coordination number. The coordination number of an ion is the number of ions to which it is linked by electrostatic flux. 

Many of the tertiary bonds reported by Preiser et al. (1999) are likely artefacts of their calculations since these were based on the use of formal ionic charges. Substituting a more physically reasonable value for the formal ionic charge will reduce the total flux starting at the cation and eliminate many of the tertiary bonds around the highly charged cations where most tertiary bonds were found. However, there are some cases where tertiary bonds undoubtedly do occur and these can provide important information about the crystal chemistry. 

One example is the tertiary bond found in the wurtzite structure of ZnO (67454). All members of the Zn chalcogenide series crystallize with structures based on the close packing of the chalcogenide ions, with Zn occupying half the tetrahedral cavities. The higher members, ZnSe and ZnTe (31840), crystallize with the cubic sphalerite structure while ZnO crystallizes with the hexagonal wurtzite structure. ZnS (60378, 67453) is known in both forms. 

In the sphalerite structure the anions form a cubic close packed array. The structure has a single adjustable parameter, the cubic cell edge. The 0 ions are too small for them to be in contact in this structure (see Fig. 6.4) so ZnO adopts the lower symmetry hexagonal wurtzite structure which has three adjustable parameters, the a and c unit cell lengths and the z coordinate of the 0 ion, allowing the environment around the Zn ion to deviate from perfect tetrahedral symmetry. In the sphalerite structure the ZnX4 tetrahedron shares each of its faces with a vacant octahedral cavity (one is shown in Fig. 2.6(a)), while in the wurtzite structure one of these faces is shared with an empty tetrahedral cavity which places an anion directly over the shared face as seen in Fig. 2.6(b). The primary coordination number of Zn in sphalerite is 4 and there are no tertiary bonds, but in wurtzite, which has the same primary coordination number, there is an additional tertiary bond with a flux of 0.02 vu through the face shared with the vacant tetrahedron. 

A fuller discussion of the factors that determine the coordination number of the cation (including Zn ) can be found in Chapter 6. 

DISCUSSION OF SPECIAL COMPOUNDS 1. Compounds with Coordination Number 2 

With a coordination number 2, no true layer structure but at best a layered chain structure is possible. In other words, macroscopically, such a crystal can well possess one perfect cleavage plane, though the bonding is linear. 

The methods used for the determination of the number of solvent molecules contained in the inner-sphere coordination shell of metal ions have been reviewed by Lincoln [12]. The two most important are isotopic dilution and nuclear magnetic resonance. 

The first method is based on the statistical distribution of an iso-topically-labelled solvent such that the ratio of the concentration of isotopic solvent in the coordinated solvent to its concentration in the bulk solvent is equal to the ratio of coordinated solvent molecules to bulk solvent molecules. One obvious requirement is that the half-life of solvent exchange must be considerably longer than the time required for isotopic sampling. Furthermore, there must be an efficient means of separating the coordinated solvent from the bulk solvent. This approach was first used by Hunt and Taube [13] to establish the existence of Cr(H2 0)g as a distinct species in aqueous solution. Although only of limited application to metal ions more labile than Cr the method has been employed to determine the solvation number of the hydrated Al ion using a flow 

On the basis that a water proton in different electronic environments experiences different magnetic field strengths and therefore exhibits different chemical shifts, two distinct proton resonances should occur corresponding to bound and unbound water molecules provided that the exchange of solvent is not too rapid. Direct comparison of the integrated areas under the respective peaks will give the solvation number of the metal ion. The resonance signal from solvent molecules in the outer-sphere 

Solvation numbers of various metal ions in aqueous solution 

A simple property which has been the subject of many investigations is the coordination number (CN). We recall that the average coordination number can be obtained from the pair distribution function (section 2.5). Here, we are interested in more detailed information on the distribution of CN. 

Let Rc be a fixed number, to serve as the radius of the first coordination shell. If a is the effective diameter of the particles of the system, a reasonable choice of Rc for our purposes could be a Rc 1.5a. This range for Rc is in conformity with the meaning of the concept of the radius of the first coordination sphere around a given particle. In what follows, we assume that Rc had been fixed, and we omit it from the notation. 

The property to be considered here is the CN of the particle i at a given configuration RN of the system. This is defined by 

Each term in (2.92) contributes unity whenever Rj — Ri Rc, i.e., whenever the center of particle j falls within the first coordination sphere of particle i. Hence, Q(R1 ) is the number of particles (j i) that falls in the coordination sphere of a particle i for a given configuration RN. Next, we define the counting function for this property by 

we have used the notation 8(x K) for the Kronecker delta function, instead of the more common notation 8X K, for the sake of unity of notation. The meaning of 8 as a Dirac or Kronecker delta should be clear from the context. In the sum of (2.94) we scan all the particles (i = 1,2. N) of the system at a given configuration RN. Each particle whose CN is exactly K contributes unity to the sum (2.94), and zero otherwise. Hence, the sum in (2.94) counts all particles whose CN is exactly K for the particular configuration RN. The average number of such particles is 

N = 4 or 6 seems to give most acceptable results, although somewhat larger values of N are within the error of calculation (see Yoshida et al., 1973). Theoretical calculation of the coordination number depends on the value of V0, which is uncertain in water and ammonia. CKJ conclude that for a reasonable value of V0, between 0.5 and -0.5 eV, N = 4 or 6 is most appropriate for both water and ammonia. 

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Taking the ratio of successive tenns and dividing by the coordination number q... 

The melting and boiling points of the aluminium halides, in contrast to the boron compounds, are irregular. It might reasonably be expected that aluminium, being a more metallic element than boron, would form an ionic fluoride and indeed the fact that it remains solid until 1564 K. when it sublimes, would tend to confirm this, although it should not be concluded that the fluoride is, therefore, wholly ionic. The crystal structure is such that each aluminium has a coordination number of six, being surrounded by six fluoride ions. 

All the other aluminium halides are covalently bonded with aluminium showing a coordination number of four towards these larger halogen atoms. The four halogen atoms arrange themselves approximately tetrahedrally around the aluminium and dimeric molecules are produced with the configuration given below ... 

The d orbital splitting depends on the oxidation state of a given ion hence twb complex ions with the same shape, ligands and coordination number can differ in colour, for example... 

The change in colour when one ligand is replaced by another can be used to determine the coordination number thus if the colour change is measured in a colorimeter as the new ligand is added, the intensity of new colour reaches a maximum When the metal/ligand ratio is that in the new complex. 

It can be readily confirmed thaf by decreases as the number of bonds N increases and/or llieir length (r ) decreases. This relationship between the bond strength and the number of neighbours provides a useful way to rationalise the structure of solids. Thus the high coordination of metals suggests that it is more effective for them to form more bonds, even though each individual bond is weakened as a consequence. Materials such as silicon achieve the balance for an infermediate number of neighbours and molecular solids have the smallest atomic coordination numbers. 

PM3/TM is an extension of the PM3 method to transition metals. Unlike the parameterization of PM3 for organics, PM3/TM has been parameterized only to reproduce geometries. This does, of course, require a reasonable description of energies, but the other criteria used for PM3 parameterization, such as dipole moments, are not included in the PM3/TM parameterization. PM3/TM tends to exhibit a dichotomy. It will compute reasonable geometries for some compounds and completely unreasonable geometries for other compounds. It seems to favor one coordination number or hybridization for some metals. 

Another reaction in the last step is the syn elimination ofhydrogen with Pd as H—Pd—X, which takes place with alkyl Pd complexes, and the Pd hydride and an alkene are formed. The insertion of an alkene into Pd hydride and the elimination of, (3-hydrogen are reversible steps. The elimination of, 3-hydrogen generates the alkene, and both the hydrogen and the alkene coordinate to Pd, increasing the coordination number of Pd by one. Therefore, the / -elimination requires coordinative unsaturation on Pd complexes. The, 3-hydrogen eliminated should be syn to Pd. 

Shannon and Prewitt base their effective ionic radii on the assumption that the ionic radius of (CN 6) is 140 pm and that of (CN 6) is 133 pm. Also taken into consideration is the coordination number (CN) and electronic spin state (HS and LS, high spin and low spin) of first-row transition metal ions. These radii are empirical and include effects of covalence in specific metal-oxygen or metal-fiuorine bonds. Older crystal ionic radii were based on the radius of (CN 6) equal to 119 pm these radii are 14-18 percent larger than the effective ionic radii. 

On the assumption that the pairs of electrons in the valency shell of a bonded atom in a molecule are arranged in a definite way which depends on the number of electron pairs (coordination number), the geometrical arrangement or shape of molecules may be predicted. A multiple bond is regarded as equivalent to a single bond as far as molecular shape is concerned. 

Coordination Number Orbitals Hybridized Geometrical Arrangement Minimum Radius Ratio... 

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