Coordination numbers contraction

Generally the structural data for a given phase are discussed by comparing the observed interatomic distances with the dimensions of the starting atoms. This can be done only if, for the considered structure, the atomic positional parameters are known with sufficient reliability. If so, a lot of information may be derived shape of the coordination polyhedron around each atomic kind and coordination number, contraction in the interatomic distances and indications concerning the type of bond. Atomic radii for the starting elements are derived from their metallic structures. These values refer to a given coordination number, which can be corrected to correspond to different coordination numbers... 

Crystal Structure and Ionic Radii. Crystal stmcture data have provided the basis for the ionic radii (coordination number = CN = 6), which are summarized in Table 9 (13,14,17). For both and ions there is an actinide contraction, analogous to the lanthanide contraction, with increasing positive charge on the nucleus. 

Instead, we believe the electronic structure changes are a collective effect of several distinct processes. For example, at surfaces the loss of the bulk symmetry will induce electronic states with different DOS compared to bulk. As the particle sizes are decreased, the contribution of these surface related states becomes more prominent. On the other hand, the decrease of the coordination number is expected to diminish the d-d and s-d hybridization and the crystal field splitting, therefore leading to narrowing of the valence d-band. At the same time, bond length contraction (i.e. a kind of reconstruction ), which was observed in small particles [89-92], should increase the overlap of the d-orbitals of the neighboring atoms, partially restoring the width of the d-band. 

The third category is the high coordination number lanthanides and actinides. The trivalent lanthanides show a decrease in with the progressive filling of the 4f orbitals, called the lanthanide contraction. Since the 4f orbitals are shielded by the filled 5s and 5p orbitals, the electronic configuration has no remarkable effect and therefore the variation in rM and an eventual change in coordination number and geometry determine the lability of the 1st coordination shell. 

The three metals are chemically similar. The especially close similarity between the Zr and Hf chemistries can be remarked. This may be mainly related to the effect of the lanthanide contraction having made their radii (both atomic and ionic) nearly identical. In comparison with Ti, the larger atomic dimensions of Zr and Hf result in more basic oxides and tendency to achieve higher coordination numbers, etc. 

On the contrary, a quite systematic behavior with the lanthanoid ion contraction is observed. A plot of the energy of CTI band versus the ionic radius at coordination number 8 of the Ln ions (16) indicates a linear decrease of this energy as the ionic radius increases. This is seen in Figure 3, and illustrates a bare size effect of the energy variation. The phenomenon is called "optical detection of the lanthanoid ion contraction by internal charge transfer absorption". 

The reaction of SiF-coupled six-membered rings with lithium organyls first produces ring contraction and subsequently eliminates LiF. As discussed in Section II, we have now obtained an intermediate ylide that contains silicon atoms with the coordination numbers three and five. This gives rise to a nucleophilic migration of a methanide ion. A fused bicyclic compound is formed (Scheme 24). This compound has also been characterized by an X-ray analysis and the structure is shown in Fig. 13. Both the four-membered rings are planar.42,46,50... 

Scheme I and, in more detail, Table 4 represent the trend of ionic radii of these large cations which prefer formal coordination numbers in the range of 8-12 [77]. For example, considering the effective Ln(III) radii for 9-co-ordination, a discrepancy of 0.164 A allows the steric fine-tuning of the metal center [60]. The structural implications of the lanthanide contraction can be visually illustrated by the well-examined homoleptic cyclopentadienyl derivatives (Fig. 2) [78], Three structure types are observed, depending on the size of the central metal atom A, [( j5—Cp)2Ln(ji— 5 rf — Cp)] x, 1 < % < 2 B Ln(fj5 —Cp)3 C, [fo -CpJjLnCi- 1 ff1—Cp)], these exhibit coordination numbers of 11 (10), 9, and 8, respectively. Also a small change in ligand substitution leads to a change in coordination behavior and number (10), as...

In these complexes anion coordination must be present with the exception of perchlorate. Lanthanide contraction may also be an influencing factor. The molecular structure [ 189] of Eu(TMU)3(N03)3 shows the presence of bidentate nitrates with a coordination number of nine. The coordination polyhedron is neither the tricapped trigonal prism nor the monocapped square antiprism which may be due to the small bite of nitrate ligand. The dimethyl acetamide (DMA) complexes behave similarly as those of tetramethyl urea (TMU) with less steric requirements as evidenced by the synthesis of [180-182] La(DMA)8(C104)3, La = La-Nd La(DMA)7(C104)3, La=Sm-Er La(DMA)6(C104)3, La = Tm-Lu. 

The second chapter deals with quantum chemical considerations, s, p, d and f orbitals, electronic configurations, Pauli s principle, spin-orbit coupling and levels, energy level diagrams, Hund s mles, Racah parameters, oxidation states, HSAB principle, coordination number, lanthanide contraction, interconfiguration fluctuations. This is followed by a chapter dealing with methods of determination of stability constants, stability constants of complexes, thermodynamic consideration, double-double effect, inclined w plot, applications of stability constant data. 

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