Valence electrons octahedral

For trinuclear cluster complexes, open (chain) or closed (cycHc) stmctures are possible. Which cluster depends for the most part on the number of valence electrons, 50 in the former and 48 in the latter. The 48-valence electron complex Os2(CO)22 is observed in the cycHc stmcture (7). The molecule possesses a triangular arrangement of osmium atoms with four terminal CO ligands coordinated in a i j -octahedral array about each osmium atom. The molecule Ru (00) 2 is also cycHc and is isomorphous with the osmium analogue. 

The octahedron is classified into the c/o o-structure by Wade [3,4]. Closo-structures with n skeletal atoms are stable when they have 4n-i- 2 valence electrons. Wade s rules predict that the 26 (= 4 x 6 + 2) valence electrons could stabilize the regular octahedrons since n is 6 for the octahedron. This prediction is contained in our 6N + 14 (N= 2) valence electron rule. Our rule also predicts the stability of octahedral metal clusters with the other numbers (14 and 20) of valence electrons. 

Solid-state cluster chemistry is dominated by octahedral (M 5L8)L6 and (MsLi2)L units which are the focus of this paper. These two cluster types are different in the way the metal octahedral core is surrounded by the ligands. In (MsLg)L6-type clusters (Fig. 6.1a), typical for molybdenum and rhenium halides, chalcogenides, and chalcohalides, eight innei hgands (L ) cap the octahedron faces and six outer ligands (L ) are located in the apical positions [9]. For metals with a smaller number of valence electrons, the (M6L i2)L -type clusters... 

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

The electronic structure of the spinel type compound NiCo204 has been investigated by XANES, EXAFS, and Ni Mdssbauer studies. On the basis of the derived cation valencies, the octahedral and tetrahedral site occupancies as well as the formula in standard notation for spinel compounds could be delineated [25]. 

However, certain polyhedra allow the inclusion of another electron pair without cleavage of any bond. This applies especially to octahedral clusters which should have 84 valence electrons according to equation (13.12), but they frequently have 86 electrons. The additional electron pair assumes a bonding action as a six-center bond inside the octahedron. An octahedral cluster with 86 valence electrons fulfills the Wade rule discussed below. 

In the Nb6Cljg ion the octahedral Nb6 cluster can be assumed to have eight 3c2< bonds on its eight octahedron faces. A chlorine atom bonded with two Nb atoms is situated next to each octahedron edge. This makes twelve Cl atoms in an Nb6Clj2 unit. The remaining six CP ions are terminally bonded to the octahedron vertices (Fig. 13.10). The number of valence electrons is ... 

KT1 does not have the NaTl structure because the K+ ions are too large to fit into the interstices of the diamond-like Tl- framework. It is a cluster compound K6T16 with distorted octahedral Tig- ions. A Tig- ion could be formulated as an electron precise octahedral cluster, with 24 skeleton electrons and four 2c2e bonds per octahedron vertex. The thallium atoms then would have no lone electron pairs, the outside of the octahedron would have nearly no valence electron density, and there would be no reason for the distortion of the octahedron. Taken as a closo cluster with one lone electron pair per T1 atom, it should have two more electrons. If we assume bonding as in the B6Hg- ion (Fig. 13.11), but occupy the t2g orbitals with only four instead of six electrons, we can understand the observed compression of the octahedra as a Jahn-Teller distortion. Clusters of this kind, that have less electrons than expected according to the Wade rules, are known with gallium, indium and thallium. They are called hypoelectronic clusters their skeleton electron numbers often are 2n or 2n — 4. 

Clusters derived from metals which have only a few valence electrons can relieve their electron deficit by incorporating atoms inside. This is an option especially for octahedral clusters which are able to enclose a binding electron pair anyway. The interstitial atom usually contributes all of its valence electrons to the electron balance. Nonmetal atoms such as H, B, C, N, and Si as well as metal atoms such as Be, Al, Mn, Fe, Co, and Ir have been found as interstitial atoms. 

The carbides with the NaCl structure may be considered to consist of alternating layers of metal atoms and layers of semiconductor atoms where the planes are octahedral ones of the cubic symmetry system. (Figure 10.1). In TiC, for example, the carbon atoms lie 3.06A apart which is about twice the covalent bond length of 1.54 A, so the carbon atoms are not covalently bonded, but they may transfer some charge to the metal layers, and they do increase the valence electron density. 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

In PF6 there are 5 + (6 x 7) +1 = 48 valence electrons or 24 electron pairs. A plausible Lewis structure follows. Since there are six atoms and no lone pairs bonded to the central atom, the electron-group geometry and molecular shape are octahedral. 

The chemistry of octahedral metal clusters culminates in the center of the Periodic Table with the heavy transition metals Nb, Ta, Mo, W, and Re. There is a plethora of clusters where the M-M bonded core is surrounded (and shielded) by non-metal ligands. When moving to the left of the Periodic Table the decrease in valence electron concentration calls for a stabilization through incorporation of interstitial atoms into the cluster core. Actually, the stabilization of the cluster occurs... 

In the dianion [Fe6(CO)i6C]2-, the carbide atom is completely encapsulated in the octahedral metal cage. This dianion (86 valence electrons) does not exhibit any redox process with characteristics of chemical reversibility.ld... 

To illustrate how the perturbation problem must be solved, we now describe one of the simplest cases, corresponding to an octahedral crystalline field acting on a single d valence electron. 

Consider the absorption spectrum of Ti + ions in AI2 O3 (sapphire), shown in Figure 5.4. (a) From this spectrum, estimate the amount lODq. (b) Assuming that the 3d valence electron describes a circular trajectory of 0.1 nm radius and that there is an octahedral environment of point charges (the ions), estimate the Ti +-0 distance in sapphire. 

Appendix A2 The Effect of an Octahedral Field on a d Valence Electron... 

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