Symmetry octahedral

The aluminium ion, charge -I- 3. ionic radius 0.045 nm, found in aluminium trifluoride, undergoes a similar reaction when a soluble aluminium salt is placed in water at room temperature. Initially the aluminium ion is surrounded by six water molecules and the complex ion has the predicted octahedral symmetry (see Table 2.5 ) ... 

Many molecules, such as carbon monoxide, have unique dipole moments. Molecules with a center of inversion, such as carbon dioxide, will have a dipole moment that is zero by symmetry and a unique quadrupole moment. Molecules of Td symmetry, such as methane, have a zero dipole and quadrupole moment and a unique octupole moment. Likewise, molecules of octahedral symmetry will have a unique hexadecapole moment. 

Figure 4.19 Scanning electron microscope picture of cuprous oxide crystals as shown in Fig. 4.18. Note the partial octahedral symmetry.

For the alkali metal doped Cgo compounds, charge transfer of one electron per M atom to the Cgo molecule occurs, resulting in M+ ions at the tetrahedral and/or octahedral symmetry interstices of the cubic Cgo host structure. For the composition MaCgg, the resulting metallic crystal has basically the fee structure (see Fig. 2). Within this structure the alkali metal ions can sit on either tetragonal symmetry (1/4,1/4,1/4) sites, which are twice as numerous as the octahedral (l/2,0,0) sites (referenced to a simple cubic coordinate system). The electron-poor alkali metal ions tend to lie adjacent to a C=C double... 

Eg term. A magnetic moment of around 5.5 BM (i.e. 4.90 BM- -orbital contribution) is expected for pure octahedral symmetry but, in practice, distortions produce values in the range 5.2-5.4BM. Similarly, in the electronic spectrum, the expected single band due to the Eg t ge g) T2g t ge ) transition is broadened... 

Indeed, in. some cases it is probable that V2 is not ob.served at all, but that the fine. structure arises from term splitting due to spin-orbit coupling or to distortions from regular octahedral symmetry. 

A theoretical basis for the description of the cationic complex [Cp Ru(PR3)2 = = SiR2]+ can also be given. For a d6 CpML2 system, a complete splitting of the three orbitals (octahedral symmetry) is to be expected. Consequently, a coordinated silylene ligand (without any base) should prefer the indicated (Fig. 10) conformation. 

Calculations of the Jann-Teller coupling constants for dx systems in octahedral symmetry via the angular overlap model. K. D. Warren, Struct. Bonding (Berlin), 1984, 57,119 (20). 

The dy. p and dp yi orbitals each interact with four point charges in precisely the same way as does the dyi yi orbital. Again the repulsion relates to electron density, so the total interaction of the combination is (4/ /2) + (4/ /2) = 16 of our repulsion units. In other words, the d.2 and dp y2 orbitals are degenerate in octahedral symmetry. 

Figure 3-4. Barycentre splitting of the d orbitals in octahedral symmetry.

Perhaps only slightly less common than octahedral symmetry is tetrahedral symmetry. We now examine the d orbital splitting in this environment. The story is much the same as above, except that it is now convenient to place the four point charges of the tetrahedron as shown in Fig. 3-6. Here ligands are put at alternate... 

In an octahedral crystal field, for example, these electron densities acquire different energies in exactly the same way as do those of the J-orbital densities. We find, therefore, that a free-ion D term splits into T2, and Eg terms in an octahedral environment. The symbols T2, and Eg have the same meanings as t2g and eg, discussed in Section 3.2, except that we use upper-case letters to indicate that, like their parent free-ion D term, they are generally many-electron wavefunctions. Of course we must remember that a term is properly described by both orbital- and spin-quantum numbers. So we more properly conclude that a free-ion term splits into -I- T 2gin octahedral symmetry. Notice that the crystal-field splitting has no effect upon the spin-degeneracy. This is because the crystal field is defined completely by its ordinary (x, y, z) spatial functionality the crystal field has no spin properties. 

Figure 3-15. Splitting of the term arising from the configuration in octahedral symmetry.

Figure 3-20. The symmetrical pattern of ground term splittings in octahedral symmetry.

Figure 4-6. Partial correlation diagram for the spin-quartets of d ions in octahedral symmetry.

In octahedral symmetry, the F term splits into Aig + T2g + Tig crystal-field terms. Suppose we take the case for an octahedral nickel(ii) complex. The ground term is 2g. The total degeneracy of this term is 3 from the spin-multiplicity. Since an A term is orbitally (spatially) non-degenerate, we can assign a fictitious Leff value for this of 0 because 2Leff+l = 1. We might employ Van Vleck s formula now in the form... 

Warren KD (1984) Calculations of the Jahn-Teller Coupling Constants for d Systems in Octahedral Symmetry via the Angular Overlap Model. 57 119-145 Warren KD (1977) Ligand Field Theory off-Orbital Sandwich Complexes. 33 97-137 Warren KD (1976) Ligand Field Theory of Metal Sandwich Complexes. 27 45-159 Watson RE, Perlman ML (1975) X-Ray Photoelectron Spectroscopy. Application to Metals and Alloys. 24 83-132... 

XANES spectroscopy shows that a narrow and intense pre-edge peak at 4967 eV, due to the Is 3pd electronic transition involving Ti atoms in tetrahedral coordination, is present in well-manufactured TS-1 (Fig. 2c). Conversely this electronic transition of Ti(IV) species in Ti02 (anatase or rutile) is characterized by a very low intensity due to the small pd hybridization in octahedral symmetry. Indeed the transitions l2g are symmetrically forbidden in the case of octahedral coordination of Ti (IV), but the transition Ai T2 is allowed in the case of tetrahedral coordination of Ti(IV), as in the case of [Ti04] units [52,58-61,63,68]. 

Ethanol-dimethoxypropane solutions of either 1-formylisoquinoline or 2-formylquinoline thiosemicarbazone and cobalt(II) salts yield [Co(L)A2] complexes where A = Cl, Br, I, NO3, NCS, or NCSe [147]. All are non-electrolytes, have magnetic moments of 4.30-4.70 B.M. and are five coordinate with approximate trigonal bipyramidal stereochemistry involving NNS coordination based on electronic and infrared spectra. [Co(21-H)2] 2H2O was isolated from a cold methanolic solution of cobalt(II) chloride and 1-formylisoquinoline thiosemicarbazone [187]. Infrared spectral studies show NNS coordination the electronic spectral bands fit a distorted octahedral symmetry, and the magnetic moment is 4.48 B.M. 

---