Consider a metal atom surrounded by a cube-shaped arrangementof eight ligand ato

Question

Consider a metal atom surrounded by a cube-shaped arrangementof eight ligand atoms (Oh Symmetry) (1) Derive the reducible representation for the 8-bands. (2) Show (step by step) how these can be reduced to a set foirreducible prpresentations (3) Which metal orbitals have the symmetry of theseitteducible representations? (4) Why do we not oberve this coordination arrangement? Consider a metal atom surrounded by a cube-shaped arrangementof eight ligand atoms (Oh Symmetry) (1) Derive the reducible representation for the 8-bands. (2) Show (step by step) how these can be reduced to a set foirreducible prpresentations (3) Which metal orbitals have the symmetry of theseitteducible representations? (4) Why do we not oberve this coordination arrangement?

Explanation / Answer

An essentially ionic approach to chemical bonding which is oftenused with coordination compounds. These compounds consist of acentral transition-metal ion that is surrounded by a regular arrayof coordinated atoms or ligands. Accordingly, the ligands areassumed to be sources of negative charge which perturb the energylevels of the central metal ion. In this respect the ligandssubject the metal ion to an electric field which is analogous tothe electric or crystal field produced by the regular distributionof nearest neighbors within an ionic crystalline lattice. Forexample, the crystal field produced by the Cl ion ligand inoctahedral TiCl63 is considered to besimilar to that produced by the octahedral array of the six Cl ionsabout each Na ion in NaCl. The Na ion with its rare-gasconfiguration has an electronic charge distribution which isspherically symmetric both within and without the crystal field.The paramagnetic Ti(III) ion, which possesses one 3delectron (d1), has a spherically symmetriccharge distribution only in the absence of the crystal fieldproduced by the ligands. The presence of the ligands destroys thespherical symmetry and produces a more complex set of energy levelswithin the central metal ion. The crystal field theory allows theenergy levels to be calculated and related to experimentalobservation.

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