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(c) An octahedral cluster molecule E6 in Oh point symmetry can be formed without a central atom and is bonded together using the six s and eighteen p orbitals on the six atoms. Each vertex comprises a sp hybrid orbital (radial) pointing into the cluster, and two p orbitals (tangential) at right angles to each other and to the centre of the cluster (see figure below). These are the same as the ligand orbitals used in o- and x-bonding in octahedral transition metal complexes. The bonding overlaps between these orbitals are shown below in A, B and C, and two of these are each part of a triply degenerate set and the other is singly degenerate - remember in O₂ symmetry x, y and z are degenerate. E E E E two tangential p orbitals B The reducible representation for these bonding orbitals is: radial sp orbital Oh E 8C 6C₂ 6C 3C₂ i 684 8S6 30h Ibonding 7 1 -1 1 -1 1 1 11 (i) Determine the three irreducible representations for the orbitals that contribute to cluster bonding to form the seven MOS. (ii) Match the symmetry labels of the irreducible representations with MOS A to C. Hint: use the inversion symmetry to do this. (iii) Deduce the order in increasing energy of A, B and C by considering the number of nodal planes that slice through the middle of the octahedral cage. 60d 3

(c) An octahedral cluster molecule E6 in Oh point symmetry can be formed without a central atom and is bonded together using the six s and eighteen p orbitals on the six atoms. Each vertex comprises a sp hybrid orbital (radial) pointing into the cluster, and two p orbitals (tangential) at right angles to each other and to the centre of the cluster (see figure below). These are the same as the ligand orbitals used in o- and x-bonding in octahedral transition metal complexes. The bonding overlaps between these orbitals are shown below in A, B and C, and two of these are each part of a triply degenerate set and the other is singly degenerate - remember in O₂ symmetry x, y and z are degenerate. E E E E two tangential p orbitals B The reducible representation for these bonding orbitals is: radial sp orbital Oh E 8C 6C₂ 6C 3C₂ i 684 8S6 30h Ibonding 7 1 -1 1 -1 1 1 11 (i) Determine the three irreducible representations for the orbitals that contribute to cluster bonding to form the seven MOS. (ii) Match the symmetry labels of the irreducible representations with MOS A to C. Hint: use the inversion symmetry to do this. (iii) Deduce the order in increasing energy of A, B and C by considering the number of nodal planes that slice through the middle of the octahedral cage. 60d 3

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Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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(c) An octahedral cluster molecule E6 in Oh point symmetry can be formed without a central atom and is bonded together using the six s and eighteen p orbitals on the six atoms. Each vertex comprises a sp hybrid orbital (radial) pointing into the cluster, and two p orbitals (tangential) at right angles to each other and to the centre of the cluster (see figure below). These are the same as the ligand orbitals used in o- and x-bonding in octahedral transition metal complexes. The bonding overlaps between these orbitals are shown below in A, B and C, and two of these are each part of a triply degenerate set and the other is singly degenerate - remember in O₂ symmetry x, y and z are degenerate. E E E E two tangential p orbitals B The reducible representation for these bonding orbitals is: radial sp orbital Oh E 8C 6C₂ 6C 3C₂ i 684 8S6 30h Ibonding 7 1 -1 1 -1 1 1 11 (i) Determine the three irreducible representations for the orbitals that contribute to cluster bonding to form the seven MOS. (ii) Match the symmetry labels of the irreducible representations with MOS A to C. Hint: use the inversion symmetry to do this. (iii) Deduce the order in increasing energy of A, B and C by considering the number of nodal planes that slice through the middle of the octahedral cage. 60d 3
Transcribed Image Text:(c) An octahedral cluster molecule E6 in Oh point symmetry can be formed without a central atom and is bonded together using the six s and eighteen p orbitals on the six atoms. Each vertex comprises a sp hybrid orbital (radial) pointing into the cluster, and two p orbitals (tangential) at right angles to each other and to the centre of the cluster (see figure below). These are the same as the ligand orbitals used in o- and x-bonding in octahedral transition metal complexes. The bonding overlaps between these orbitals are shown below in A, B and C, and two of these are each part of a triply degenerate set and the other is singly degenerate - remember in O₂ symmetry x, y and z are degenerate. E E E E two tangential p orbitals B The reducible representation for these bonding orbitals is: radial sp orbital Oh E 8C 6C₂ 6C 3C₂ i 684 8S6 30h Ibonding 7 1 -1 1 -1 1 1 11 (i) Determine the three irreducible representations for the orbitals that contribute to cluster bonding to form the seven MOS. (ii) Match the symmetry labels of the irreducible representations with MOS A to C. Hint: use the inversion symmetry to do this. (iii) Deduce the order in increasing energy of A, B and C by considering the number of nodal planes that slice through the middle of the octahedral cage. 60d 3
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