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Lecture_12 - MIT OpenCourseWare http/ocw.mit.edu 5.04...

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MIT OpenCourseWare http://ocw.mit.edu 5.04 Principles of Inorganic Chemistry II Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.04, Principles of Inorganic Chemistry II Prof. Daniel G. Nocera Lecture 12: Octahedral ML 6 Sigma Complexes An octahedral complex comprises a central metal ion and six terminal ligands. If the ligands are exclusively σ -donors, then the basis set for the ligands is defined as follows, Ligands that move upon the application of an operation, R, cannot contribute to the diagonal matrix element of the representation. Since the σ bond is along the internuclear axis that connects the ligand and metal, the transformation properties of the ligand are correspondent with that of the M–L σ bond. Moreover, a σ bond has no phase change within the internuclear axis, hence the bond can only transform into itself (+1) or into another ligand (0). E 8C 3 6C 2 6C 4 3C 2 (=C 4 2 ) i 6S 4 8S 6 3 σ h 6 σ d O h 6 0 0 2 2 0 0 0 4 2 Γ L σ Γ L σ = a 1g + t 1u + e g Need now to determine the SALCs of the L σ basis set. Three different methods will deliver the SALCs. Method 1 As we have done previously, the SALCs of L σ may be determined using the projection operator. Note that the ligand mixing in O h is retained in the pure rotational subgroup, O. Can thus drop from O h O, thereby saving 24 operations. O E C 3 C 3 C 3 C 3 C 3 C 3 C 3 C 3 C 2 C 2 C 2 C 2 C 2 C 2 C 4 C 4 C 4 C 4 C 4 C 4 C 2 C 2 C 2 L 1 L 1 L 3 L 4 L 4 L 5 L 6 L 5 L 6 L 3 L 2 L 2 L 6 L 5 L 4 L 3 L 1 L 1 L 5 L 3 L 4 L 6 L 1 L 2 L 2 The A 1 irreducible representation is totally symmetric. Hence the projection is simply the sum of the above ligand transformations.
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