By Claus E. Schà ffer (auth.), D Michael P. Mingos, Thomas Schönherr (eds.)
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Additional resources for Optical Spectra and Chemical Bonding in Inorganic Compounds: Special Volume dedicated to Professor Jørgensen I
56 . . . . . . 41 . . 43 44 45 51 . . . . . . . . . . 52 © Springer-Verlag Berlin Heidelberg 2004 38 Patrick E. Hoggard 1 In the Beginning One can scarcely imagine a more obscure venue than Det Kongelige Danske Videnskabernes Selskab, Matematisk-fysiske Meddelelser for the landmark paper on the angular overlap model (AOM). Appearing in 1965, “Energy Levels of Orthoaxial Chromophores and the Interrelation Between Cubic Parent Configurations”, by Claus Erik Schäffer and Christian Klixbüll Jørgensen, laid out the now familiar one-electron ligand field matrix elements for orthoaxial (all ligands on the Cartesian axes) complexes in terms of AOM parameters : odz 2 |V|dz 2 p = es z + 214 (es x + es y) + 243 (ed x + ed y) (1) odx2 – y2 |V|dx2 – y2 p = 243 (es x + es y) + ed z + 214 (ed x + ed y) (2) odxz |V|dxz p = ep x + ep z + ed y (3) odyz |V|dyz p = ep y + ep z + ed x (4) odxy |V|dxz p = ep x + ep y + ed x (5) l3 odz 2 |V|dx2 – y2 p = j 3 4 (es x – es x + ed x – ed y) (6) These matrix elements follow directly from the central premise of the angular overlap model, which is that each ligand exerts its effects separately on the metal d orbitals, and the net result for the metal ion can be taken as a sum of the effects of all ligands.
The parameters to be evaluated supply important information about the structure, chemical bonding, electron distribution, and other properties of these compounds. Among the parameters of the semiempirical models obtained, more attention should be directed to the parameters describing the d electron-electron interaction. , their values either follow some sequences independent of the central metal ion (nephelauxetic series) or they must fulfill some fundamental conditions concerning relative sizes as it is dealt with in the present chapter.
38 1 In the Beginning 2 The Problem of Nonunique Parameter Values 3 Experimental Approaches to AOM Parameter Values . . . . . 4 Anchor Parameters by Setting ep for Saturated Amines to Zero . Use Both Magnetic and Spectroscopic Data . . . . . . . Include Sharp-line Spin-forbidden Bands, Exact Geometry, and CI . Use Charge Transfer Bands to Find ep . . . . . . . . 4 Applications of AOM Parameters 5 Concluding Remarks . . . . . . . . .