By Claus E. Schà ffer (auth.), D Michael P. Mingos, Thomas Schönherr (eds.)
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Extra info for Optical Spectra and Chemical Bonding in Inorganic Compounds: Special Volume dedicated to Professor Jørgensen I
Sample text
With Angular Overlap Model Parameters 43 crystal field theory it would be quite difficult to estimate a set of parameters for a new complex and predict the spectrum, something that is particularly easy with the angular overlap model. 3 Experimental Approaches to AOM Parameter Values Despite the grim outlook in the orthoaxial general case, there are several approaches to the problem of nonunique AOM parameters for particular types of complexes. 1 Anchor Parameters by Setting ep for Saturated Amines to Zero The earliest approach was offered by Schäffer and Jørgensen in the Mat Fys Medd paper.
17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. Schäffer CE, Jørgensen CK (1965) Mat Fys Medd Dan Vid Selsk 34(13) Jørgensen CK, Pappalardo R, Schmidtke H-H (1963) J Chem Phys 39:1422 Schäffer CE, Jørgensen CK (1965) Mol Phys 9:401 Schmidtke H-H (1964) Z Naturforsch 19A:1502 Ballhausen CJ, Moffitt W (1956) J Inorg Nucl Chem 3:178 Ballhausen CJ (1962) Introduction to ligand field theory. McGraw-Hill, New York Perumareddi JR (1967) J Phys Chem 71:3144 Lever ABP (1968) Coord Chem Rev 3:119 Jørgensen CK (1971) Modern aspects of ligand field theory.
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 [1]: 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.