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Additional resources for Advances in Chemical Physics: The Application of Wave Mechanical Methods to the Study of Molecular Properties, Volume 8
60 CHR. KLIXBULL J0RGENSEN Our conclusion today is that ligand-field theory is essentially the one-electron approximation used for the classification of the energy levels of inorganic chromophores. Note Added in Proof A certain revival of the ligand-field theory has recently taken place through the introduction of the angular overlap model [Jsrgensen, C. , and Schmidtke, H. , J . Chem. Phys. 39, 1422 (1963); Schmidtke, H. Naturjorsch. Teil a, in press; Schaffer, C. , and Jsrgensen, C. , submitted to Mol.
A+S-E B B a-E B 0 0 B a,-E 0.. 0.. o B . O = o (15) For sufficiently large 6 the depression of the trap level is given by the perturbation expression (16): AE = 2B2/d and E = a + 6 + 2/la18 (16) X. Energies for the Example rn = 6 The general character of the solutions to the energy problem can be shown in a specific example. We choose m = 6 because the analogue in molecular-orbital theory, namely the orbitals of benzene and heterocyclic derivatives, is a familiar one. The results hold independently of n, the total number of centres 38 D.
It is thus possible to concentrate on the manifold Y = 0. VII. Further Consideration of the r = 0 Manifold If the delocalized excitation functions (10) are re-written in the real form (13) the trigonometric coefficients are symmetric or 36 D. P. )4, j=O = (21%)' n-1 zsin (2~j/rt)$~ (13)* j=O antisymmetric to reflection at the site j == 0. If each function $j is mapped on to another of the same set by this reflection it is clear that the are symmetric and the @; antisymmetric. Now perturbation by regularly spaced guest molecules, one of which is at the site j = 0, varies as the cosine of 2nj/m and its multiples.