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By Iain D. Campbell

Publication through Campbell, Iain D., Dwek, Raymond A.

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It is clear that the expression tends to infinity as ε tends  Setting the scene towards zero (orbitals of the same energy). For orbitals whose energies are only slightly different, it is safer to use the result from the preceding paragraph (proportional to S). 3. 2. Interaction diagram for two orbitals with different energies. 2). From a chemical viewpoint, this means that the bonding MO is mainly based on the more electronegative centre (or fragment), but the antibonding MO on the less electronegative centre (or fragment).

2. 1. 5 for the analytical expressions of these symmetry-adapted orbitals and the method for finding them).  None of the ligand orbitals σi , considered individually, is a basis for the irreducible representations of the Oh group. For the construction of the orbital interaction diagram, it is therefore necessary to use linear combinations of these orbitals which are adapted to the symmetry of the octahedron. 1, next to the metal orbitals with the same symmetry. In the orbital of A1g symmetry, all the coefficients have the same value and sign.

Character table of the point group Oh Oh E 8C3 6C2′ 6C4 3C2 i 8S6 6σd 6S4 3σh A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u 1 1 2 3 3 1 1 2 3 3 1 1 −1 0 0 1 1 −1 0 0 1 −1 0 −1 1 1 −1 0 −1 1 1 −1 0 1 −1 1 −1 0 1 −1 1 1 2 −1 −1 1 1 2 −1 −1 1 1 2 3 3 −1 −1 −2 −3 −3 1 1 −1 0 0 −1 −1 1 0 0 1 −1 0 −1 1 −1 1 0 1 −1 1 −1 0 1 −1 −1 1 0 −1 1 1 −1 2 −1 −1 −1 −1 −2 1 1 x 2 + y2 + z2 (z2 , x 2 − y2 ) (xy, xz, yz) (x, y, z) d orbitals have Eg symmetry for the z2 and x 2−y2 pair, but T2g for the xy, xz, and yz set. It is thus important to realize that the five d orbitals, which clearly have the same energy for an isolated atom, are separated into two groups according to their symmetry properties: a doubly degenerate representation Eg and a triply degenerate set T2g .

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