Tetrahedral complexes

The pattern of d-orbital splitting predicted by CFT depends on the specific geometry of the surrounding ligand field, and the tetrahedral case gives a splitting pattern that is essentially the OPPOSITE of the octahedral one (Fig. 9.4 shows the tetrahedral geometry itself -- a central metal M with four ligands occupying the four corners of a tetrahedron, none of which lie directly along the x, y or z axes). In this tetrahedral arrangement, the three orbitals dxy, dyz and dzx (whose lobes lie diagonally, roughly pointing TOWARD where the ligands actually sit in a tetrahedral field) experience the GREATER repulsion and are pushed UP in energy; meanwhile dx2-y2 and dz2 (whose lobes lie more nearly BETWEEN the metal-ligand bond directions in this geometry) experience LESS repulsion and are pushed DOWN in energy -- exactly the reverse pairing of high-energy and low-energy orbital sets compared with the octahedral case (Fig. 9.5). Quantitatively, each electron placed in the higher-energy set (labelled simply t2 in a tetrahedral field, without the 'g' subscript used in the octahedral case, since a tetrahedron has no centre of symmetry) raises the total energy by 4 Dq, while each electron in the lower-energy set (labelled e) lowers it by 6 Dq. The overall magnitude of tetrahedral splitting, Delta-tet, works out to only about 4/9 of the equivalent octahedral splitting Delta-o for the same metal and ligands -- because in a tetrahedral arrangement, no single d orbital ever points directly at a ligand the way dz2 or dx2-y2 does along the axes in an octahedral field, so the repulsion (and hence the splitting) stays comparatively small throughout. Because Delta-tet is essentially always smaller than the electron-pairing energy, electron PAIRING is never energetically fa …