Valence Bond Theory

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The octahedral complex [Co(NH3)6]^{3+} is found to be diamagnetic; which hybridisation of cobalt does valence bond theory assign to it?

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Valence bond theory describes octahedral complexes using either d^2sp^3 (inner orbital) or sp^3d^2 (outer orbital) hybridisation, the choice depending on whether inner (n-1)d orbitals are available. Cobalt in the +3 state has a 3d^6 configuration. Ammonia is a strong-field ligand, so it forces the six 3d electrons to pair up, vacating two inner 3d orbitals. These two empty 3d orbitals combine with one 4s and three 4p orbitals to give d^2sp^3 hybridisation, producing an inner-orbital, low-spin, diamagnetic octahedral complex. The sp^3d^2 option uses outer 4d orbitals and would leave unpaired electrons, making it paramagnetic, which contradicts the data. dsp^2 corresponds to square planar geometry, not octahedral. Plain sp^3 is tetrahedral and uses only four orbitals. The pairing forced by strong-field NH3, discussed in NCERT, is exactly why this complex is low spin. Plausibility check: complete pairing of all six d electrons leaves zero unpaired spins, consistent with the observed diamagnetism, confirming the inner-orbital assignment.

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