Valence bond theory (VBT)

Valence Bond Theory (VBT) explains complex formation through hybridisation of the metal ion's atomic orbitals. Although the resulting hybrid orbitals are a purely theoretical construct -- they cannot actually be observed or detected spectroscopically -- they remain a useful tool for describing a complex's real structure. The theory's core steps: (i) the metal ion offers up its VACANT d orbitals to form coordinate bonds with incoming ligands; (ii) these vacant d orbitals mix together with the metal's available s and p orbitals to form a new set of hybrid orbitals; (iii) the NUMBER of hybrid orbitals formed always equals the number of ligand donor atoms bonding to the metal, which is exactly the complex's coordination number; (iv) each vacant hybrid orbital on the metal overlaps with a FILLED donor orbital on a ligand, and this orbital overlap is what forms each individual metal-ligand coordinate bond; (v) since hybrid orbitals have fixed spatial directions, they point exactly toward where each ligand sits, so the hybridisation type directly determines the complex's overall geometry (Table 9.5): sp gives linear (C.N.=2), sp3 gives tetrahedral (C.N.=4), dsp2 gives square planar (C.N.=4), and d2sp3/sp3d2 both give octahedral (C.N.=6); (vi) crucially, WHICH d orbitals get used in the hybridisation matters -- using the lower-energy (n-1)d orbitals (already partly occupied) gives an 'inner orbital' complex, generally low spin, while using the higher-energy, empty nd orbitals instead gives an 'outer orbital' complex, generally high spin. Putting this into practice for any specific complex follows a fixed sequence of steps: find the metal ion's oxidation state; write out its free-ion valence-shell electron configuration in a box diagram; decide whether the complex is high spin or low spin (this distinction only matters for octahedral complexes with a d4 to d8 free-ion configuration); count how many metal orbitals are needed, from the number of ligands (=coordination number); identify exactly which m …