Crystal Field Theory

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In an octahedral crystal field, the five degenerate d orbitals split into two sets; which orbitals are raised to the higher-energy e_g level?

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Crystal field theory treats ligands as point negative charges that approach the metal along specific directions. In an octahedral field the six ligands approach along the x, y and z axes, so d orbitals pointing directly at the ligands feel greater electrostatic repulsion and rise in energy. The d_{z^2} and d_{x^2-y^2} orbitals are axially oriented and therefore form the higher-energy, doubly degenerate e_g set. The remaining d_{xy}, d_{yz} and d_{zx} orbitals point between the axes, experience less repulsion, and constitute the lower-energy t_{2g} set. The option naming d_{xy} and d_{yz} describes t_{2g} members, not e_g. The triple set d_{xy}, d_{yz}, d_{zx} is the entire t_{2g} group. The mixed pair d_{z^2} and d_{yz} is inconsistent because d_{yz} is not axial. This splitting pattern is the foundation of CFT in NCERT. Plausibility check: only two axial orbitals can lie in e_g, matching the e_g superscript notation and the 3:2 t_{2g}:e_g division of five d orbitals.

Crystal Field Theory

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