Crystal Field Stabilisation Energy

Crystal field stabilisation energy (CFSE) measures the net energy lowering when d electrons occupy the split t_{2g} and e_g levels rather than the hypothetical unsplit set. Each t_{2g} electron contributes -0.4 Delta_o and each e_g electron contributes +0.6 Delta_o, and any electron pairing forced beyond the free-ion arrangement adds the pairing energy P. In a low-spin d^6 case all six electrons crowd into the three t_{2g} orbitals as three pairs. The orbital term is therefore 6 × (-0.4 Delta_o) = -2.4 Delta_o. Because strong-field pairing creates two extra electron pairs compared with the high-spin distribution, a term +2P is added, giving CFSE = -2.4 Delta_o + 2P. The value -0.4 Delta_o describes only a single t_{2g} electron. The term -1.6 Delta_o + 2P miscounts the electrons as four. The bare -2.0 Delta_o ignores pairing entirely. This calculation follows the standard NCERT-level CFSE method. Plausibility check: a fully filled t_{2g}^6 low-spin set should give the maximum orbital stabilisation for an octahedral ion, consistent with the large -2.4 Delta_o magnitude obtained.