crystal field stabilization energy
/ CFSE, 'see-eff-ess-ee' /
Splitting the d orbitals does more than make colors — it can lower a complex's total energy and make it more stable. The reason is simple bookkeeping: in an octahedral field, electrons that fall into the lower t2g set sit below where they would have been in the unsplit ion, while electrons forced up into eg sit above. If enough electrons land in the lower set, the ion comes out ahead. That net energy saving is the crystal field stabilization energy, or CFSE.
Computing it is easy once you fix the reference. Take the unsplit ion as zero. In an octahedron each t2g electron is worth -2/5 delta-o (it dropped) and each eg electron is worth +3/5 delta-o (it rose). So CFSE = (number in t2g) times (-2/5 delta-o) + (number in eg) times (+3/5 delta-o), and for low-spin cases you must also add back the extra pairing energy you paid to cram electrons together. A worked example: low-spin d6 [Co(NH3)6]3+ has all six electrons in t2g, giving 6 times -2/5 delta-o = -12/5 delta-o = -2.4 delta-o (before counting pairing), a very large stabilization that helps explain why this ion is so robust.
CFSE is the quiet hand behind many trends across the d block. It is largest for d3 and d8 in octahedral fields and for low-spin d6, and it is exactly zero for d0, d5 high-spin, and d10 (those distribute symmetrically and gain nothing). This extra stabilization, riding on top of the smooth electrostatic background, is what produces the famous double-humped curves in ionic radii, hydration energies, and lattice energies across a transition series — the fingerprints of CFSE in real thermodynamic data.
High-spin d5, like Mn2+ in [Mn(H2O)6]2+, has one electron in each of the five d orbitals: three in t2g (3 times -2/5) and two in eg (2 times +3/5), summing to -6/5 + 6/5 = 0. Its CFSE is zero, which is one reason Mn2+ complexes are pale, relatively unstable toward ligand exchange, and sit at the dip between the two humps of the radius curve.
Symmetrically filled d configurations (d0, high-spin d5, d10) gain no CFSE at all.
CFSE is only a small correction sitting on top of the much larger total bonding energy; it is enough to bias trends and tip close decisions, but it does not by itself hold a complex together — most of the binding comes from the overall metal-ligand attraction, including covalency the simple model ignores.