high-spin and low-spin complexes
/ hy-spin / loh-spin /
When a metal ion has between four and seven d electrons, nature faces a choice. Should the electrons spread out to occupy as many orbitals as possible, keeping their spins parallel? Or should they crowd into the lowest orbitals, pairing up even though same-orbital partners repel each other? The first choice gives a high-spin complex with many unpaired electrons; the second gives a low-spin complex with few. Which one wins is one of the most consequential decisions in transition-metal chemistry.
Picture a d6 ion in an octahedral field, with three lower t2g orbitals and two upper eg orbitals separated by delta-o. The first three electrons drop into t2g singly. The fourth electron now has a dilemma: it can either pair up with an electron already in t2g — paying the pairing energy P, the cost of forcing two electrons into one orbital — or it can climb into the higher eg set, paying the splitting energy delta-o instead. The cheaper option wins. If delta-o is large (a strong-field ligand), pairing is cheaper, electrons stack into t2g, and you get low-spin with maximum pairing. If delta-o is small (a weak-field ligand), the climb is cheaper, electrons spread into eg, and you get high-spin with maximum unpaired spins. So the rule is simply: compare delta against P.
This is why magnetism is a direct readout of the spin state, and why the same metal can be magnetic in one complex and nearly not in another. [Fe(H2O)6]2+ is high-spin d6 with four unpaired electrons (paramagnetic), while [Fe(CN)6]4- is low-spin d6 with zero unpaired electrons (diamagnetic) — identical Fe2+, opposite spin states, because cyanide's large delta beats the pairing energy and water's small delta does not. A crucial honesty: the spin state is set by the balance of delta and P, not by the metal alone, and it depends just as much on the ligand.
Octahedral d6: high-spin fills t2g with four electrons (one paired, two single) and eg with two, leaving four unpaired; low-spin packs all six into t2g as three pairs, leaving zero unpaired. Measuring the magnetic moment tells you instantly which one you have — and therefore whether delta-o beat the pairing energy.
Counting unpaired electrons via magnetism directly reveals high-spin versus low-spin.
The high-spin/low-spin choice only arises for d4 through d7 in an octahedral field; d1, d2, d3, d8, d9, d10 have only one way to fill the levels and so have no spin-state ambiguity, and tetrahedral complexes are almost always high-spin because delta-t is too small to ever beat P.