Molecular Geometry & Bonding
what the shape decides
Concept

Low spin — where it appears

The filling of a d shell that pairs electrons in the lower orbitals rather than occupying the upper ones, taken when the splitting exceeds the pairing energy. It gives fewer unpaired electrons and a smaller magnetic moment than the high-spin arrangement of the same electron count.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

d⁶: two states, and where they cross. The energy of the high-spin and low-spin fillings of d⁶ against the splitting, in units of the pairing energy. They cross at Δ = P exactly, with 4 unpaired electrons below it and 0 above.

The pairing energy decides the moment

Whether the sixth d electron pairs up in the lower set or goes alone into the upper one is a competition between the splitting and the cost of pairing. Run the filling rules over the whole shell and exactly four configurations have a choice — and every one of them changes state at Δ = P exactly.

applied · Magnetism The total is the same in both columns; nothing else is. Ten complexes counted by both conventions. The neutral method gives the metal its group number and every ligand what it brings as a neutral fragment; the ionic method assigns an oxidation state and gives every anionic ligand a pair. The two totals agree in every row. The oxidation state and the d count do not agree wherever the oxidation state is not zero, and the moments the two d counts predict differ by as much as 2.83 Bohr magnetons.

The same count, two oxidation states

Count a complex by the neutral method and by the ionic one and the total is the same integer every time — eighteen for ferrocene, sixteen for tetrachloroplatinate, twenty for hexaaquanickel. The oxidation state and the d count are not: hexaaquairon is d⁶ on one convention and d⁸ on the other, and the two predict spin-only moments of 4.90 and 2.83 against a measured 5.40.

applied · Electron count

Named alongside it

The objects these essays reach for when they reach for this one.

d orbitalsHigh-spinLigand fieldMagnetic momentConventionCoordination complexEighteen-electron ruleElectron correlationElectron countModel limitOxidation statePairing energy

All concepts