spin selection rule

When light pushes an electron into a higher orbital, the electron is allowed to change where it sits — but not, ordinarily, to flip its spin in the process. The spin selection rule captures this: an electronic transition is allowed only if the total spin does not change. In symbols, the change in total spin S must be zero, which means the number of unpaired electrons stays the same before and after the jump.

Spin is a tiny intrinsic magnetism each electron carries, pointing up or down. The total spin of an ion, and the related spin multiplicity (counted as 2S+1, which appears as the leading superscript in a term symbol), is a kind of bookkeeping of how many electrons are unpaired. Light interacts mainly with an electron's position, not its spin, so a transition that would require an electron to reverse its spin — turning a pair into two unpaired electrons, or vice versa — is spin-forbidden. A transition that leaves the spin count untouched is spin-allowed. This is why most observed d-d bands connect states of the same multiplicity.

The rule matters because it explains a second tier of faintness on top of the Laporte rule. The palest of all colored ions are those whose only available transitions are both Laporte- and spin-forbidden. The textbook case is manganese(II) in an octahedral field: its high-spin d5 ion has every d transition requiring a spin flip, so [Mn(H2O)6]2+ is a famously washed-out, barely-there pink. The rule is not absolute — spin-orbit coupling mixes states of different spin and lets a trickle of intensity through — but it is strong enough that doubly forbidden bands are roughly a thousand times weaker than fully allowed ones.