Exchange energy and the stability of half-filled and fully-filled subshells:

Exchange energy is a purely quantum mechanical stabilising effect that arises when two or more electrons of identical spin occupy different but degenerate orbitals (orbitals of the same energy, such as the five d orbitals or three p orbitals). Because such electrons are indistinguishable, they can be thought of as continuously "exchanging" places between the equivalent orbitals without any change in the overall state of the atom. Each possible exchange between a pair of same-spin electrons in degenerate orbitals lowers the energy of the system by a fixed amount; the more such exchanges are possible, the greater the total stabilisation.

• According to Hund's rule of maximum multiplicity, electrons first singly occupy all degenerate orbitals with parallel spin before any pairing occurs.
• In a half-filled subshell (for example, d⁵: one electron in each of the five d orbitals, all spins parallel — ↑ ↑ ↑ ↑ ↑), the number of possible pairwise exchanges among same-spin electrons is at its maximum for that subshell.
• This maximises the exchange energy, which in turn lowers the total energy of the configuration and makes it unusually stable — this is why configurations such as d⁵ and d¹⁰ (and their s-block analogues, e.g. in chromium and copper) are especially stable compared to what a naive filling order would predict.
• The effect depends specifically on same-spin (parallel) electrons; two electrons with opposite (antiparallel/paired) spins in the same orbital do not contribute exchange stabilisation — instead they experience additional coulombic repulsion from occupying the same region of space.

Hence, it is the presence of the maximum possible number of parallel-spin electrons in degenerate orbitals — not nuclear attraction and not opposite spins — that produces the extra exchange energy responsible for the stability of half-filled (and fully-filled) subshells. Nuclear attraction certainly contributes to the overall binding of electrons, but it does not explain the specific extra stability seen at half-filled configurations, and the claim that exchange energy plays no role is directly contrary to quantum mechanical theory and experimental evidence (ionisation energies, atomic radii trends, etc.).