Exchange energies

Filled and half-filled shells are often referred to as possessing a ‘special stability. However, this is misleading, and we should really consider the exchange energy of a given configuration. This can only be justified by an advanced quantum mechanical treatment but we can summarize the idea as follows. Consider two electrons in different orbitals. The repulsion between the electrons if they have anti-parallel spins is greater than if they have parallel spins, e.g. for a p² configuration:

   The difference in energy between these two configurations is the exchange energy, K, i.e. this is the extra stability that the right-hand configuration has with respect to the left-hand one. The total exchange energy is expressed in terms of K (the actual value of K depends on the atom or ion):