To use electron affinities properly, it is essential to keep track of sign. For any reaction that releases energy, the change ΔE in total energy has a negative value and the reaction is called an exothermic process. Electron capture for almost all non-noble gas atoms involves the release of energy and thus is exothermic. The positive values that are listed in tables of E are amounts or magnitudes. It is the word "released" within the definition "energy released" that supplies the negative sign to ΔE. Confusion arises in mistaking E for a change in energy, ΔE, in which case the positive values listed in tables would be for an endo- not exo-thermic process. The relation between the two is E = −ΔE(attach).
However, if the value assigned to E is negative, the negative sign implies a reversal of direction, and energy is required to attach an electron. In this case, the electron capture is an endothermic process and the relationship, E = −ΔE(attach) is still valid. Negative values typically arise for the capture of a second electron, but also for the nitrogen atom.
The usual expression for calculating E when an electron is attached is
This expression does follow the convention ΔX = X(final) − X(initial) since −ΔE = −(E(final) − E(initial)) = E(initial) − E(final).
Equivalently, electron affinity can also be defined as the amount of energy required to detach an electron from the atom while it holds a single-excess-electron thus making the atom a negative ion, i.e. the energy change for the process
:X → X + e
If the same table is employed for the forward and reverse reactions, without switching signs, care must be taken to apply the correct definition to the corresponding direction, attachment (release) or detachment (require). Since almost all detachments (require +) an amount of energy listed on the table, those detachment reactions are endothermic, or ΔE(detach) > 0.