Out of the elements phosphorus (P), sulphur (S), chlorine (CI) and fluorine (F), the elements having the most negative and least negative electron gain enthalpy, respectively are

Electron gain enthalpy (Δ_egH) is the energy released when an electron is added to a neutral gaseous atom. Generally, it becomes more negative across a period from left to right and less negative down a group. However, there are key exceptions:

• Most Negative: Chlorine (Cl) has the most negative electron gain enthalpy (-349 kJ/mol). Although Fluorine (F) is above Chlorine, its small size leads to strong inter-electronic repulsions in the compact 2p subshell, making it less favorable to add an electron compared to Chlorine's 3p subshell.
• Least Negative: Phosphorus (P) has the least negative value (-74 kJ/mol) among the given elements. This is because Phosphorus has a stable, half-filled 3p³ electronic configuration, which resists the addition of an extra electron.

The order of electron gain enthalpy (magnitude of negative value) is Cl > F > S > P. Therefore, the most negative is Cl and the least negative is P.