The HOMO-LUMO gap is the energy difference between the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) in a molecule, which is crucial for determining its electronic properties and chemical reactivity. A smaller gap often correlates with higher reactivity and lower stability, influencing phenomena such as color, conductivity, and the efficiency of photovoltaic and light-emitting devices.