We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy
(also known as the exchange-correlation energy) of a general many-particle quantum
state, with a lower constant than the original statement but involving an additional
gradient correction. The result is similar to an inequality of Benguria, Bley and Loss,
except that our correction term is purely local, which is more usual for density
functional theory. No previous knowledge of the subject will be assumed; a short tutorial
on the subject and its importance to quantum chemistry will be presented.