  We prove a new lower bound on the indirect Coulomb energy in two dimensional
quantum mechanics in terms of the single particle density of the system. The
new universal lower bound is an alternative to the Lieb--Solovej--Yngvason
bound with a smaller constant, C=(4/3)^{3/2}\sqrt{5 \pi -1} \approx 5.90 <
C_{LSY}= 192\sqrt{2 \pi} \approx 481.27, which also involves an additive
gradient energy term of the single particle density.
