  The density functional determining the Coulomb energy of nuclei is calculated
to the first order in $e^2$. It is shown that the Coulomb energy includes three
terms: the Hartree energy; the Fock energy; and the correlation Coulomb energy
(CCE), which contributes considerably to the surface energy, the mass
difference between mirror nuclei, and the single-particle spectrum. A CCE-based
mechanism of a systematic shift of the single-particle spectrum is proposed. A
dominant contribution to the CCE is shown to come from the surface region of
nuclei. The CCE effect on the calculated proton drip line is examined, and the
maximum charge $Z$ of nuclei near this line is found to decrease by 2 or 3
units. The effect of Coulomb interaction on the effective proton mass is
analyzed.
