  We prove the first correction to the leading Thomas-Fermi energy for the
ground state energy of atoms and molecules in a model where the kinetic energy
of the electrons is treated relativistically. The leading Thomas-Fermi energy,
established in [Sorensen], as well as the correction given here are of
semi-classical nature. Our result on atoms and molecules is proved from a
general semi-classical estimate for relativistic operators with potentials with
Coulomb-like singularities. This semi-classical estimate is obtained using the
coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a
unified treatment of the relativistic as well as the non-relativistic case.
