  We present low-energy electron diffraction (LEED) as elastic electron-atom
scattering (EEAS) operating in a target crystal waveguide where a Coulombic
carrier wave is wavenumber modulated by exchange-correlation (XC) interaction.
Carrier potential is designed using a KKR (Korringa-Kohn-Rostoker) muffin-tin
model built on overlapping free atoms. XC potential is constructed using
Sernelius's many-particle theory on electron self-energy. EEAS phase shifts are
derived from Dirac's differential equations, and four recent LEED
investigations are recalculated: Cu(111)+$( 3\!\surd3\times\!\surd3 )
\mathrm{R30^\circ}$-TMB, Ag(111)+$(4\!\times \!4 )$-O, Ag(111)+$(
7\!\times\!\surd3 ) \mathrm{rect}$-$\mathrm{SO}_4$, Ru(0001)+$(
\surd3\!\times\!\surd3 ) \mathrm{R30^\circ}$-C. TMB stands for
1,3,5-tris(4-mercaptophenyl)-benzene with chemical formula
C$_{24}$H$_{15}$S$_3$. We are able to report substantially improved reliability
factors.
