The extra-atomic relaxation R(ea) in surface systems consists of the p
olarization E(pol), image charge potentials E(z) and charge transfer c
ontributions E(q). The theory is given for polarization calculations i
n surface systems of molecules and gases, which form molecular lattice
s in the solid state. Calculations for extra-atomic relaxation are per
formed for 1-2-3-4 layered systems Xe/Pd(xyz), where (xyz) = (100), (1
10) and (111) planes as well as for 1-2-3 layered systems A/Ag(111) or
AI(111), where A is Ne, Ar, Kr, Xe. Formulae are obtained for non-met
allic substrate and calculations are performed for 1-2-3 layered syste
ms of Ar, Kr and Xe on graphite. E(pol) and E(z) are the main contribu
tors to R(ea) values. For the core levels theory agrees with experimen
t on average within 0.1-0.2 eV. The theory is applied for valence leve
ls of simple molecules such as CO and N2 adsorbed on metallic and non-
metallic substrate.