The paper investigates the magnetic and electronic structure of GdX2Si2 (X is Cu, Ag, Au) compounds in terms of the density functional theory with the emphasis on the spin-orbit interaction affecting the electronic structure of the GdX2Si2 (001) surface. It is found that these compounds demonstrate an interlayer antiferromagnetism, which, however, does not affect the electronic structure of the GdX2Si2 (001) surface near the Fermi level. The spin-orbit splitting of two-dimensional states on the GdX2Si2 (001) surface, which combines the intrinsic spin-orbit splitting and Bychkov-Rashba splitting, grows with increasing atomic number of a noble metal in the intermetallic compound. Based on the analysis of the spatial extension of d-shells and their interaction with silicon orbitals, the spin-orbit interaction is explained for compositions containing noble metals. A comparison of rare-earth- and noble metal-based intermetallic compounds and isostructural intermetallic compounds with transition elements, shows that d-shell filling affects the spin-orbit interaction.