The applicability of the relativistic density functional theory (RDFT) with conventional generalized gradient and hybrid exchange-correlation functionals to the description of the interactions of element 112 (Cn) and its lighter homolog Hg with a gold surface is assessed. The comparison of Cn-Au (Hg-Au) bond properties for two simple models of adsorption complexes on Au(111) surface obtained by RDFT and accurate many-body calculations indicates a strong underestimation of binding energies by conventional RDFT schemes. This effect provides a possible explanation of the discrepancies between the RDFT-based theoretical and experimental data concerning the thermochromatographic registration of the alpha-decay chain element 114-->Cn.