The experiments on perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride and 16FCuPc on Ag(111) surfaces by the normal incidence x-ray standing wave are poorly reproduced by first-principles ground state calculations but well reproduced by considering initial- and final-state effects, which include the response of the valence electrons to screen a core hole created by x-ray photoemission and further induced ionic structural relaxation. This study shows that the initial- and final-state effects due to screening are of great importance in characterizing molecules on metal surfaces in the normal incidence x-ray standing wave experiments.