The adsorption and ordering of zinc phthalocyanine ( ZnPc) and octachloro zinc phthalocyanine ( ZnPcCl8) on an Ag( 111) surface is studied in situ by scanning tunneling microscopy under ultrahigh vacuum. Two- dimensional self- assembled supramolecular domains are observed for these two molecules. We show how substituting chlorine atoms for half of the peripheral hydrogen atoms on ZnPc influences the self- assembly mechanisms. While intermolecular interactions are dominated by van der Waals forces in ZnPc molecular networks, ZnPcCl8 molecular packing undergoes a sequential phase evolution driven by the creation of C - Cl center dot center dot center dot H - C hydrogen bonds between adjacent molecules. At the end of this evolution, the final molecular assembly involves all possible hydrogen bonds. Our study also reveals the influence of molecule- substrate interactions through the presence of fault lines generating a stripe structure in the molecular film.