The adsorption mechanism of single thiophene (C4H4S), 4-thiophene (C16H10S4), and their dimers on the Cu(111) surface has been studied in the framework of the density functional theory (DFT). The importance of the London dispersion effects on the molecule-surface adsorption geometry and the corresponding binding energy was investigated by using semiempirical and first-principles methods. Interestingly, the physisorption character of the thiophene bonding on Cu(111) suggested by strength of the molecule-surface interaction as revealed by the DFT calculations turns out to be a weak chemisorption even for the DFT ground-state geometry when a nonlocal correlation energy functional [Dion et al., Phys. Rev. Lett. 92, 246401 (2004)] is used. Our ab initio calculations also suggest that the formation of thiophene and 4-thiophene dimers is energetically favorable with respect to the adsorption of single molecules.