We present a density functional theory study of the structure and stability of self-assembled monolayers (SAMs) of alkylthiolate on Au(111) as a function of the alkyl chain length. The most favorable structure of the SAMs involves an RS–Au–SR complex (S being sulfur, R being an alkyl chain) formed through sandwiching one Au adatom by two alkylthiolates (RSs). Comparing a generalized gradient (GGA-PBE) and a meta-GGA (MGGA-M06-L) exchange-correlation functional we find that only the meta-GGA functional predicts the experimentally observed attractive intermolecular interactions within the SAMs. In particular, the use of M06-L yields an increased stability of the SAMs with increasing alkyl chain length and an increased attractive interaction between RS–Au–SR complexes at shorter distances.