Benzene, pyrimidine, and naphthalene dimers have been studied at canonical MP2, LMP2, and MP4(SDTQ) levels of theory. It has been shown that the LMP2 method is superior to canonical MP2 due to reduced BSSE. Thus, basis set limit-extrapolated LMP2 binding energies of T-shaped and parallel displaced (PD) benzene dimers are nearly the same, as has been found in higher level ab initio calculations. MP4(SDTQ) binding energies calculated at LMP2 optimized geometries are always more negative than those calculated for MP2-optimized geometries. MP4(SDTQ)/CC-pVDZ-corrected complete basis set-extrapolated LMP2 binding energies of T-shaped and PD dimers of benzene and naphthalene were found to be -2.80, -2.59 and -4.39, -6.29 kcal/mol, respectively.