Characteristics of the heavy rare gas dimers (Ar-2,Kr-2,Xe-2) have been studied by correlated ab initio calculations. All-electron CCSD(T) calculations were performed for Ar and Kr dimers, and calculations with relativistic effective core potentials were performed for Kr and Xe dimers. Extended basis sets (aug-cc-pVXZ, X=D, T, Q, 5, 6) were combined with bond functions (spd, spdfg). The use of bond functions significantly improves the basis set convergence. For the argon dimer, we have included also a CCSDT correction yielding a higher quality potential energy curve. This correction has been calculated using aug-cc-pVTZ+spd basis set. All possible sources of errors have been analyzed for the argon dimer [basis set saturation, correlation contributions going beyond CCSD(T) method, effect of core corrections and relativistic corrections]. In the case of the Ar dimer, the highest level of theory reproduces the semiempirical stabilization energy within 1.3 cm(-1). To obtain even closer agreement with experiment it would be necessary to fully include quadruple and higher excitations as well as to account properly for the core corrections with yet unpublished core oriented basis sets. Further improvement of one electron basis set will not lead to a better agreement with experiment. In the case of the other two dimers, the agreement between theory and experiment is also acceptable but not quantitative as in the case of the Ar dimer. Apparently, current calculations are close to the basis set limit and better agreement can only be obtained by proper covering of contributions mentioned for the argon dimer. The newly developed ECP oriented aug-cc-pVXZ basis set is very effective and can be recommended for high level calculations of molecular clusters containing heavier rare gas elements. The fast DZ/TZ extrapolation technique has been extended so that the use of empirical parameters can be avoided. Results obtained by extrapolations with medium size basis sets are surprisingly close to the most accurate ones. Further, the MP2-CCSD(T) difference was shown to be much less dependent on the size of the basis set than the energies themselves. These two conditions allow to construct the true stabilization energy of extended complexes as a sum of extrapolated complete basis set limit of MP2 stabilization energy and [MP2-CCSD(T)] term determined in a smaller basis set. The ab initio pair intermolecular potential results have been fitted to suitably chosen analytical formulas, and tested on experimental data for the second virial coefficients, spectral characteristics, and scattering data. For argon, an excellent agreement between the theoretical and the experimental values has been found. In the case of krypton and xenon the agreement is not as good but still acceptable. (C) 2003 American Institute of Physics.