A simple extrapolation formula of (X+gamma)(-3) which fits correlation energies with correlation consistent (aug-)cc-pVXZ and (aug-)cc-pV(X+1)Z[X=D(2),T(3),Q(4)] basis sets to estimate the basis set limit was devised by varying the parameter gamma according to basis set quality and correlation level. The explicit extrapolation formulas suitable for calculations at the second order Moller-Plesset perturbation theory and single and double excitation coupled cluster theory with perturbative triples correction level are presented and applications are made to estimate the basis set limit binding energies of various hydrogen-bonded and van der Waals clusters. A comparison of the results by this formula with the reference basis set limit results and the results by other extrapolation methods reveals that the extrapolation formulas proposed here can yield the reliable basis set limit estimates even with the small basis sets and could be used effectively for investigating large weakly bound complexes. (C) 2003 American Institute of Physics.