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In this paper the convergence pattern of correlation-consistent (cc-pVxZ) and polarized-consistent (PC-n) hierarchies relative to the complete basis set limit have been considered in a small set of diatomic molecules. Using the sequence of these basis sets it was demonstrated that potential energy surfaces derived from basis-set-dependent solution of the Hartree-Fock equations achieves the exact numerical derived potential energy surfaces (PESs) in an ordered manner. So it was possible to compute the spectroscopic parameters in the complete basis set limit with considerable accuracy using the most extended members of both hierarchies. On the other hand, for the first time the detailed convergence patterns of total energies in three separate inter-nuclear distances have been considered in these molecules and it was demonstrated that the total energies arrive at microhartree accuracy at a considerable rate. Possible performance of extrapolation schemes is discussed and it was demonstrated that reliable extrapolation procedures indeed exist. A successful test of the proposed extrapolation method, using the three most extended members of polarized-consistent basis sets, has been accomplished on selected polyatomic molecules. [ABSTRACT FROM AUTHOR]