We applied the Infinite Basis (IB) set extrapolation and Double Hybrid Density Functional Theory (DHDF) to calculate the electron affinities, reaction barrier heights, proton affinities, non-covalent interactions, atomization, ionization, and alkyl bond dissociation energies. We previously found that the mean unsigned error of the B2KPLYP-IB calculation with the combination of cc-pVTZ and cc-pVQZ reach the chemical accuracy limit (similar to 2 kcal/mol) where the largest deviation occurred in the electron affinity calculations and the weak interactions between noble gases and nonpolar molecules. Here, we investigated the basis set effect using the B2KPLYP-IB extrapolation scheme that involves (1) the addition of extra tight d basis functions to the second row elements (i.e. cc-pV(L+d)Z), (2) the addition of extra s,p, and d diffuse basis functions, and (3) a comparison between Dunning's Correlation Consistent and Jensen's Polarization Consistent (pc-L) basis sets. We found that the addition of extras and p diffuse basis functions formed the minimal augmented basis sets proposed by Truhlar. This addition permitted the B2KPLYP-IB to reach the chemical accuracy limit with the combination of the double zeta and triple zeta basis sets. Adding extra s, p diffuse functions to the pc-L series permitted only a small improvement. This small improvement is due to the fact that the pc-L basis sets already contain a large number of functions for the p block elements. Taken together, the results suggest that this minimal augmented basis sets is useful for due to its accuracy and affordable computational cost.