New atomic energy parameters for rapid estimation of basis set error, the correlation energy, zero-point energy, and thermal and relativistic corrections were obtained for HF/6-311+G(2d,p) and HF/6-31G(d) energies and atomic partial charges (natural population analysis and Mulliken). A total of 161 closed-shell neutral molecules from the G2/97 and G3/99 database composed of H, C, N, 0, F, Si, S, and Cl atoms were selected to test the performance of the rapid estimation of enthalpies of formation from Hartree-Fock (REEF-HF) method. The best REEF-HF results were obtained using the HF/6-311+G(2d,p) total energies and the corresponding natural population analysis charges. The average absolute deviation from the experimental enthalpies of formation for 159 molecules is 1.55 kcal/mol. Leaving out the five most problematic molecules yielded 1.38 kcal/mol average absolute deviation for the remaining 154 molecules. This compares well to our previous best results on a smaller test set of 117 molecules composed of molecules containing only first-row elements (1.48 kcal/ mol average absolute deviation). The REEF-HF method works well for molecules containing second-row elements. Our method compares favorably to G3 method in terms of computational time and to B3LYP method in terms of computational time and precision. For a set of 27 simple hydrocarbons the proposed method yielded 0.77 or 0.64 kcal/mol average absolute deviations using HF-SCF/6-31G(d) energies and NPA or Mulliken charges, respectively.