Gaussian-3 total energies has been approximated using single-point Hartree-Fock-self-consistent field (HF-SCF) total energies plus the correlation energy corrections calculated from the HF-SCF partial atomic charges according to the rapid estimation of correlation energy from partial charges (RECEP) method (Chem. Phys. Lett. 1999, 307, 469). Sixty-five closed-shell neutral molecules (composed of H, C, N, O, and F atoms) of the G2/97 thermochemistry database were used to obtain the fitted RECEP atomic correlation parameters. Four different mathematical definitions of partial charges were used to calculate the molecular correlation energies. The best results were obtained using the natural population analysis, although the other three are also recommended for use. The overall root-mean-square deviation of the RECEP-3 total energies from Gaussian-3 total energies for the 65 energies is 1.76 kcal/mol (the average absolute deviation is 1.43 kcal/mol). The root-mean-square deviation of fitted RECEP-3 enthalpies of formation from experimental enthalpies of, formation for the 65 molecules is 2.17 kcal/mol (the average absolute deviation is 1.75 kcal/mol). The current fitted parameters of the RECEP method are recommended to estimate total correlation energies of closed-shell ground-state neutral molecules at stationary points of the potential-energy surface.