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A general method in considering the core electromc correlation energies has been proposed and introduced into the standard Gaussian-2 (G2)[7] theory hy small post-Hartree-Fock calculations. In this papcr an additional MP2(FC)/6-31G(d) calculation over the G2 procedures is employed and examined in modihcation in modification to the flaw of Frozen-Core (FC) approximation of G2 vai eq:E(full)= E[MP2(full)/6-31G(d)]-E[MP2(FC)/6-31G(d)]where the MP2(full)/6-31G(d) cnergy has been obtaincd in the molefular gcometry optimizations. This energy, E(full), is directly added into the total G2 energy of a molecule in facilitating the effect of core electronic correlations for each molecule in chemical reactions. It has been shown that the over-all avcrage absolute deviation for the 125 reaction energies of the G2 test set (test set 1) is slightly reduced from 5.09 to 5.01 kJ, mol(-1) while for the 55 D0 values, which have been used for the derivation of the A coefficient of the empirical High-Level-Correction (HLC), it is also reduced from 4.99 [for both G2 and G2(COMPLETE)[8]]to 4.77 kJ, mol(-1). In addition, Iargcr crrors (greater than ±8.4 kJ. mol(-1) for the D0 energies are improved, especially for the largest error of the D0of SO2 This error is reduced from 21.3 to 15.4 kJ. mol(-1), in which the experimental geometry would further reduce it by 7.1kJ.mol(-1)[8].Another improvement is the absolute value of the A coefficient in HLC being reduced from 4.81 for G2 to 4.34 milli-hartrees which is believed to be useful in isolating the relationship between the HLC and the FC approximation.Modifications to the original G2 from this work is denoted as G2(fu 1) and thus the G2 (fu 1) total energy for a molecule isE[G2(fu 1)]= E[G2]+ E(full)with a new E[HLC] =0.19α- 4.34nβ milli-hartree.