In addition to our previous work of G2(ful) in Ref.[8],we proposed a further core electronic correlation modifieation at MP2/6-31G(d) level to G2(QCI),namely G2(QCI/ful),and that at MP2/6-311G(d,p) level to G2 and G2(QCI) theories,namely G2(fu2) and G2(QCI/fu2).The latter would need no additional calculation if the geometry is optimized at MP2(full)/6-311G(d,p) level/The modification energies,ΔE(fu2),were calculated via eq. ΔE(ful)=E[MP2](full)/6-31G(d)]-E[MP2(FC)/6-31G(d)] ΔE(fu2)=E[MP2](fu2)/6-311G(d,p)]-E[MP2(FC)/6-311G(d,p)] G2 and G2(QCI) theories were modified via eq. E[G2(fu2)]=E(G2)=ΔE(fu2)-HLC(G2)=HLC[G2(fu2)] E[G2(QCI/ful)]=E[G2(QCI)]+ΔE(ful)-HLC[G2(QCI)]+HLC[G2(QCI/ful)] E[G2(QCI/fu2)]=E[G2(QCI)]+ΔE(fu2)-HLC[G2(QCI)]+HLC[G2(QCI/fu2)] where, HLC[G2(fu2)]=-0.19nα-4.32nβ HLC[G2(QCI/ful)]=-0.19nα-4.77nβ HLC[G2(QCI/fu2)]=-0.19nα-4.65nβ It has been shown that the empirical High-Level-Correction(HLC) to either of the original G2 or G2(QCI) theory was reduced.G2(fu2) did not improve the over-all accuracy for the 125 G2-l test set reaction energies,however both G2(QCI/ful) and G2(QCI/fu2) did.The average absolute deviations (AAD) for the 125 reaction energse in the G2-l test set were reduced from 4.97 forG2(QCI) to 4.74 for G2(QCI/ful) and to 4.81kJ mol-1 for G2(QCI/fu2).The AAD was5.11 for G(fu2) compared with 5.09kJ mol-1 for G2.The reason for the larger AAD of G2(fu2) is probably due to that we did not use the better geometry of MP2(full)/6-311G(d,p) as presented in Ref.[11],and the 6-311G basis sets was somewhat unsatisfactory to describe both of the first-an secone-row atoms as had been criticized in Ref.[9].