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Energy differences between frozen core and all electrons correlated.
MP2, MP3, MP4, B2PLYP, CCSD, and CCSD(T)

For C2 (Carbon diatomic)

Energies in Hartree
Methods with standard basis sets
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ
Moller Plesset perturbation MP2=FULL -0.000788 -0.003140 -0.003140 -0.002489 -0.008445 -0.008445 -0.008696 -0.035871 -0.035871 -0.010495 -0.032625 -0.003788 -0.023218 -0.051616 -0.004154 -0.027279 -0.052378 -0.023218 -0.069484 -0.093533
MP3=FULL         -0.008185   -0.012929       -0.034020 -0.003342 -0.023645              
MP4=FULL   -0.002891     -0.008334       -0.037367     -0.003359 -0.023770   -0.003720 -0.028119        
B2PLYP=FULL -0.000234 -0.000942 -0.000942 -0.000741 -0.002526 -0.002526 -0.002599 -0.010279 -0.010279 -0.003114 -0.009360 -0.001136 -0.006836   -0.001246 -0.007991        
Quadratic configuration interaction QCISD(T)=FULL         -0.008371             -0.003293 -0.023940   -0.003651 -0.028346        
QCISD(TQ)=FULL         -0.008395   -0.008646         -0.003295 -0.023983 -0.054451 -0.003651 -0.028402 -0.059222      
Coupled Cluster CCSD=FULL         -0.007980         -0.010035 -0.033686 -0.003118 -0.023154 -0.053089 -0.003460 -0.027535 -0.053886      
CCSD(T)=FULL         -0.008374           -0.034305 -0.003295 -0.023931 -0.054411 -0.003652 -0.028340 -0.055217 -0.023931 -0.073174 -0.097637
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ