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

For C3 (carbon trimer)

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) 6-311+G(3df,2p) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
Moller Plesset perturbation MP2=FULL -0.001063 -0.004732 -0.004732 -0.003752 -0.013338 -0.013338 -0.013735 -0.054477 -0.054477 -0.017943 -0.062988 -0.049500 -0.006056 -0.037914 -0.079335 -0.006671 -0.045156 -0.080815 -0.037914
MP3=FULL         -0.013184   -0.013563       -0.065586 -0.051849 -0.005645 -0.038966          
MP4=FULL   -0.004457     -0.013052       -0.056723   -0.065951   -0.005500 -0.038584   -0.006103 -0.046329    
B2PLYP=FULL -0.000322 -0.001425 -0.001425 -0.001127 -0.003962 -0.003962 -0.004079 -0.015602 -0.015602 -0.005290 -0.018159 -0.014186 -0.001818 -0.011104   -0.002005 -0.013161    
Quadratic configuration interaction QCISD(T)=FULL         -0.013026   -0.013379       -0.065829   -0.005466 -0.038695   -0.006051 -0.046486    
QCISD(TQ)=FULL         -0.013049   -0.013391       -0.065860   -0.005478 -0.038820   -0.006040 -0.046685    
Coupled Cluster CCSD=FULL         -0.012902         -0.017580 -0.065161 -0.051618 -0.005536 -0.038528 -0.082258 -0.005935 -0.046229 -0.083559  
CCSD(T)=FULL         -0.013041           -0.065821 -0.051969 -0.005474 -0.038726 -0.083129 -0.006062 -0.046552 -0.084689  
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z