7.12. Frozen Core Options

The frozen core (FC) approximation is usually applied in correlated calculation and consists in neglecting correlation effects for electrons in the low-lying core orbitals. The FC approximation and the number of core electrons per element can be adjusted in the %method block. The default number of core electrons per element is listed in Table 7.15.

Table 7.15 Default values for number of frozen core electrons.

H																	He
0																	0
Li	Be											B	C	N	O	F	Ne
0	0											2	2	2	2	2	2
Na	Mg											Al	Si	P	S	Cl	Ar
2	2											10	10	10	10	10	10
K	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge	As	Se	Br	Kr
10	10	10	10	10	10	10	10	10	10	10	10	18	18	18	18	18	18
Rb	Sr	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd	In	Sn	Sb	Te	I	Xe
18	18	28	28	28	28	28	28	28	28	28	28	36	36	36	36	36	36
Cs	Ba	Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg	Tl	Pb	Bi	Po	At	Rn
36	36	46	46	46	46	46	46	46	46	46	46	68	68	68	68	68	68
Fr	Ra	Lr	Rf	Db	Sg	Bh	Hs	Mt	Ds	Rg	Cn
68	68	68	100	100	100	100	100	100	100	100	100
Lanthanides			La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb
			36	36	36	36	36	36	36	36	36	36	36	36	36	36
Actinides			Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No
			68	68	68	68	68	68	68	68	68	68	68	68	68	68

For systems containing heavy elements, core electrons might have higher orbital energies compared to the orbital energies of valence MOs of some lighter elements. In that case, core electrons might be included in the correlation calculation, which ultimately leads to large errors in correlation energy. In order to prevent this, the MO ordering is checked: Do all lower energy MOs in the core region have core electron character, i.e. are they strongly localized on the individual elements? For post-(CAS)SCF calulations, this check is always performed both after the SCF calculation, and after the initial guess (because the SCF may be skipped with !NoIter). For other calculations, the check is off by default but may be switched on with the CheckFrozenCore keyword in the %method block. If core orbitals are found in the valence region, while more delocalized orbitals are found in the core region, the corresponding MO pairs are swapped. This behavior can be disabled using the CorrectFrozenCore keyword.

%method 
  FrozenCore FC_ELECTRONS #Freeze all core electrons
             FC_EWIN      #Freeze selected core electrons via an energy window
                          #e.g. for MP2: %mp2 EWin EMin,EMax      
             FC_NONE      #No frozencore approximation 
             -n           #Freeze a total of n electrons

  NewNCore Bi 68 end      #Set the number of core electrons for Bi to 68
  CheckFrozenCore   true  #Check whether frozen core orbitals are ordered correctly
                          #Default: true only for post-(CAS)SCF calculations
  CorrectFrozenCore true  #Whether to rotate valence orbitals out of the core region
end

Note

• The FrozenCore options are applied to all post Hartree-Fock methods.

• If including all electrons is desired, the !NoFrozenCore keyword can be simply inserted. For MP2: Frozen virtual orbitals are not allowed in gradient runs or geometry optimization!

• If ECPs are used, the number for NewNCore has to include the electrons represented by the ECPs as well. E.g. if an element is supposed to have 60 electrons in the ECP and additional 8 electrons should be frozen in the correlation calculation, NewNCore should be 68.

• In ORCA we use rather conservative frozencore settings, i. e. a large number of electrons are included in the correlation treatment. Therefore, we recommend to use properly optimized correlating basis functions in all cases, such as the cc-pwCVXZ basis sets.

• For DLPNO calculations the virtual space for core-core and core-valence correlation is adjusted by default, which is described in detail in section Including (semi)core orbitals in the correlation treatment.

• In general, NewNCore only has an effect in calculations with FC_ELECTRONS. In calculations using the DLPNO approximation (except DLPNO-NEVPT2), NewNCore has also an effect in the other cases, as is described in section Including (semi)core orbitals in the correlation treatment.

• Double-hybrid density functional (section DFT Calculations with Second Order Perturbative Correction (Double-Hybrid Functionals)) calculations by default use the FrozenCore option for the perturbative part, as is the case for MP2.