Double-hybrid DFT

Double hybrid DFT calculations are probably the most accurate way of computing reliable energies of maingroup and organic systems at the DFT/MP2 level as found in the GMTKN30 database study by Grimme et al.

The composition of a double hybrid functional means that it is essentially a hybrid-DFT calculation plus an MP2 calculation (using the DFT orbitals) with the contributions scaled and added up to give the final energy. Use of the RI-MP2 approximation is strongly recommended to speed up the MP2 step as is the use of either RIJK or RIJCOSX approximations to speed up the hybrid-DFT step. See RI and auxiliary basis sets. Note that double hybrids are much more basis set dependent than GGA or hybrid-GGA functionals, going to the quadruple-zeta level is often needed for accurate energies. Geometry optimizations are possible but inefficient, thus single-point energy evaluations with double hybrids on geometries calculated by GGA or hybrid-GGA functionals, are usually a better strategy.

- The frozen-core core approximation is active by default (since ORCA 4.0) for double hybrid functionals for the MP2 step.

Standard double hybrid functionals implemented in ORCA

Grimme’s original B2-PLYP functional. 54 % Hartree-Fock exchange. Input below without RI approximations, very expensive (not recommended).

! B2PLYP D3BJ def2-TZVP TIGHTSCF

B2-PLYP with the RI approximation for the perturbation step, much cheaper and very reliable.

! RI-B2PLYP D3BJ def2-TZVP def2-TZVP/C TIGHTSCF

B2-PLYP with the RI approximation for the perturbation step and RIJK for the SCF step. The fastest double hybrid setup for small molecules. Both single-points and optimizations available when using RIJK in ORCA 4.0.

! RIJK RI-B2PLYP D3BJ def2-TZVP def2/JK def2-TZVP/C TIGHTSCF

B2-PLYP with the RI approximation for the perturbation step and RIJCOSX for the SCF step. Quite fast for small molecules, the fastest method for medium to large molecules. Generally recommended. Geometry optimizations are possible with this option.

! RIJCOSX RI-B2PLYP D3BJ def2-TZVP def2/J def2-TZVP/C TIGHTSCF

PWPB95 is Grimme’s most recent spin-opposite-scaled double hybrid functional. One of two best performers in the GMTKN30 benchmark study. The functional uses only scaled spin-opposite MP2 correlation, making it cheaper than other double hybrids, but still more accurate than most. 50 % Hartree-Fock exchange.

! RIJK RI-PWPB95 D3BJ def2-TZVP def2/JK def2-TZVP/C TIGHTSCF

B2GP-PLYP is a variant of B2-PLYP. Has 65 % Hartree-Fock exchange.

! RIJK RI-B2GP-PLYP D3BJ def2-TZVP def2/JK def2-TZVP/C TIGHTSCF

Defining double hybrid functionals manually

Due to the general hybrid/double-hybrid implementation in ORCA it is possible to define any kind of hybrid-DFT or double hybrid-DFT functional as long as the separate exchange and correlation functionals are available. The scaling factors for the various components are set in the method block.

DSD-PBEP86 is an improved version of the Martin group’s spin-component-scaled double-hybrid functional recipe. First version from 2011 (Kozuch and Martin), later modified in 2013 (Kozuch, Martin 2013). PBE exchange (instead of Becke) and P86 correlation (instead of LYP) and reparameterization. 70 % Hartree-Fock exchange.

Most recent parameterization found here (Kozuch, Martin 2013). SI shows the ORCA inputfile format which is reproduced below (minor modifications below due to updated D3 keywords). Input below also uses the RI-MP2 approximation and RIJK approximation.

! B2PLYP D3BJ RIJK def2-TZVP def2-TZVP/C def2/JK TIGHTSCF

%method
FrozenCore FC_ELECTRONS
Exchange x_PBE
Correlation c_P86
LDAOpt C_VWN5
ScalHFX 0.69
ScalDFX 0.31
ScalGGAC 0.44
ScalLDAC 0.44
ScalMP2C 1.00
end
%method
D3S6 0.48
D3A1 0.0
D3S8 0.0
D3A2 5.6
end
%mp2
RI on
DoSCS True
Ps 0.52
Pt 0.22
end