Relativistic approximations

Using scalar relativistic methods in DFT calculations with ORCA is made easy if the recommended basis sets are used. The Ahlrichs def2 basis set family has been recontracted for use in ZORA or DKH2 calculations (Pantazis et al.) and the relativistic contraction of the def2-XVP basis should be selected (ORCA may tell you off if you forget this). For elements for which the standard def2-XVP basis set is only available with the use of ECPs (third-row transition metal row etc. ) then the segmented all-electron relativistically contracted (SARC) basis sets by Pantazis et al. should be used.

For relativistic WFT calculations the relativistic Douglas-Kroll correlation-consistent basis set, cc-pVnZ-DK basis sets could be used.

Note that as the elements get heavier, the ZORA or DKH2 methods require even more dense grids for the exchange-correlation term in DFT.

Single-point ZORA/DKH2 calculation with DFT and Ahlrichs & SARC basis sets

Elements H-Kr:

Input below uses either the ZORA or DKH2 method the ZORA/DKH2 relativistic contraction of basis sets (Pantazis et al.) for a hydrogen-fluoride molecule.

Note the basis set name: ZORA-def2-TZVP (which is a relativistically recontracted version of the all-electron def2-TZVP Ahlrichs basis set).

Note also that we use the SARC/J auxiliary basis set which is a decontracted def2/J auxiliary that is more accurate for relativistic ZORA/DKH calculations and recommended.

! BP86 ZORA ZORA-def2-SVP SARC/J

*xyz 0 1

H 0 0 0

F 0 0 1

*

! BP86 DKH2 DKH-def2-SVP SARC/J

*xyz 0 1

H 0 0 0

F 0 0 1

*

Elements Rb-I:

This row in the periodic table previously caused some confusion. The Ahlrichs def2-XVP basis set for this row is only a valence basis set (not an all-electron basis set) and comes with a def2-ECP for the core electrons. In earlier versions of ORCA (2,3) specifying a def2-TZVP basis set for these elements resulted in the all-electron "TZVPalls" basis set by Ahlrichs et al. and the ZORA/DKH def2-TZVP versions were relativistically recontracted versions by Pantazis et al. of the TZVPalls" basis set.

Nowadays there are SARC basis sets available for this row. See below.

Elements Rb-I, Xe-Rn, Ac-Lr:

If your molecule contains a heavy element e.g. 2nd and 3rd transition metal-row atom then you have to explicitly define the SARC basis set (there is no ZORA-def2-TZVP or DKH-def2-TZVP basis set keyword for such elements). Here done for a hypothetical Pt-hydrogen-fluoride complex. Note that now we can not define the whole basis set for this molecule in the simple-input line anymore. Instead we first define the ZORA-def2-TZVP for everything (for H and F; Pt will be ignored because there is no ZORA-def2-TZVP available for Pt) and then the SARC-ZORA-TZVP basis set set for Pt is defined explicitly using the %basis block.

! BP86 ZORA ZORA-def2-TZVP SARC/J

%basis

NewGTO Pt "SARC-ZORA-TZVP" end

end

*xyz 0 1

H 0 0 0

F 0 0 1

Pt 0 0 2

*

! BP86 DKH DKH-def2-TZVP SARC/J

%basis

NewGTO Pt "SARC-DKH-TZVP" end

end

*xyz 0 1

H 0 0 0

F 0 0 1

Pt 0 0 2

*

Using diffuse basis sets and ZORA and DKH

If diffuse functions are necessary in ZORA/DKH2 DFT calculations then the minimally augmented def2 ZORA/DKH basis sets can be recommended. See the basis sets page for more details.

ma-ZORA-def2-SV(P) (H-Rn)

ma-ZORA-def2-SVP (H-Rn)

ma-ZORA-def2-TZVP (H-Rn)

ma-ZORA-def2-TZVP(-f) (H-Rn)

ma-ZORA-def2-TZVPP (H-Rn)

ma-ZORA-def2-QZVP (H-Rn)

ma-ZORA-def2-QZVPP (H-Rn)

ma-DKH-def2-SV(P) (H-Rn)

ma-DKH-def2-SVP (H-Rn)

ma-DKH-def2-TZVP (H-Rn)

ma-DKH-def2-TZVP(-f) (H-Rn)

ma-DKH-def2-TZVPP (H-Rn)

ma-DKH-def2-QZVP (H-Rn)

ma-DKH-def2-QZVPP (H-Rn)

For WFT calculations the aug-cc-VnZ-DK family may be a good idea.:

aug-cc-pVDZ-DK (H-Ar, Sc-Kr)

aug-cc-pVTZ-DK (H-Ar, Sc-Kr, Y-Xe, Hf-Rn)

aug-cc-pVQZ-DK (H-Ar, Sc-Kr, In-Xe, Tl-Rn)

aug-cc-pV5Z-DK (H-Ar, Sc-Kr)

Geometry optimization with ZORA/DKH

! Important: Due to the use of the one-center approximation (see manual) in geometry optimizations, energies from a ZORA/DKH2 geometry optimization are not the same as those from a single-point calculation. Be careful not to mix energies from optimization and single-point relativistic jobs.

Note that geometry optimizations of heavy element molecules are usually more stable with ZORA than with DKH. This appears to be due to a reduced grid-sensitivity of ZORA. ZORA is thus usually recommended.

! BP86 def2-TZVP SARC/J ZORA Opt

or

! BP86 def2-TZVP SARC/J DKH2 Opt

Relativistic molecular properties

Molecular properties calculated with a scalar relativistic Hamiltonian can become complicated due to so called picturechange effects. See chapter 6.12.4 in the ORCA manual. It is important to be aware of these effects but a brief description is as follows:

• With ZORA, magnetic properties are fine without picture change.

• With ZORA, the electric properties do in principle require a picture change but the situation is unfortunate due to the lack of gauge invariance in ZORA. A workaround is to use a so called ZORA-4 density as defined by van Lenthe. This is what you get when you set picturechange to true in ORCA. This, however, does not seem to improve the agreement with fully relativistic four component calculations.

• With DKH the picture change effects on electric properties are relatively easy and should be included.

• With DKH the picture change effects on the magnetic properties are severely complicated because the transformations become dependent on the vector potential. ORCA, however, has an implementation of these picturechange effects.

• All relativistic calculations become singular if the basis set is approaching completeness because the relativistic orbitals diverge with a point nucleus. The workaround is to use a finite nucleus.

%rel
picturechange true
end

Finite nucleus model

%rel FiniteNuc true/false end