# Relativistic corrections

When calculating properties or geometries of systems that contain heavy elements (fourth row and beyond), relativistic effects can have a big impact and should not be ignored.

Currently, there are two methods that can be used in ORCA to include that, the Zero-Order Regular Approximation (ZORA, [Baerends1996]) or the Douglas-Kroll-Hess (DKH, [Kroll1974] [Hess1985]) Hamiltonian. They are somewhat different and have specific strengths - so one should consider the results carefully - but maybe the most widely used is ZORA and its variants.

## Including relativistic corrections

The actual use is quite simple, one can just ask for ZORA or DKH on the main input, such as:

!B3LYP ZORA ZORA-DEF2-TZVP

or

!B3LYP DKH DKH-DEF2-TZVP


Note that here we are using specific basis for each method, named ZORA- or DKH-DEF2-TZVP. This is necessary because these basis have been specifically designed for these all-electrons calculations, and the relativistic correction should NOT be used together with the regular basis or pseudopotentials. For a detailed description of options, please check the ORCA manual.

## RI and ZORA/DKH

If you want to use any of the RI methods to accelerate the SCF, another set of special /J basis has to be used:

!B3LYP ZORA ZORA-DEF2-TZVP RIJDX SARC/J

or

!B3LYP DKH DKH-DEF2-TZVP RIJDX SARC/J


For instance, the SARC/J auxiliary basis can be used for all the ZORA or DKH-DEF2 basis. If no specific basis is available, then one can always use AUTOAUX to automatically generate one.

Important

The SARC/J basis were optimized for RI on the SCF part, not the MP2 or higher-level correlated methods! For correlation specific /C basis consult the manual and in case of abscence use !AUTOAUX.

## Example: the Hg dimer

Let's test the impact of these effects on the Hg dimer, that has an experimental bond length of $$3.69 Å$$ [Sattler2017]. This a rather extreme case of a very heavy element in a homodiatomic molecule, however it highlights the importance and magnitude of these effects.

The geometry can be optimized at a regular Double-hybrid density functionals (DHDF) level using the DEF2-TZVP basis, that makes use of pseudopotentials for the core orbitals that try to simulate relativistic effects or using the all-electron ZORA-DEF2-TZVP basis:

!B2PLYP DEF2-TZVP DEF2-TZVP/C OPT
* XYZ 0 1
Hg 0 0 0
Hg 0 0 3
*

or

!B2PLYP ZORA SARC-ZORA-TZVP SARC/J AUTOAUX OPT
* XYZ 0 1
Hg 0 0 0
Hg 0 0 3
*


The first results in a molecule with a $$3.84 Å$$ bond, and the relativistic ZORA results in $$3.78 Å$$, which is in better agreement with the experimental results!

Note

The auxiliary basis for the RIJ approximation used during the relativistic case here was chosen as the appropriate SARC/J.

Warning

Geometry optimizations using relativistic corrections turn on by default a one-center approximation by default, that changes the energy values. Do not compare single point energies from those you obtain from an !OPT run, these numbers are be incompatible.