.. _relcorr:

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, :ref:`bib:[Baerends1996]`) or the Douglas-Kroll-Hess (DKH, :ref:`bib:[Kroll1974]`  :ref:`bib:[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 <https://orcaforum.kofo.mpg.de/app.php/dlext/?view=detail&df_id=186>`_.

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 :math:`3.69 Å` :ref:`bib:[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.

.. image:: relat/Hgdimer.png
   :align: center
   :width: 450

The geometry can be optimized at a regular :ref:`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 :math:`3.84 Å` bond, and the relativistic ZORA results in :math:`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.