====== Relativistic corrections ======

There are three ways in Molpro  to take into account scalar relativistic effects:

  - Use the Douglas-Kroll-Hess or eXact-2-Component (X2C) relativistic one-electron integrals.
  - Compute a perturbational correction using the Cowan-Griffin operator (see section [[program control#One-electron operators and expectation values (GEXPEC)|One-electron operators and expectation values (GEXPEC)]]).
  - Use relativistic effective core potentials (see section [[effective core potentials]]).

===== Using the Douglas–Kroll–Hess or eXact-2-Component Hamiltonians =====

For all-electron calculations, the prefered way is to use either the Douglas–Kroll–Hess (DKH) or eXact-2-Component (X2C) Hamiltonians, the former of which is available up to (in principle) arbitrary order in Molpro. DKH is activated by setting any of

''%%SET,DKROLL=1%%''\\
''%%SET,DKHO=%%''$n$,  ($n=2,\dots,99$),\\
''%%SET,DKHP=%%''$m$,  ($m=1,\dots,5$)

or for X2C by setting

''%%SET,DKHO=101%%''\\
somewhere in the input before the first energy calculation.

Alternatively, these values can be given as options on the ''INT'' command:

''%%INT,[DKROLL=1],DKHO=%%''$n$,''DKHP''=$m$.

or

''%%INT,DKHO=101%%''

The DKH option ''DKROLL'' is available for compatibility with earlier versions of Molpro. If only ''DKROLL=1'' is given, the default for ''DKHO'' is 2. Setting ''DKROLL=0'' disables DKH and X2C, independently of the setting of ''DKHO''. DKH is also disabled by setting ''DKHO=0'', unless ''DKROLL=1'' is set. In order to avoid confusion, it is recommended only to use ''DKHO'' and never set ''DKROLL''.

The value of ''DKHP'' specifies the parametrization for the DKH treatment (it has no effect for X2C):

  * **''DKHP=1'':** Optimum parametrization (OPT, default)
  * **''DKHP=2'':** Exponential parametrization (EXP)
  * **''DKHP=3'':** Square-root parametrization (SQR)
  * **''DKHP=4'':** McWeeny parametrization (MCW)
  * **''DKHP=5'':** Cayley parametrization (CAY)

**Example:**

|''%%SET,DKHO=8%%''  |  !  |DKH order = 8                                                                 |
|''%%SET,DKHP=2%%''  |  !  |choose exponential parametrization for unitary transformations (recommended)  |

Up to fourth order (''DKHO=4'') the DKH Hamiltonian is independent of the chosen parametrization. Higher-order DKH Hamiltonians depend slightly on the chosen paramterization of the unitary transformations applied in order to decouple the Dirac Hamiltonian.

For details on the infinite-order DKH Hamiltonians see\\
M. Reiher, A. Wolf, JCP **121**, 2037–2047 (2004),\\
M. Reiher, A. Wolf, JCP **121**, 10945–10956 (2004).

For details on the different parametrizations of the unitary transformations see\\
A. Wolf, M. Reiher, B. A. Hess, JCP **117**, 9215–9226 (2002).

The current implementation is the polynomial-cost algorithm by Peng and Hirao: D. Peng, K. Hirao, JCP 130, 044102 (2009).\\
A detailed comparison of the capabilities of this implementation as well as the current implementation of the X2C approach is provided in:\\
D. Peng, M. Reiher, TCA 131, 1081 (2012).

See [[program_control#example_for_computing_relativistic_corrections|here]] for an example for computing relativistic corrections.