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relativistic_corrections [2020/06/11 18:17] – external edit 127.0.0.1relativistic_corrections [2024/07/12 08:37] (current) – external edit 127.0.0.1
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 +====== 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.