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39.1 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).



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