Using the Douglas-Kroll-Hess (DKH) Hamiltonian

For consideration of scalar-relativistic effects in all-electron calculations the scalar-relativistic Douglas-Kroll-Hess (DKH) Hamiltonian can be employed in the modules dscf and ridft. Please make sure to use an all-electron basis set (in particular, ECPs are not allowed).

This Hamiltonian is defined up to a certain order in the external potential and is available up to arbitrary order (for actual calculations, however, it is advisable not to go beyond 4th order (the parameter settings of the implementation allow to run calculations up to about 10th order in the electron-nucleus potential).

The current implemtation is restricted to single-point calculations (gradients are not available) in C1-symmetry and cannot be used in parallel mode. Moreover, calculated properties using the DKH density do not take care of the 'picture-change' effect.

The arbitrary-order Hamiltonian requires in the control file:

$dkhorder integer

where integer specifies the order of the DKH Hamiltonian in the external potential, i.e. for the standard 2nd-order DKH Hamiltonian one should use $dkhorder 2.

The parametrization of the unitary transformation used in the DKH transformation can be optionally selected by

$dkhparam integer

The possible parametrizations in the DKH transformation are:

$dkhparam 1:

Optimum parametrization (OPT)

$dkhparam 2:

Exponential parametrization (EXP)

$dkhparam 3:

Square-root parametrization (SQR)

$dkhparam 4:

McWeeny parametrization (MCW)

$dkhparam 5:

Cayley parametrization (CAY)

Note in particular that the parametrization does not affect the Hamiltonian up to fourth order. Therefore, as long as you run calculations with DKH Hamiltonians below 5th order you may use any symbol for the parametrization as they would all yield the same results. Higher-order DKH Hamiltonians depend slightly on the chosen paramterization of the unitary transformations applied in order to decouple the Dirac Hamiltonian, but this effect can be neglected.

For details on the arbitrary-order DKH Hamiltonians see Ref. [63] for details on the infinite-order DKH theory, [64] for the implementation, and [65] for a conceptual review of DKH theory. For details on the different parametrizations of the unitary transformations see [66].