16.1 Using the Douglas-Kroll-Hess Hamiltonian

For all-electron calculations, the prefered way is to use the Douglas-Kroll-Hess (DKH) Hamiltonian, which is available up to arbitrary order in MOLPRO. It is activated by setting

DKROLL=1

somewhere in the input before the first energy calculation. If no further input is specified, the standard second-order Douglas-Kroll-Hess Hamiltonian (DKH2) is used.

Starting with version 2006.1, MOLPRO does, however, also provide the DKH Hamiltonian up to (in principle) any arbitrary order of decoupling (DKH$n$). The desired DKH order (DKHO) and the chosen parametrization for the unitary transformations have to be specified by

DKHO=$n$, ($n=2,\dots,12$),
DKHP=$m$, ($m=1,\dots,5$)

below the DKROLL=1 statement in the input file. The possible parametrizations supported by MOLPRO are:

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:

DKROLL=1	!	activate Douglas-Kroll-Hess one-electron integrals
DKHO=8	!	DKH order = 8
DKHP=4	!	choose McWeeny parametrization for unitary transformations

(Note: For DKHO $\ge 13$ the values of some parameters in the file src/common/dkhparameters.inc have to be suitably increased. Only recommended for experts who do exactly know what they are doing!! For most cases DKHO=10 is sufficient.)

Up to fourth order (DKHO=4) the DKH Hamiltonian is independent of the chosen paramterization. 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).