:orphan:
Selecting a two-component Hamiltonian other than X2C
====================================================
There are several two-component Hamiltonians besides the X2C Hamiltonian (see :ref:`HAMILTONIAN_.X2C`) implemented
in DIRAC arising from the decoupling transformation of the one-electron DIRAC Hamiltonian.
Likewise spin-orbit interaction terms can be left out and calculations can be performed
in the spin-free mode (i.e. in boson symmetry).
Besides having spin-orbit effects from the decoupling transformation, there is
the external AMFI spin-orbit operator which can contribute either with the
one-electron spin-orbit operator (accurate to the first order in V, very poor)
or with the more valuable mean-field contribution, u\_so(1) (also in the first
order), which is a reasonable approximation of the 'Gaunt' term at the
four-component level.
The best two-component Hamiltonian is X2C+MFSSO (similar to BSS+MFSSO or IOTC+MFSSO)
where one-electron scalar and spin-orbit effects are up to infinite order, and AMFI
MFSSO contributions (mean-field spin-same orbit) provide a 'screening' of
one-electron spin-orbit terms.
Examples
--------
Both scalar and spin-orbit relativistic effects up to infinite order::
.BSS
099
Scalar relativistic effects of type "from the beginning" up to the infinite
order, no spin-orbit interaction::
.SPINFREE
.BSS
109
Scalar relativistic effects "from the end" up to the infinite order::
.SPINFREE
.BSS
009
Traditional scalar relativistic "from the beginning" second-order
Douglas-Kroll-Hess Hamiltonian::
.SPINFREE
.BSS
102
Scalar relativistic "from the end" second-order Douglas-Kroll-Hess Hamiltonian::
.SPINFREE
.BSS
002
Douglas-Kroll-Hess Hamiltonian with first-order spin-orbit and second-order
scalar relativistic effects::
.BSS
012
Douglas-Kroll-Hess Hamiltonian with second-order spin-orbit and second-order
scalar relativistic effects::
.BSS
022
In the two-component variational scheme is possible to combine external AMFI
spin-orbit terms, :cite:`Ilias2001`, together with BSS integrals - see the
:ref:`\*AMFI` section. Note that AMFI provides only one-center atomic
integrals.
Infinite order scalar and spin-orbit terms, (one-electron) mean-field
spin-same-orbit (MFSSO2) from AMFI::
.BSS
2999
This is in fact the 'maximum' of two-component relativity, resembling
Dirac-Coulomb Hamiltonian.
Second-order Douglas-Kroll-Hess spin-free from 'the beginning' with
first order spin-orbit (SO1) term plus mean-field spin-same-orbit
(MFSSO) from AMFI::
.BSS
2112
SO1 may come either from BSS-transformation or from AMFI. In the latter case it
is only for one-center and for point nucleus.
Infinite order scalar and spin-orbit terms, (one-electron) mean-field spin-same
and spin-other-orbit (MFSO2) from AMFI::
.BSS
3999
This mimics the Dirac-Coulomb-Gaunt Hamiltonian, as the spin-other-orbit (SOO) term comes
from the Gaunt interaction term.
DIRAC allows to switch off AMFI spin-orbit contributions from various centers.
See the keyword :ref:`AMFI_.NOAMFC`.
Infinite order scalar terms "from the beginning", (one-electron) spin orbit
(SO1) and the mean-field spin-same-orbit (MFSSO2) terms exclusively from AMFI::
.BSS
4109
Second order (DKH) scalar terms "from the beginning", (one-electron)
spin orbit (SO1) and the mean-field spin-same-orbit (MFSSO2) terms
exclusively from AMFI::
.BSS
4102
Infinite order scalar terms "from the end", (one-electron) spin orbit
(SO1) and the mean-field spin-same-orbit and spin-other-orbit (MFSO2)
terms from AMFI::
.BSS
5009
Infinite order scalar terms "from the end", and the (one-electron) spin orbit
term (SO1) from AMFI::
.BSS
6009
AMFI one-electron spin-orbit terms - SO1 - are currently for the point nucleus.
For the BSS value 'axyz' of y=0, DIRAC employs spin-free picture change
transformation of property operators, although the system is not in the boson
(spin-free) symmetry for a>1.
Rough first order, DKH1 (not recommended for practical calculations)::
.BSS
111
For comparison purposes between BSS-SO1 and AMFI-SO1 atomic one-center
integrals (point nucleus only) use::
.BSS
001