Dear Alvin Chang,

Starting from the four-component fully relativistic Dirac equation DFT.
 
1. neglect only spin-orbit coupling => spin-free Dirac equation (Dyall)

2. exact transformation to two component => the exact Foldy-Wouthuysen
transformation is in principle no approximation.

3. approximate transformation to two component (Pauli, ZORA, DKH), these
Hamiltonains still include spin-orbit coupling

4. equal to 3 plus neglect of spin-orbit coupling (Pauli, ZORA, DKH) one
component, also
  called scalar relativistic.

5. frozen cores or relativistic pseupopotentials can in principle be
used in any of the above
With ADF you can use frozen cores.

The Pauli Hamiltonian can suffer from variational stability.
Sometimes the use of the Pauli Hamiltonian variationally for valence
orbitals is called
quasi-relativistic.

The ZORA and Douglas-Kroll Hess Hamiltonian are both variational stable,
but use a different way of
approximating the exact Foldy-Wouthuysen transformation, see the literature.
In ADF you can use the ZORA Hamiltonian.

In a frozen core calculation the core orbitals are kept frozen.
The valence orbitals are orthogonalized on these core orbitals.
In the core region the description of the valence orbital is correct,
for example, the number of core wiggles for a valence orbital is correct.

In pseudopotential calculations an effective potential is constructed
such that
the core orbitals and the strong nuclear potential are removed and the
valence orbitals
see a much weaker potential.
In the core region the description of the valence orbital is not correct,
for example, the number of core wiggles for a valence orbital can be
wrong compared to an all electron calculation.

Best regards,
Erik van Lenthe
SCM

you wrote:

>several iterms are found in the literatures on the calculation works
>of TM system,such as:
>
>scalar-relativistic(for example,ZORA,DKH)
>quasi-relativistic(for example,pseudopotential)
>two-component relativistic
>one-component realtivistic
>
>what's the relation and difference among them ?
>and what levels of approximation are they at relative to
>full-relativistic(also as four-component relativistic),respectively ?
>
>thanks!
>--
>so let us be up and doing
>with a heart for any fate
>still pursuing and still achieving
>learn to labor and to wait
>
>
Received on 2005-11-30 15:40:25