[Wien] Questions about forces on nuclei in the presence of spin orbit coupling

[Zhiyong Zhu]

Dear Prof. Blaha,

Thank you so much for your prompt reply and clear clarifications.
Sorry that I have to open a new thread, because I don't know how to
reply your message in the maillist.

I still have some questions:

>>* As shown in the Wien2k webpage and maillist, "*In spin-orbit calculations forces are
*>>* not yet implemented*". The forces on nuclei (even after Pulay
correction) are
*>>* meaningless when the spin-orbit coupling is switched on, even though forces
*>>* are produced without any warnings.
*>>*
*>*> However, I don't understand exactly the reason why the forces are
meaningless.
*>*>** As I guess, (not for sure), the reason is that the force
calculations in wien2k is based
*>*>** on the paper by Yu, et al ( PhysRevB.43.6411(1991)All-electron
and pseudopotential
*>*>** force calculations using the linearized-augmented-plane-wave
method), in which,
*>*> however, only the nonrelativistic case is treated.
*>>*
*>>* If I am right, then my questions are:
*>>*
*>>* 1)  Has the scalar relativistic effect (i.e. the mass and Darwin
terms) already been
*>>* considered in the force calculations in wien2k? If yes, what is
the difference between
*>>* the cases with and without scalar relativistic effect? Is there
any additional force,
*>>* compared with the formula in PhysRevB.43.6411(1991), due to the presence of
*>>* scalar relativistic effect?
*>
> Yes, the force calculations are based on the paper by Yu et al.. but already in a scalar relativistic
> formulation. Thus there are no extra terms for scalar relativistic wf, only the meaning of "psi"
> is different in that sense that the scalarrelativistic psi has to be taken,.....
================================================================
Actually, this question arises because I read one sentence in the
Appendix of the paper by Yu, et al -- "Using the nonrelativistic
Hamiltonian...". That's why I thought that scalar relativistic effect
is not considered in that paper...

PS, I cannot find scalar relativistic terms (-p^4/8m^3c^2 -
(h^2/4m^2c^2)*(dV/dr)(d/dr)) explicitly in that paper.
Does this mean that the scalar relativistic terms are already
implicitly included in the Hamiltonian (for example the Kinetic
operator T)?
Does this also mean that (compared with nonrelativistic case) scalar
relativistic effect does not produce extra terms in Pulay correction,
and only modifies the wavefunctions?



>>* 2)  What is the meaning of "*In spin-orbit calculations forces are not yet implemented*"?
*>>* As I understand, "*not yet implemented*" means that the
additional forces due to the presence
*>>* of spin-orbit coupling are not calculated at all. If this is
true, then the forces calculated with and
*>>* without spin-orbit coupling should be same. However, I find that
the forces on nuclei are changed
*>>* very much when spin-orbit coupling is switched on.

*
> It means what it means: in SO calculations there is an additional term in the Hamiltonian, which would
> give rise to an additional term in the Pulay corrections, which is not implemented.
> Why should the forces be the same ? You change the wavefunctions with SO, but not the Pulay corrections,
> thus the result will change.
=================================================================
I see....
If possible, could you please show me what the additional term due to
spin-orbit coupling looks like, or give me some references?


>>* 3)  Is there any physical meaning, (although perhaps not the real physics or not the
*>>* correct physics), of the forces on nuclei (after Pulay
correction) in the presence of
*>>* spin-orbit coupling? Take a nonmagnetic calculation as an
example. As I understand,
*>>* (not for sure), without spin-orbit coupling, the Pulay correction
from the valence
*>>* electrons is calculated using the wavefunctions and energy eigenvalues from
*>>* non-spin-polarized lapw1 calculations. With spin-orbit coupling,
two sets of data
*>>* (wavefunctions and energy eigenvalues) are obtained from lapw1 and lapwso
*>>* calculations: one is for spin up and one is for spin down. Then
the Pulay correction
*>>* of forces from valence electrons is calculated using these two
sets of data.
*>>* This means that the additional forces due to spin-orbit coupling
are caused by
*>>* the modification of wavefunctions due to spin-orbit coupling. Is
my statement
*>>* correct?
*
> Yes.

>>* 4)  If the forces calculated with spin-orbit coupling are indeed incorrect and meaningless,
*>>* can we use PORT option in case.inM when doing atomic relaxation
(min_lapw)? This
*>>* question arises because I read in the wien2k user guide that "It
(PORT) minimizes the
*>>* total energy and NOT the forces (using the forces as derivative
of E vs. atomic positions).".
*>>* As I understand, the PORT method will use "total energy", instead
of "force on nuclei",
*>>* as a criterion to find the equilibrium positions of atoms, i.e.,
the PORT method will find
*>>* an energy minimum by a real displacement of atoms, rather than by
find a structure in
*>>* which forces on atoms are zero. This means that the forces on
nuclei is NOT the essential
*>>* ingredient in the PORT method, and PORT method is still valid (as
long as the total
*>>* energy are calcuated correctly) even in the presence of
spin-orbit coupling. Is my
*>>* ratiocination correct?
*
> No, you can't use PORT. PORT uses the "gradiant of E-tot", i.e. the forces in order to move
> atoms "in the proper direction" and if they do not fit with the resulting E-tot, it will give up.


>>* 5) Could you please also explain to me the meaning of some variables in the source code
*>>* of lapw2? In the SUBROUTINE FOMAI1 (fomai1.f), there are four
variables relating to the
*>>* Pulay correction from the valence electrons: fsph, fsph2, forb,
and fnsp. In the SUBROUTINE
*>>* fsumai1 (fsumai1.F) there is one variable: fsur.  In the
SUBROUTINE FOMAI2 (fomai2.F), there
*>>* is one variable: fvdrho. As I understand, (not for sure),
"fvdrho" comes from Eq. A8 in
*>>* PhysRevB.43.6411(1991), "fsur" comes from Eq. A12 in the paper,
and "fnsp" comes from
*>>* Eq. A20 in the paper. Am I right? Then my question is which
formula are related to "fsph",
*>>* "fsph2", and "forb"?
*
> This is a long time ago and I would have to go through all equations again to
> identify them. But it should not be too difficult ....

> PS: As mentioned in UG, you can switch off SO for light atoms (eg. oxygens), and then the forces for
> those atoms are still ok and meaningful.
=====================================================
Thank you so much for you kind suggestions.
This does not help me, because spin-orbit coupling for all atoms are
important in my calculations.


Best Regards,
Zhiyong Zhu
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