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

[Peter Blaha]

> 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,.....


> 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.


> 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.
-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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