<div dir="ltr"><pre><font size="4">Dear Prof. Blaha,<br><br>Thank you so much for your prompt reply and clear clarifications.<br>Sorry that I have to open a new thread, because I don't know how to reply your message in the maillist.<br>
<br>I still have some questions:<br><br>>><i> As shown in the Wien2k webpage and maillist, "*In spin-orbit calculations forces are<br></i>>><i> not yet implemented*". The forces on nuclei (even after Pulay correction) are<br>
</i>>><i> meaningless when the spin-orbit coupling is switched on, even though forces<br></i>>><i> are produced without any warnings.<br></i>>><i><br></i>><i>> However, I don't understand exactly the reason why the forces are meaningless.<br>
</i>><i>></i><i> As I guess, (not for sure), the reason is that the force calculations in wien2k is based<br></i>><i>></i><i> on the paper by Yu, et al ( PhysRevB.43.6411(1991)All-electron and pseudopotential<br>
</i>><i>></i><i> force calculations using the linearized-augmented-plane-wave method), in which,<br></i>><i>> however, only the nonrelativistic case is treated.<br></i>>><i><br></i>>><i> If I am right, then my questions are:<br>
</i>>><i><br></i>>><i> 1) Has the scalar relativistic effect (i.e. the mass and Darwin terms) already been<br></i>>><i> considered in the force calculations in wien2k? If yes, what is the difference between<br>
</i>>><i> the cases with and without scalar relativistic effect? Is there any additional force,<br></i>>><i> compared with the formula in PhysRevB.43.6411(1991), due to the presence of<br></i>>><i> scalar relativistic effect?<br>
</i>><br>> Yes, the force calculations are based on the paper by Yu et al.. but already in a scalar relativistic<br>> formulation. Thus there are no extra terms for scalar relativistic wf, only the meaning of "psi"<br>
> is different in that sense that the scalarrelativistic psi has to be taken,.....<br>================================================================<br>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...<br>
<br>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. <br>Does this mean that the scalar relativistic terms are already implicitly included in the Hamiltonian (for example the Kinetic operator T)? <br>
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?<br><br><br><br>>><i> 2) What is the meaning of "*In spin-orbit calculations forces are not yet implemented*"?<br>
</i>>><i> As I understand, "*not yet implemented*" means that the additional forces due to the presence<br></i>>><i> of spin-orbit coupling are not calculated at all. If this is true, then the forces calculated with and<br>
</i>>><i> without spin-orbit coupling should be same. However, I find that the forces on nuclei are changed<br></i>>><i> very much when spin-orbit coupling is switched on.<br><br></i><br>> It means what it means: in SO calculations there is an additional term in the Hamiltonian, which would<br>
> give rise to an additional term in the Pulay corrections, which is not implemented.<br>> Why should the forces be the same ? You change the wavefunctions with SO, but not the Pulay corrections,<br>> thus the result will change.<br>
=================================================================<br>I see....<br>If possible, could you please show me what the additional term due to spin-orbit coupling looks like, or give me some references?<br><br><br>
>><i> 3) Is there any physical meaning, (although perhaps not the real physics or not the<br></i>>><i> correct physics), of the forces on nuclei (after Pulay correction) in the presence of<br></i>>><i> spin-orbit coupling? Take a nonmagnetic calculation as an example. As I understand,<br>
</i>>><i> (not for sure), without spin-orbit coupling, the Pulay correction from the valence<br></i>>><i> electrons is calculated using the wavefunctions and energy eigenvalues from<br></i>>><i> non-spin-polarized lapw1 calculations. With spin-orbit coupling, two sets of data<br>
</i>>><i> (wavefunctions and energy eigenvalues) are obtained from lapw1 and lapwso<br></i>>><i> calculations: one is for spin up and one is for spin down. Then the Pulay correction<br></i>>><i> of forces from valence electrons is calculated using these two sets of data.<br>
</i>>><i> This means that the additional forces due to spin-orbit coupling are caused by<br></i>>><i> the modification of wavefunctions due to spin-orbit coupling. Is my statement<br></i>>><i> correct?<br>
</i><br>> Yes.<br><br>>><i> 4) If the forces calculated with spin-orbit coupling are indeed incorrect and meaningless,<br></i>>><i> can we use PORT option in case.inM when doing atomic relaxation (min_lapw)? This<br>
</i>>><i> question arises because I read in the wien2k user guide that "It (PORT) minimizes the<br></i>>><i> total energy and NOT the forces (using the forces as derivative of E vs. atomic positions).".<br>
</i>>><i> As I understand, the PORT method will use "total energy", instead of "force on nuclei",<br></i>>><i> as a criterion to find the equilibrium positions of atoms, i.e., the PORT method will find<br>
</i>>><i> an energy minimum by a real displacement of atoms, rather than by find a structure in<br></i>>><i> which forces on atoms are zero. This means that the forces on nuclei is NOT the essential<br></i>>><i> ingredient in the PORT method, and PORT method is still valid (as long as the total<br>
</i>>><i> energy are calcuated correctly) even in the presence of spin-orbit coupling. Is my<br></i>>><i> ratiocination correct?<br></i><br>> No, you can't use PORT. PORT uses the "gradiant of E-tot", i.e. the forces in order to move<br>
> atoms "in the proper direction" and if they do not fit with the resulting E-tot, it will give up.<br><br><br>>><i> 5) Could you please also explain to me the meaning of some variables in the source code<br>
</i>>><i> of lapw2? In the SUBROUTINE FOMAI1 (fomai1.f), there are four variables relating to the<br></i>>><i> Pulay correction from the valence electrons: fsph, fsph2, forb, and fnsp. In the SUBROUTINE<br></i>>><i> fsumai1 (fsumai1.F) there is one variable: fsur. In the SUBROUTINE FOMAI2 (fomai2.F), there<br>
</i>>><i> is one variable: fvdrho. As I understand, (not for sure), "fvdrho" comes from Eq. A8 in<br></i>>><i> PhysRevB.43.6411(1991), "fsur" comes from Eq. A12 in the paper, and "fnsp" comes from<br>
</i>>><i> Eq. A20 in the paper. Am I right? Then my question is which formula are related to "fsph",<br></i>>><i> "fsph2", and "forb"?<br></i><br>> This is a long time ago and I would have to go through all equations again to<br>
> identify them. But it should not be too difficult ....<br><br>> PS: As mentioned in UG, you can switch off SO for light atoms (eg. oxygens), and then the forces for<br>> those atoms are still ok and meaningful.<br>
=====================================================<br>Thank you so much for you kind suggestions. <br>This does not help me, because spin-orbit coupling for all atoms are important in my calculations.<br><br><br>Best Regards,<br>
Zhiyong Zhu<br></font></pre><font size="4"><span></span></font><br></div>