<div dir="ltr">Dear Prof. Blaha,<br>Dear Wien2k users and authors,<br><br>Happy New Year!<br><br>I am using wien2k(_11.1) to do atomic relaxations in some materials.<br><br>I have some questions about the force calculations (in particular the Pulay correction <br>
of valence electron force) in the presence of spin orbit coupling.<br><br>As shown in the Wien2k webpage and maillist, "<b>In spin-orbit calculations forces are <br>not yet implemented</b>". The forces on nuclei (even after Pulay correction) are<br>
meaningless when the spin-orbit coupling is switched on, even though forces <br>are produced without any warnings.<br><br>However, I don't understand exactly the reason why the forces are meaningless.<br>As I guess, (not for sure), the reason is that the force calculations in wien2k is based<br>
on the paper by Yu, et al ( PhysRevB.43.6411(1991)All-electron and pseudopotential<br>force calculations using the linearized-augmented-plane-wave method), in which,<br>however, only the nonrelativistic case is treated.<br>
<br>If I am right, then my questions are:<br><br>1) Has the scalar relativistic effect (i.e. the mass and Darwin terms) already been<br>considered in the force calculations in wien2k? If yes, what is the difference between<br>
the cases with and without scalar relativistic effect? Is there any additional force,<br>compared with the formula in PhysRevB.43.6411(1991), due to the presence of <br>scalar relativistic effect?<br><br>2) What is the meaning of "<b>In spin-orbit calculations forces are not yet implemented</b>"?<br>
As I understand, "<b>not yet implemented</b>" means that the additional forces due to the presence <br>
of spin-orbit coupling are not calculated at all. If this is true, then the forces calculated with and <br>
without spin-orbit coupling should be same. However, I find that the forces on nuclei are changed<br>
very much when spin-orbit coupling is switched on.<br><br>3) Is there any physical meaning, (although perhaps not the real physics or not the <br>correct physics), of the forces on nuclei (after Pulay correction) in the presence of <br>
spin-orbit coupling? Take a nonmagnetic calculation as an example. As I understand,<br>(not for sure), without spin-orbit coupling, the Pulay correction from the valence <br>electrons is calculated using the wavefunctions and energy eigenvalues from<br>
non-spin-polarized lapw1 calculations. With spin-orbit coupling, two sets of data<br>(wavefunctions and energy eigenvalues) are obtained from lapw1 and lapwso<br>calculations: one is for spin up and one is for spin down. Then the Pulay correction<br>
of forces from valence electrons is calculated using these two sets of data.<br>This means that the additional forces due to spin-orbit coupling are caused by<br>the modification of wavefunctions due to spin-orbit coupling. Is my statement<br>
correct?<br><br>4) If the forces calculated with spin-orbit coupling are indeed incorrect and meaningless,<br>can we use PORT option in case.inM when doing atomic relaxation (min_lapw)? This <br>question arises because I read in the wien2k user guide that "It (PORT) minimizes the <br>
total energy and NOT the forces (using the forces as derivative of E vs. atomic positions).".<br>As I understand, the PORT method will use "total energy", instead of "force on nuclei",<br>as a criterion to find the equilibrium positions of atoms, i.e., the PORT method will find<br>
an energy minimum by a real displacement of atoms, rather than by find a structure in<br>which forces on atoms are zero. This means that the forces on nuclei is NOT the essential<br>ingredient in the PORT method, and PORT method is still valid (as long as the total <br>
energy are calcuated correctly) even in the presence of spin-orbit coupling. Is my <br>ratiocination correct? <br><br>5) Could you please also explain to me the meaning of some variables in the source code<br>of lapw2? In the SUBROUTINE FOMAI1 (fomai1.f), there are four variables relating to the<br>
Pulay correction from the valence electrons: fsph, fsph2, forb, and fnsp. In the SUBROUTINE <br>fsumai1 (fsumai1.F) there is one variable: fsur. In the SUBROUTINE FOMAI2 (fomai2.F), there <br>is one variable: fvdrho. As I understand, (not for sure), "fvdrho" comes from Eq. A8 in <br>
PhysRevB.43.6411(1991), "fsur" comes from Eq. A12 in the paper, and "fnsp" comes from <br>Eq. A20 in the paper. Am I right? Then my question is which formula are related to "fsph", <br>"fsph2", and "forb"?<br>
<br>Thank you very much.<br><br>Best Regards,<br>Zhiyong Zhu<br>Post Doctoral Fellow<br><span class="st"><em>King Abdullah University of Science and Technology</em> (<em>KAUST</em>)</span><br><br><br><br><br><br></div>