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--></style></head><body lang=EN-US link=blue vlink="#954F72"><div class=WordSection1><p class=MsoNormal>Dear professor,</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thanks for your reply, which helps me a lot.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>But I still feel a little confused about the time reversal symmetry in wien2k, From your answer, I know when the system has not the inversion symmetry but has time reversal symmetry, the symmetry can also produce the (-1, -1, -1) diagonal matrix to reduce the number of k points which need to calculate in the BZ.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>However, for example, the case : GaAs, the system is complex, which I can understand, caused by the absence of inversion symmetry. but the system don’t have the (-1, -1, -1) diagonal matrix, Is this mean GaAs also without the time reversal symmetry? </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Is the (-1 -1 -1) diagonal both shows if the system has the inversion symmetry or the time reversal symmetry? But the (-1 -1 -1) diagonal matrix absent cause the system has not only inversion symmetry, but also the time reversal symmetry?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>By the way, why the system is complex when the system without the inversion symmetry? As I know ,the result of inversion symmetry is : <r| -k, j> = <-r | k, j> , Only the time reversal symmetry has some relationship with the complex conjugate: <r|- k, j> = <r |k, j >*. Do you have some relevant references of this ? </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Looking forward to your reply.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Sincerely,</p><p class=MsoNormal>Jasmine. </p><p class=MsoNormal><o:p> </o:p></p><div style='mso-element:para-border-div;border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='border:none;padding:0in'><b>From: </b><a href="mailto:pblaha@theochem.tuwien.ac.at">Peter Blaha</a><br><b>Sent: </b>Thursday, February 6, 2020 7:31 PM<br><b>To: </b><a href="mailto:wien@zeus.theochem.tuwien.ac.at">wien@zeus.theochem.tuwien.ac.at</a><br><b>Subject: </b>Re: [Wien] inversion vs time reversal</p></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>time inversion symmetry is used in WIEN2k only for the generation of the </p><p class=MsoNormal>k-mesh when "inversion" is not present (and it is not a magnetic case </p><p class=MsoNormal>with spin-orbit). In that case we use the fact that </p><p class=MsoNormal>epsilon(k)=epsilon(-k) and "add" the (-1,-1,-1) diagonal matrix to the </p><p class=MsoNormal>symmetry operations reducing the full BZ mesh to the IBZ.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Everywhere else, only "inversion" is used (if present), which makes </p><p class=MsoNormal>wavefunctions "real" and one can use lapw1 instead of lapw1c.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>If you try to run Si with (0,0,0) and (1/4,1/4,1/4), you must "trick" </p><p class=MsoNormal>the initialization procedure, because WIEN2k will normally not allow it, </p><p class=MsoNormal>because it requires an 4 times larger computational effort.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>On 2/6/20 6:26 AM, <span lang=ZH-CN style='font-family:DengXian'>姜若诗</span> wrote:</p><p class=MsoNormal>> Dear professors,</p><p class=MsoNormal>> </p><p class=MsoNormal>> Do you know how to deal with the inversion symmetry and time reversal </p><p class=MsoNormal>> symmetry in wien2k, how do you make them different ?</p><p class=MsoNormal>> </p><p class=MsoNormal>> For example, if the positions of two atoms Si is in (0.125 0.125 0.125) </p><p class=MsoNormal>> and (0.875 0.875 0.875), the system has inversion and time reversal </p><p class=MsoNormal>> symmetry, then the point group symmetry matrix has number 48.</p><p class=MsoNormal>> </p><p class=MsoNormal>> But if the positions are (0 0 0) and (0.25 0.25 0.25), the system </p><p class=MsoNormal>> doesn’t has the inversion symmetry, with time reversal symmetry left, </p><p class=MsoNormal>> will the symmetry matrix reduce to number 24, or also number 48?</p><p class=MsoNormal>> </p><p class=MsoNormal>> In a word, what my question is : Does the symmetry matrix (-1 0 0, 0 </p><p class=MsoNormal>> -1 0, 0 0 -1) show not only the inversion symmetry , but also time </p><p class=MsoNormal>> reversal symmetry in a system?</p><p class=MsoNormal>> </p><p class=MsoNormal>> Looking forward to your reply</p><p class=MsoNormal>> </p><p class=MsoNormal>> Regards,</p><p class=MsoNormal>> </p><p class=MsoNormal>> Jasmine.</p><p class=MsoNormal>> </p><p class=MsoNormal>> </p><p class=MsoNormal>> _______________________________________________</p><p class=MsoNormal>> Wien mailing list</p><p class=MsoNormal>> Wien@zeus.theochem.tuwien.ac.at</p><p class=MsoNormal>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</p><p class=MsoNormal>> SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html</p><p class=MsoNormal>> </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>-- </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal> P.Blaha</p><p class=MsoNormal>--------------------------------------------------------------------------</p><p class=MsoNormal>Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna</p><p class=MsoNormal>Phone: +43-1-58801-165300 FAX: +43-1-58801-165982</p><p class=MsoNormal>Email: blaha@theochem.tuwien.ac.at WIEN2k: http://www.wien2k.at</p><p class=MsoNormal>WWW: http://www.imc.tuwien.ac.at/TC_Blaha</p><p class=MsoNormal>--------------------------------------------------------------------------</p><p class=MsoNormal>_______________________________________________</p><p class=MsoNormal>Wien mailing list</p><p class=MsoNormal>Wien@zeus.theochem.tuwien.ac.at</p><p class=MsoNormal>http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</p><p class=MsoNormal>SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html</p><p class=MsoNormal><o:p> </o:p></p></div></body></html>