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--></style></head><body lang=EN-US link=blue vlink="#954F72"><div class=WordSection1><p class=MsoNormal>Dear professor, am I understand right? </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>If the system has inversion symmetry, there is (-1 -1 -1) diagonal matrix and also the system is real. </p><p class=MsoNormal>If the system doesn’t have inversion symmetry, but without magnetism and neglect the spin-orbit interactions( time reversal symmetry present), the system doesn’t have (-1 -1 -1) diagonal matrix and the system is complex, the symmetry operators shows in case.struct is reduced a half(24 sym.ops), but when calculate the k-mesh, we use the time reversal as if inversion present (48 sym.ops) ?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I calculate the GaAs, which with time reversal but without inversion, there are only 24 symmetry operators in case.struct file. Is this the situation that you said?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>If I understand right, what the final file you use describes the right symmetry operators, Is case.outputkgen, or in case.struct, with the origin 24 symmetry operators adding another (-1 -1 -1) * 24 sym.ops?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Regards,</p><p class=MsoNormal>Jasmine.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>--------------------------------------------------GaAs.struct-------------------------------------------------</p><p class=MsoNormal>GaAs </p><p class=MsoNormal>F LATTICE,NONEQUIV.ATOMS: 2 </p><p class=MsoNormal>MODE OF CALC=RELA unit=bohr </p><p class=MsoNormal> 10.683000 10.683000 10.683000 90.000000 90.000000 90.000000 </p><p class=MsoNormal>ATOM 1: X=0.00000000 Y=0.00000000 Z=0.00000000</p><p class=MsoNormal> MULT= 1 ISPLIT= 2</p><p class=MsoNormal>Ga NPT= 781 R0=0.00005000 RMT= 2.30 Z: 31.000 </p><p class=MsoNormal>LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</p><p class=MsoNormal> 0.0000000 1.0000000 0.0000000</p><p class=MsoNormal> 0.0000000 0.0000000 1.0000000</p><p class=MsoNormal>ATOM 2: X=0.25000000 Y=0.25000000 Z=0.25000000</p><p class=MsoNormal> MULT= 1 ISPLIT= 2</p><p class=MsoNormal>As NPT= 781 R0=0.00005000 RMT= 2.30 Z: 33.000 </p><p class=MsoNormal>LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</p><p class=MsoNormal> 0.0000000 1.0000000 0.0000000</p><p class=MsoNormal> 0.0000000 0.0000000 1.0000000</p><p class=MsoNormal> 24 NUMBER OF SYMMETRY OPERATIONS</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 0-1 0 0.00000000</p><p class=MsoNormal> 0 0-1 0.00000000</p><p class=MsoNormal> 1</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 0 0-1 0.00000000</p><p class=MsoNormal> 0-1 0 0.00000000</p><p class=MsoNormal> 2</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal>-1 0 0 0.00000000</p><p class=MsoNormal> 0 0-1 0.00000000</p><p 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0.00000000</p><p class=MsoNormal> 10</p><p class=MsoNormal> 0-1 0 0.00000000</p><p class=MsoNormal> 0 0-1 0.00000000</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 11</p><p class=MsoNormal> 0 0-1 0.00000000</p><p class=MsoNormal> 0-1 0 0.00000000</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 12</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 13</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 14</p><p class=MsoNormal>-1 0 0 0.00000000</p><p class=MsoNormal> 0 0-1 0.00000000</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 15</p><p class=MsoNormal>-1 0 0 0.00000000</p><p class=MsoNormal> 0-1 0 0.00000000</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 16</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 17</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 18</p><p class=MsoNormal> 0 0-1 0.00000000</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal>-1 0 0 0.00000000</p><p class=MsoNormal> 19</p><p class=MsoNormal> 0-1 0 0.00000000</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal>-1 0 0 0.00000000</p><p class=MsoNormal> 20</p><p class=MsoNormal> 0 0-1 0.00000000</p><p class=MsoNormal>-1 0 0 0.00000000</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 21</p><p class=MsoNormal> 0-1 0 0.00000000</p><p class=MsoNormal>-1 0 0 0.00000000</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 22</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 23</p><p class=MsoNormal> 1 0 0 0.00000000</p><p class=MsoNormal> 0 1 0 0.00000000</p><p class=MsoNormal> 0 0 1 0.00000000</p><p class=MsoNormal> 24</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>Friday, February 7, 2020 4:02 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>> However, for example, the case : GaAs, the system is complex, which I </p><p class=MsoNormal>> can understand, caused by the absence of inversion symmetry. but the </p><p class=MsoNormal>> system don’t have the (-1, -1, -1) diagonal matrix, Is this mean GaAs </p><p class=MsoNormal>> also without the time reversal symmetry?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>As I said: WITHOUT magnetism and neglecting Spin-orbit interactions, </p><p class=MsoNormal>time reversal is always present.</p><p class=MsoNormal>Therefore, when we calculate the IBZ k-mesh, we use not only the 24 </p><p class=MsoNormal>symops of this space group, but multiply every operation also with </p><p class=MsoNormal>inversion and use 48 sym.ops.</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 </p><p class=MsoNormal>> symmetry or the time reversal symmetry? But the (-1 -1 -1) diagonal </p><p class=MsoNormal>> matrix absent cause the system has not only inversion symmetry, but also </p><p class=MsoNormal>> the time reversal symmetry?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The (-1,-1,-1) diagonal matrix (in case.struct) shows, that we have </p><p class=MsoNormal>INVERSION symmetry. Time reversal has nothing to do with the local </p><p class=MsoNormal>symmetry, but depends on ... (see above).</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 </p><p class=MsoNormal>> inversion symmetry? As I know ,the result of inversion symmetry is : <r| </p><p class=MsoNormal>> -k, j> = <-r | k, j> , Only the time reversal symmetry has some </p><p class=MsoNormal>> relationship with the complex conjugate: <r|- k, j> = <r |k, j >*. Do </p><p class=MsoNormal>> you have some relevant references of this ?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Now it becomes quite basic:</p><p class=MsoNormal>We use plane waves, right ? These are complex functions psi= exp**(i k r).</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>However, this can be expanded into cos (k r) + i sin (k r)</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>With inversion we know that psi (r) = psi (-r).</p><p class=MsoNormal>Since sin (k r) is "odd"; (sin (k r) .ne. sin (k -r)), we know that </p><p class=MsoNormal>this term must vanish and we can replace exp**(i k r) by cos (k r) </p><p class=MsoNormal> and this is purely "real".</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>> </p><p class=MsoNormal>> Looking forward to your reply.</p><p class=MsoNormal>> </p><p class=MsoNormal>> Sincerely,</p><p class=MsoNormal>> </p><p class=MsoNormal>> Jasmine.</p><p class=MsoNormal>> </p><p class=MsoNormal>> *From: *Peter Blaha <mailto:pblaha@theochem.tuwien.ac.at></p><p class=MsoNormal>> *Sent: *Thursday, February 6, 2020 7:31 PM</p><p class=MsoNormal>> *To: *wien@zeus.theochem.tuwien.ac.at </p><p class=MsoNormal>> <mailto:wien@zeus.theochem.tuwien.ac.at></p><p class=MsoNormal>> *Subject: *Re: [Wien] inversion vs time reversal</p><p class=MsoNormal>> </p><p class=MsoNormal>> time inversion symmetry is used in WIEN2k only for the generation of the</p><p class=MsoNormal>> </p><p class=MsoNormal>> k-mesh when "inversion" is not present (and it is not a magnetic case</p><p class=MsoNormal>> </p><p class=MsoNormal>> with spin-orbit). In that case we use the fact that</p><p class=MsoNormal>> </p><p class=MsoNormal>> epsilon(k)=epsilon(-k) and "add" the (-1,-1,-1) diagonal matrix to the</p><p class=MsoNormal>> </p><p class=MsoNormal>> symmetry operations reducing the full BZ mesh to the IBZ.</p><p class=MsoNormal>> </p><p class=MsoNormal>> Everywhere else, only "inversion" is used (if present), which makes</p><p class=MsoNormal>> </p><p class=MsoNormal>> wavefunctions "real" and one can use lapw1 instead of lapw1c.</p><p class=MsoNormal>> </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>> </p><p class=MsoNormal>> the initialization procedure, because WIEN2k will normally not allow it,</p><p class=MsoNormal>> </p><p class=MsoNormal>> because it requires an 4 times larger computational effort.</p><p class=MsoNormal>> </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>> </p><p class=MsoNormal>> > Dear professors,</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></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>> </p><p class=MsoNormal>> > symmetry in wien2k, how do you make them different ?</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></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>> </p><p class=MsoNormal>> > and (0.875 0.875 0.875), the system has inversion and time reversal</p><p class=MsoNormal>> </p><p class=MsoNormal>> > symmetry, then the point group symmetry matrix has number 48.</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></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>> </p><p class=MsoNormal>> > doesn’t has the inversion symmetry, with time reversal symmetry left,</p><p class=MsoNormal>> </p><p class=MsoNormal>> > will the symmetry matrix reduce to number 24, or also number 48?</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></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>> </p><p class=MsoNormal>> > -1 0, 0 0 -1) show not only the inversion symmetry , but also time</p><p class=MsoNormal>> </p><p class=MsoNormal>> > reversal symmetry in a system?</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></p><p class=MsoNormal>> </p><p class=MsoNormal>> > Looking forward to your reply</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></p><p class=MsoNormal>> </p><p class=MsoNormal>> > Regards,</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></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>> ></p><p class=MsoNormal>> </p><p class=MsoNormal>> > _______________________________________________</p><p class=MsoNormal>> </p><p class=MsoNormal>> > Wien mailing list</p><p class=MsoNormal>> </p><p class=MsoNormal>> > Wien@zeus.theochem.tuwien.ac.at</p><p class=MsoNormal>> </p><p class=MsoNormal>> > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</p><p class=MsoNormal>> </p><p class=MsoNormal>> > SEARCH the MAILING-LIST at: </p><p class=MsoNormal>> http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html</p><p class=MsoNormal>> </p><p class=MsoNormal>> ></p><p class=MsoNormal>> </p><p class=MsoNormal>> -- </p><p class=MsoNormal>> </p><p class=MsoNormal>> P.Blaha</p><p class=MsoNormal>> </p><p class=MsoNormal>> --------------------------------------------------------------------------</p><p class=MsoNormal>> </p><p class=MsoNormal>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna</p><p class=MsoNormal>> </p><p class=MsoNormal>> Phone: +43-1-58801-165300 FAX: +43-1-58801-165982</p><p class=MsoNormal>> </p><p class=MsoNormal>> Email: blaha@theochem.tuwien.ac.at WIEN2k: http://www.wien2k.at</p><p class=MsoNormal>> </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>> </p><p class=MsoNormal>> _______________________________________________</p><p class=MsoNormal>> </p><p class=MsoNormal>> Wien mailing list</p><p class=MsoNormal>> </p><p class=MsoNormal>> Wien@zeus.theochem.tuwien.ac.at</p><p class=MsoNormal>> </p><p class=MsoNormal>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</p><p class=MsoNormal>> </p><p class=MsoNormal>> SEARCH the MAILING-LIST at: </p><p class=MsoNormal>> http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html</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>