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</o:shapelayout></xml><![endif]--></head><body lang=JA link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Dear Professors Stefano Baroni and Stefano de Gironcoli, <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>I now understand what you said: "The ILDOS sums the squared moduli of all the molar orbitals in a given energy range. px, py, and pz are degenerate, and their square modules spherically symmetric." <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Thank you very much.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Best regards,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Toshiharu Higuchi<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0mm 0mm 0mm'><p class=MsoNormal><b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'> Stefano de Gironcoli <degironc@sissa.it> <br><b>Sent:</b> Wednesday, December 18, 2024 10:54 PM<br><b>To:</b> toshi1higu@docomo.ne.jp; 'Quantum ESPRESSOusers Forum' <users@lists.quantum-espresso.org>; 'Stefano Baroni' <baroni@sissa.it><br><b>Subject:</b> Re: [QE-users] What is the difference between ILDOS and |psi|^2?<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p><span lang=EN-US>you may want to read and understand the basics of spherical harmonics, for instance from the wikipedia page<o:p></o:p></span></p><p><span lang=EN-US><a href="https://en.wikipedia.org/wiki/Spherical_harmonics">https://en.wikipedia.org/wiki/Spherical_harmonics</a><o:p></o:p></span></p><p><span lang=EN-US>in particular see the attached bit.<o:p></o:p></span></p><p><span lang=EN-US>Stefano deGironcoli<o:p></o:p></span></p><p><span lang=EN-US><o:p> </o:p></span></p><div><p class=MsoNormal><span lang=EN-US>On 18/12/24 09:47, <a href="mailto:toshi1higu@docomo.ne.jp">toshi1higu@docomo.ne.jp</a> wrote:<o:p></o:p></span></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Dear Professor Stefano Baroni,</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Thank you for your quick response.</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'> </span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>I think LDOS & ILDOS are defined as,</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=ES style='font-size:10.5pt;font-family:游ゴシック'>LDOS=</span><span style='font-size:10.5pt;font-family:游ゴシック'>Σ</span><span lang=ES style='font-size:10.5pt;font-family:游ゴシック'>|psi|^2 * </span><span style='font-size:10.5pt;font-family:游ゴシック'>δ</span><span lang=ES style='font-size:10.5pt;font-family:游ゴシック'>(E-En,k)</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>and ILDOS=</span><span style='font-size:10.5pt;font-family:游ゴシック'>∫<span lang=EN-US>(LDOS) dE</span></span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'> </span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>I don't understand the relationship between the above ILDOS and what you said, "x^2 + y^2 + z^2 is spherically symmetric."</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'> </span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Sorry, but could you please explain?</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Best regards,</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'>Toshiharu Higuchi</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.5pt;font-family:游ゴシック'> </span><span lang=EN-US><o:p></o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0mm 0mm 0mm'><p class=MsoNormal><b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'> Stefano de Gironcoli <a href="mailto:degironc@sissa.it"><degironc@sissa.it></a> <br><b>Sent:</b> Wednesday, December 18, 2024 5:09 PM<br><b>To:</b> <a href="mailto:toshi1higu@docomo.ne.jp">"toshi1higu@docomo.ne.jp"</a> <a href="mailto:toshi1higu@docomo.ne.jp"><toshi1higu@docomo.ne.jp></a>; Quantum ESPRESSOusers Forum <a href="mailto:users@lists.quantum-espresso.org"><users@lists.quantum-espresso.org></a>; Stefano Baroni <a href="mailto:baroni@sissa.it"><baroni@sissa.it></a><br><b>Subject:</b> Re: [QE-users] What is the difference between ILDOS and |psi|^2?</span><span lang=EN-US><o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-US> <o:p></o:p></span></p><div><p class=MsoNormal><span lang=EN-US> x^2 + y^2+ z^2 is spherically symmetric, isn't it ?<o:p></o:p></span></p></div><div><p class=MsoNormal><span lang=EN-US>Stefano<o:p></o:p></span></p></div><div id=ms-outlook-mobile-signature><div><p class=MsoNormal><span lang=EN-US> <o:p></o:p></span></p></div><p class=MsoNormal><span lang=EN-US>Get <a href="https://aka.ms/AAb9ysg">Outlook for Android</a><o:p></o:p></span></p></div><div class=MsoNormal align=center style='text-align:center'><span lang=EN-US><hr size=1 width="98%" align=center></span></div><div id=divRplyFwdMsg><p class=MsoNormal><b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:black'>From:</span></b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:black'> users <<a href="mailto:users-bounces@lists.quantum-espresso.org">users-bounces@lists.quantum-espresso.org</a>> on behalf of Toshiharu Higuchi via users <<a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a>><br><b>Sent:</b> Wednesday, December 18, 2024 8:38:54 AM<br><b>To:</b> <a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a> <<a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a>>; Stefano Baroni <<a href="mailto:baroni@sissa.it">baroni@sissa.it</a>><br><b>Subject:</b> Re: [QE-users] What is the difference between ILDOS and |psi|^2?</span><span lang=EN-US> <o:p></o:p></span></p><div><p class=MsoNormal><span lang=EN-US> <o:p></o:p></span></p></div></div><div><div><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt'>Dear Professor Stefano Baroni,<br>Thank you for your quick response.<br>The |psi|^2 (square of absolute value of wave function) of the 2p orbital is 2-lobes, and the |psi|^2 of the 3d orbital is 4-lobes, so they are not spherically symmetric. I don't quite understand the relationship between this and what you said, "px, py, and pz are degenerate, and their square coefficients are spherically symmetric." <br>Sorry, but could you please explain?<br>Best regards,<br>Toshiharu Higuchi<br><br>-----Original Message-----<br>From: Stefano Baroni <<a href="mailto:baroni@sissa.it">baroni@sissa.it</a>> <br>Sent: Wednesday, December 18, 2024 3:38 PM<br>To: "<a href="mailto:toshi1higu@docomo.ne.jp">toshi1higu@docomo.ne.jp</a>" <<a href="mailto:toshi1higu@docomo.ne.jp">toshi1higu@docomo.ne.jp</a>>; "<a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a>" <<a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a>><br>Subject: Re: [QE-users] What is the difference between ILDOS and |psi|^2?<br><br>Dear Toshiharu: The ILDOS sums the squared moduli of all the molecular orbitals in a given energy range. px, py, and pz are degenerate, and their square modulus spherically symmetric (can you see why?) </span><span style='font-size:11.0pt'>…<span lang=EN-US> Can you now draw the conclusions yourself? Stefano<br><br>___<br>Stefano Baroni, Trieste -- <a href="http://stefano.baroni.me">http://stefano.baroni.me</a><br><br>> On 18 Dec 2024, at 03:56, Toshiharu Higuchi via users <<a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a>> wrote:<br>> <br>> </span></span><span lang=EN-US style='font-size:11.0pt;font-family:"Tahoma",sans-serif'></span><span lang=EN-US style='font-size:11.0pt'>Dear QE Users<br>> I have a question about the difference between ILDOS and |psi|^2.<br>> When I calculated the ILDOS (plot_num=10) and |psi|^2 (plot_num =7) of <br>> a hydrogen atom, the patterns were different.<br>> In the case of |psi|^2, 1s orbital </span><span style='font-size:11.0pt'>→<span lang=EN-US> spherical, 2p orbital </span>→<span lang=EN-US> 2-lobes, <br>> and 3d orbital </span>→<span lang=EN-US> 4-lobes were obtained.<br>> However, in the case of ILDOS, all patterns were spherical.<br>> According to the literature, ILDOS can be calculated from |psi|^2 and <br>> Dirac's delta function.<br>> Even if |psi|^2 is a pattern other than spherical, ILDOS will be spherical.<br>> I don't understand the reason for this.<br>> Please tell me,<br>> (1) In Quantum-ESPRESSO, are ILDOS and |psi|^2 calculated in separate <br>> processes? Or is |psi|^2 calculated first and then ILDOS is calculated <br>> using this value?<br>> (2) Does Dirac's delta function have any effect?<br>> <br>> Best regards,<br>> Toshiharu Higuchi<br>> <br>> ______________________________________________________________________<br>> _________ The Quantum ESPRESSO Foundation stands in solidarity with <br>> all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare.<br>> ----------------------------------------------------------------------<br>> ---------- Quantum ESPRESSO is supported by MaX (<a href="http://www.max-centre.eu">www.max-centre.eu</a>) <br>> users mailing list <a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a> <br>> <a href="https://lists.quantum-espresso.org/mailman/listinfo/users">https://lists.quantum-espresso.org/mailman/listinfo/users</a><br>_______________________________________________________________________________<br>The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare.<br>--------------------------------------------------------------------------------<br>Quantum ESPRESSO is supported by MaX (<a href="http://www.max-centre.eu">www.max-centre.eu</a>)<br>users mailing list <a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a><br><a href="https://lists.quantum-espresso.org/mailman/listinfo/users">https://lists.quantum-espresso.org/mailman/listinfo/users</a></span></span><span lang=EN-US><o:p></o:p></span></p></div></div></blockquote></div></body></html>