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<div dir="auto"> x^2 + y^2+ z^2 is spherically symmetric, isn't it ?</div>
<div dir="auto">Stefano</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> users <users-bounces@lists.quantum-espresso.org> on behalf of Toshiharu Higuchi via users <users@lists.quantum-espresso.org><br>
<b>Sent:</b> Wednesday, December 18, 2024 8:38:54 AM<br>
<b>To:</b> users@lists.quantum-espresso.org <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?</font>
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<div class="PlainText">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 <baroni@sissa.it> <br>
Sent: Wednesday, December 18, 2024 3:38 PM<br>
To: "toshi1higu@docomo.ne.jp" <toshi1higu@docomo.ne.jp>; "users@lists.quantum-espresso.org" <users@lists.quantum-espresso.org><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?) … 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 <users@lists.quantum-espresso.org> wrote:<br>
> <br>
> 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 → spherical, 2p orbital → 2-lobes, <br>
> and 3d orbital → 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>
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