[QE-users] What is the difference between ILDOS and |psi|^2?

[toshi1higu at docomo.ne.jp]

Dear Professor Stefano Baroni,
Thank you for your quick response.
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." 
Sorry, but could you please explain?
Best regards,
Toshiharu Higuchi

-----Original Message-----
From: Stefano Baroni <baroni at sissa.it> 
Sent: Wednesday, December 18, 2024 3:38 PM
To: "toshi1higu at docomo.ne.jp" <toshi1higu at docomo.ne.jp>; "users at lists.quantum-espresso.org" <users at lists.quantum-espresso.org>
Subject: Re: [QE-users] What is the difference between ILDOS and |psi|^2?

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

___
Stefano Baroni, Trieste -- http://stefano.baroni.me

> On 18 Dec 2024, at 03:56, Toshiharu Higuchi via users <users at lists.quantum-espresso.org> wrote:
> 
> Dear QE Users
> I have a question about the difference between ILDOS and |psi|^2.
> When I calculated the ILDOS (plot_num=10) and |psi|^2 (plot_num =7) of 
> a hydrogen atom, the patterns were different.
> In the case of |psi|^2, 1s orbital → spherical, 2p orbital → 2-lobes, 
> and 3d orbital → 4-lobes were obtained.
> However, in the case of ILDOS, all patterns were spherical.
> According to the literature, ILDOS can be calculated from |psi|^2 and 
> Dirac's delta function.
> Even if |psi|^2 is a pattern other than spherical, ILDOS will be spherical.
> I don't understand the reason for this.
> Please tell me,
> (1) In Quantum-ESPRESSO, are ILDOS and |psi|^2 calculated in separate 
> processes? Or is |psi|^2 calculated first and then ILDOS is calculated 
> using this value?
> (2) Does Dirac's delta function have any effect?
> 
> Best regards,
> Toshiharu Higuchi
> 
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