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

Tue Dec 24 08:37:41 CET 2024

Dear Professors Stefano Baroni and Stefano de Gironcoli, 

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." 

Thank you very much.

Best regards,

Toshiharu Higuchi

From: Stefano de Gironcoli <degironc at sissa.it> 
Sent: Wednesday, December 18, 2024 10:54 PM
To: toshi1higu at docomo.ne.jp; 'Quantum ESPRESSOusers Forum' <users at lists.quantum-espresso.org>; 'Stefano Baroni' <baroni at sissa.it>
Subject: Re: [QE-users] What is the difference between ILDOS and |psi|^2?

you may want to read and understand the basics of spherical harmonics, for instance from the wikipedia page

https://en.wikipedia.org/wiki/Spherical_harmonics

in particular see the attached bit.

Stefano deGironcoli

On 18/12/24 09:47, toshi1higu at docomo.ne.jp <mailto:toshi1higu at docomo.ne.jp>  wrote:

Dear Professor Stefano Baroni,

Thank you for your quick response.

I think LDOS & ILDOS are defined as,

LDOS=Σ|psi|^2  * δ(E-En,k)

and  ILDOS=∫(LDOS) dE

I don't understand the relationship between the above ILDOS and what you said, "x^2 + y^2 + z^2 is spherically symmetric."

Sorry, but could you please explain?

Best regards,

Toshiharu Higuchi

From: Stefano de Gironcoli  <mailto:degironc at sissa.it> <degironc at sissa.it> 
Sent: Wednesday, December 18, 2024 5:09 PM
To:  <mailto:toshi1higu at docomo.ne.jp> "toshi1higu at docomo.ne.jp"  <mailto:toshi1higu at docomo.ne.jp> <toshi1higu at docomo.ne.jp>; Quantum ESPRESSOusers Forum  <mailto:users at lists.quantum-espresso.org> <users at lists.quantum-espresso.org>; Stefano Baroni  <mailto:baroni at sissa.it> <baroni at sissa.it>
Subject: Re: [QE-users] What is the difference between ILDOS and |psi|^2?

  x^2 + y^2+ z^2 is spherically symmetric, isn't it ?

Stefano

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  _____  

From: users <users-bounces at lists.quantum-espresso.org <mailto:users-bounces at lists.quantum-espresso.org> > on behalf of Toshiharu Higuchi via users <users at lists.quantum-espresso.org <mailto:users at lists.quantum-espresso.org> >
Sent: Wednesday, December 18, 2024 8:38:54 AM
To: users at lists.quantum-espresso.org <mailto:users at lists.quantum-espresso.org>  <users at lists.quantum-espresso.org <mailto:users at lists.quantum-espresso.org> >; Stefano Baroni <baroni at sissa.it <mailto:baroni at sissa.it> >
Subject: Re: [QE-users] What is the difference between ILDOS and |psi|^2? 

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 <mailto:baroni at sissa.it> > 
Sent: Wednesday, December 18, 2024 3:38 PM
To: "toshi1higu at docomo.ne.jp <mailto:toshi1higu at docomo.ne.jp> " <toshi1higu at docomo.ne.jp <mailto:toshi1higu at docomo.ne.jp> >; "users at lists.quantum-espresso.org <mailto:users at lists.quantum-espresso.org> " <users at lists.quantum-espresso.org <mailto: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 <mailto: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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