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

[Stefano de Gironcoli]

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 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 <degironc at sissa.it>
> *Sent:* Wednesday, December 18, 2024 5:09 PM
> *To:* "toshi1higu at docomo.ne.jp" <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?
>
>   x^2 + y^2+ z^2 is spherically symmetric, isn't it ?
>
> Stefano
>
> Get Outlook for Android <https://aka.ms/AAb9ysg>
>
> ------------------------------------------------------------------------
>
> *From:*users <users-bounces at lists.quantum-espresso.org> on behalf of 
> Toshiharu Higuchi via users <users at lists.quantum-espresso.org>
> *Sent:* Wednesday, December 18, 2024 8:38:54 AM
> *To:* users at lists.quantum-espresso.org 
> <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?
>
> 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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