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 <[email protected]> Sent: Wednesday, December 18, 2024 10:54 PM To: [email protected]; 'Quantum ESPRESSOusers Forum' <[email protected]>; 'Stefano Baroni' <[email protected]> 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, [email protected] <mailto:[email protected]> 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:[email protected]> <[email protected]> Sent: Wednesday, December 18, 2024 5:09 PM To: <mailto:[email protected]> "[email protected]" <mailto:[email protected]> <[email protected]>; Quantum ESPRESSOusers Forum <mailto:[email protected]> <[email protected]>; Stefano Baroni <mailto:[email protected]> <[email protected]> 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 <[email protected] <mailto:[email protected]> > on behalf of Toshiharu Higuchi via users <[email protected] <mailto:[email protected]> > Sent: Wednesday, December 18, 2024 8:38:54 AM To: [email protected] <mailto:[email protected]> <[email protected] <mailto:[email protected]> >; Stefano Baroni <[email protected] <mailto:[email protected]> > 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 <[email protected] <mailto:[email protected]> > Sent: Wednesday, December 18, 2024 3:38 PM To: "[email protected] <mailto:[email protected]> " <[email protected] <mailto:[email protected]> >; "[email protected] <mailto:[email protected]> " <[email protected] <mailto:[email protected]> > 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 > <[email protected] <mailto:[email protected]> > > 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 > > ______________________________________________________________________ > _________ The Quantum ESPRESSO Foundation stands in solidarity with > all civilians worldwide who are victims of terrorism, military aggression, > and indiscriminate warfare. > ---------------------------------------------------------------------- > ---------- Quantum ESPRESSO is supported by MaX (www.max-centre.eu > <http://www.max-centre.eu> ) > users mailing list [email protected] > <mailto:[email protected]> > https://lists.quantum-espresso.org/mailman/listinfo/users _______________________________________________________________________________ The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare. -------------------------------------------------------------------------------- Quantum ESPRESSO is supported by MaX (www.max-centre.eu <http://www.max-centre.eu> ) users mailing list [email protected] <mailto:[email protected]> https://lists.quantum-espresso.org/mailman/listinfo/users
_______________________________________________________________________________ The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare. -------------------------------------------------------------------------------- Quantum ESPRESSO is supported by MaX (www.max-centre.eu) users mailing list [email protected] https://lists.quantum-espresso.org/mailman/listinfo/users
