[QE-users] unit mismatch between PH generated frequencies and manually generated eigenvalues

Thu May 1 17:21:10 CEST 2025

Dear Shubham,

first of all, I'm happy that you have had the chance to go through your
calculations and figure out one of the issues
you were facing.

I did not check your unit factors, because I suspect that before making the
two y axes having exactly the same units you
need to further check your diagonalization.
At this point, the issue is even more subtle than at the beginning. Indeed,
while in the previous plots  the whole spectrum seemed
to suffer from a not uniform scaling (that you then checked was due to a
missing square root), in the last plots that issue seems
to be confined only to the higher frequency modes. The 6th band is
separated by a small gap from the 5th in the leftmost plot,
whereas it shares some frequency range with the same band in the other two
plots.

Now, it is difficult without trying to reproduce your calculation to really
figure out what's happening. I would suggest to check:
i) the coordinates and units of q-points (it is just for safety, if there
is a gap you can choose q-points even at random and you
cannot get frequencies within that gap);
ii) check that the dynamical matrix you're diagonalizing is correct. How do
you get that dynamical matrix? Are you sure that you're diagonalizing
the dynamical matrix? I insist, even though it could not be the case, that
the dynamical matrix you diagonalize is obtained from the Fourier transform
of the force constant matrix dividing by the square root of the product of
the atomic masses involved in each matrix element. Such a factor is a global
factor only if you have just one atomic species, otherwise different
factors will multiply different matrix elements.

I'm not able to provide further insight with the information you provided.

Hope this helps.
Giovanni

-- 

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at spin.cnr.it <giovanni.cantele at spin.cnr.it>
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: https://sites.google.com/view/giovanni-cantele/home

Il giorno gio 1 mag 2025 alle ore 11:34 Shubham Patel <
spatelphy at iitkgp.ac.in> ha scritto:

> Dear Prof. Giovanni,
>
> Thank you very much for taking time and replying in detail and explaining
> things.
>
> I have indeed gone through tutorials and examples and produced thing very
> well using the well established Quantum Espresso code.
> However, here I am trying to reproduce the phonon frequencies using
> diagonalizing the q-dependent dynamical matrices. After checking I realized
> that I was missing the Square root (SQRT) function of eigenvalues which now
> I incorporate in my code. I am attaching the figure here (middle figure in
> the figure attached). Now we can see that both the bands (the lowest point)
> are almost on the same level. Indeed as you righteously pointed out that
> there could be some other factor, such as, mass factor, be involved which
> brings in a little discrepancy in higher frequency regions.
>
> As I came to know from the documentations and literature that the mass
> factor is already incorporated in the q-dependent matrix elements
> calculated using Fourier transform of Force constant matrices, therefore I
> have a suspicion that it is the mass factor which brings the mismatch in
> the dispersion. I also looked into the source code but did not find the
> mass factor involved while collecting frequency data.
>
> Additionally, after a careful inspection and found that the matrix
> elements have the units of Ry/au^2 (energy/length^2) and when I take the
> SQRT of matrix elements I should also take a SQRT of the energy in cm^-1
> (Ry--> cm^-1). So now the frequencies should be *SQRT[eigenvalue (in Ry)
> of Matrix x 109737]*. This gives me the rightmost figure. Now it looks
> like that the the frequencies are *almost* matching but not exactly
> identical. I doubt that length^2 (au = 0.529x10^-10 m^-1) and mass (AMU =
> 9.31 x 10^-31 kg) could remedy this mismatch here.
>
> I would appreciate any comment.
>
> Thank you,
> Shubham
>
> ------------------------------
> *From: *"Giovanni Cantele" <giovanni.cantele at spin.cnr.it>
> *To: *"Quantum ESPRESSO users Forum" <users at lists.quantum-espresso.org>
> *Sent: *Wednesday, April 16, 2025 2:29:37 PM
> *Subject: *Re: [QE-users] unit mismatch between PH generated frequencies
> and manually generated eigenvalues
>
> Dear Shubham,
> I will add a little contribution to the discussion. Prior to it, I would
> strongly recommend, as it has been correctly pointed out, that before doing
> ANY calculation
> you become aware (using tutorials, textbooks and so on) about exactly what
> you are calculating, what are the units, and so on. In many cases (but I do
> not know if
> this is your case!), skipping a necessary initial (self!) training
> produces much more waste of time than spending time in understanding how
> things work.
>
> After inspection of the plots you sent, it seems that the problem you have
> is other than a magnitude mismatch. Indeed, a magnitude mismatch is just
> a scaling factor, all the bands get multiplied by 10 or 100 or any odd
> factor that might be obtained by combinations of Ry = 13.6 eV, bohr radius
> and any
> other relevant scale unit might apply in this case.
>
> What I simply tried is to superimpose the two phonon band structures and
> to stretch one to try to make it overlap with the other. No success in
> doing that.
> Effectively, you could for example look at the 6th band. The one on the
> left is almost flat, the one on the right is not. Moreover, in the left
> plot its maximum is
> maybe the small dip at the x-axis center, whereas on the right there are
> two pronounced maxima around the x-axis extrema. As further proof, the 7-th
> band
> shares a frequency range with the 6th one on the right, whereas in the
> left the two are separated by a small gap.
> So, I would conclude that the two band structures do not differ by a
> scaling factor and are, for some reason, definitely different! This is also
> confirmed by the s
> econd image you sent, with three plots. In that case, the right plot was
> obtained after multiplying the middle one by a factor and indeed the two
> band structures
> look identical, apart from the y-axis scale.
>
> How could it happen? Some possible answers:
> i) you diagonalized a wrong matrix (for example: did you properly include
> the mass factors?)
> ii) you are not plotting the same quantity. If I'm not wrong, and there is
> not just a scaling factor between left and right, could it be that for
> example
> when you make the diagonalization you get the squares of the frequencies,
> which would explain the NOT UNIFORM stretching of one band structure with
> respect to
> the other? This or similar things can explain your issue if you
> diagonalized the matrix by hand, not of course if the diagonalization was
> produced
> by a quantum-espresso executable, where units are correctly fixed.
>
> So, the suggestion is to start from scratch, trying to understand, at each
> step, what you're doing, which quantity you obtained and with which units.
> I'm pretty sure that
> it will not be that difficult for you to figure out what's happening!
>
> Giovanni
> --
>
> Giovanni Cantele, PhD
> CNR-SPIN
> c/o Dipartimento di Fisica
> Universita' di Napoli "Federico II"
> Complesso Universitario M. S. Angelo - Ed. 6
> Via Cintia, I-80126, Napoli, Italy
> e-mail: giovanni.cantele at spin.cnr.it <giovanni.cantele at spin.cnr.it>
> Phone: +39 081 676910
> Skype contact: giocan74
>
> ResearcherID: http://www.researcherid.com/rid/A-1951-2009
> Web page: https://sites.google.com/view/giovanni-cantele/home
>
>
> Il giorno mar 8 apr 2025 alle ore 17:03 Shubham Patel <
> spatelphy at iitkgp.ac.in> ha scritto:
>
>> Dear developers and users,
>>
>> I am trying to calculate the frequencies (freqs) using Quantum Espresso
>> PHonon calculations as well as using dynamical matrices generated using
>> matdyn.x. I find that there is a unit mismatch in the freqs which gives
>> rise to a magnitude difference. In the first case, I calculate phonon band
>> structure using matdyn.x --> plotband.x. While in the second case I
>> generate dynamical matrices using matdyn.x and then diagonalize the
>> matrices along the kpath and generated exactly same band dispersion except
>> the magnitude on the y-axis (frequency range). Could anyone please tell
>> what is this factor which brings the magnitude mismatch? I am also
>> attaching a figure to compare.
>>
>> Thank you very much for any help.
>>
>> Sincerely,
>>
>> Shubham_______________________________________________________________________________
>> The Quantum ESPRESSO Foundation stands in solidarity with all civilians
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>
>
> _______________________________________________________________________________
> 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 users at lists.quantum-espresso.org
> 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 users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
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