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

[Shubham Patel]

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 
[ mailto:giovanni.cantele at spin.cnr.it | e-mail: giovanni.cantele at spin.cnr.it ] 
Phone: +39 081 676910 
Skype contact: giocan74 

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


Il giorno mar 8 apr 2025 alle ore 17:03 Shubham Patel < [ mailto:spatelphy at iitkgp.ac.in | 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_______________________________________________________________________________ 
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