Thanks for the answer @Ty. Which code do you use for DFPT, and do you study bulk crystalline systems?

@HitanshuSachania I use ABINIT for DFPT. It is VERY powerful but is honestly a little hard to get the hang of at first, at least for DFPT. I study bulk crystals, mainly correlated electron materials (which is ironically somewhere DFT is expected to not be valid ... ). If you are interested in learning DFPT, I do recommend ABINIT as there are numerous, very good tutorials and all the input variables are explained very well on the site docs.abinit.org/tutorial

@TySterling thanks, will check it. I use VASP (my lab has a license, so...), but I've only used the finite difference method to calculate phonon frequencies so far. I'm on a tight deadline for a calculation and wanted to see if DFPT could be quicker as compared to the frozen phonon method. My knowledge in this area is lacking. From mattermodeling.stackexchange.com/questions/89/…, I got the idea of trying DFPT, but I have a doubt about an input parameter which I'm unable to put into words. (ʘᗩʘ')

@TySterling basically, VASP input description on its wiki says it only calculates phonon frequencies at the $\Gamma$ point. Right now, I'm not sure if just those frequencies are enough to calculate thermal properties like $C_p$, %G%, or $S$.

@HitanshuSachania I understand your problem. The way to get phonon energies and eigenvectors at q /= 0 with VASP is via PHONOPY or some other package. The VASP implementation of DFPT only performs calculations at Gamma (IBRION = 7 of 8). The way to get energies away from the zone center is to use supercells. You can do this with VASP DFPT and the BZ folding will give you the energies at the commensurate q points. Or you use PHONOPY and use finite differences. See the PHONOPY website (phonopy.github.io/phonopy) particularly the examples (one uses DFPT).

@TySterling, that's where I'm confused. I understand that we write the partition function using phonon energies and get thermal properties from there. There are two ways to get these frequencies: the frozen phonon method and DFPT. Let's say I create a supercell using \texttt{phonopy}, but that still requires me to do only one DFPT calculation, whereas with the frozen phonon method, I might end up with very many displaced supercells based on the symmetry of the system under study (SQS for example). Doesn't that make DFPT faster and better than the frozen phonon method?

@HitanshuSachania you are along the right lines! Actually for finite displacement, (e.g.) PHONOPY will find the minimum irreducible displacements and you do 1 ground state calc. per file. If you do PHONOPY+DFPT, you use the undistorted supercell file and VASP determines the irreducible displacements and performs a ground state run and many self consistent DFPT calculations (1 per irreducible displacement) in one go. If this particular way of doing DFPT is 'faster' and 'better' isn't a question I will answer, but there is a reason VASP 6.x will have DFPT at arbitrary q points ...

See for instance phonopy.github.io/phonopy/vasp-dfpt.html#vasp-dfpt-interface

PHONOPY will read the hessian elements (second derivatives of total energy with respect to atomic displacements) from VASP output and then determine the dynamical matrix. Phonopy does the same thing with finite displacements, the difference is really numerical vs. analytical differentiation. After this point, it is the same to use PHONOPY to compute dispersions, calculate thermodynamics properties, etc.

Thank you, Ty, you've been of great help. I didn't realise a calculation with DFPT still makes a self-consistent calculation per irreducible displacement. I believe the difference between the two methods is more of an algorithmic nature than physical - finite difference vs linear response? I use these words often, but I'm not all that acquainted with them. Pardon my lack of understanding, please.

Understood.

@TySterling understood!

If you don't mind, can I get your email id?

No worries, we are here to learn! DFPT is a hard thing to get a grasp on at first. There are many good reviews, but they are very dense and not at all at an introductory level. See for instance journals.aps.org/rmp/abstract/10.1103/RevModPhys.73.515 which explains how DFPT works. Finite displacement is much simpler to start with, it is where I began. I am only recently able to get good results with DFPT using ABINIT

ty.sterling@colorado.edu

@TySterling I figured as much. Finite difference is pretty straightforward (to an extent).

You can try doing DFPT with VASP for just the primitive unit cell and see what you the code does and what results you get. You should get the true phonon energies at Gamma and can compare these to other data/ finite displacement.

Yea, I've started one calculation already to compare it with what I got with frozen phonon.

Will write to you once I get the results.

Keep in mind, when doing FD calculations, the displaced atom induces ~long range forces in some cases. Even for metals, it is necessary to use supercells to avoid the forces induced by moving an atom interacting with the next periodic image of the supercell.

Glad to help, I will wait for your email

Yup, Dr Atsushi Togo suggested I use a sort of heuristic that each side of the cell should be 7 angstrom or more.

Thank you, Ty. I'm greatful. Stay safe.

In ionic crystals (eg. Na Cl) you might need more. A robust way to check is to calculate the forces for the undistorted supercell (should be near 0, but numerically not exactly as we already learned) and then do a calculation for a displaced atom. You can read the forces on the atoms from the OUTCAR and determine how much the force changes on atoms far away from the displaced atom. If the cell is big enough, the force induced on the most distant atoms in the distorted cell should be negligible

Interesting, that's a great way to decide the size.