Imaginary phonon frequencies on relaxed structure

[reynaldo.putra]

Hello everyone,

I plan to use phonon frequency calculations to confirm whether a relaxed/optimized structure is truly stable by observing whether there are any imaginary/soft-mode frequencies (f/i); currently I conducted a test run on the cubic unit cell of SrTiO3 as shown here:https://next-gen.materialsproject.org/m ... -O#summary

Here are the steps I have followed for the calculation (and I have attached the input and output files below; POTCAR files used: Sr_sv, Ti_sv, O):
1) I have used a stricter criteria for the unit cell electronic and ionic convergences (EDIFF = 1e-8, EDIFFG = -0.005)
2) Next, I expanded the relaxed unit cell into a 2x2x2 supercell, and conducted the phonon frequency calculation (currently using DFPT)

I suppose I have two questions
1) Is confirming the (non)existence of large soft-mode frequencies indeed an appropriate way to confirm the stability of a structure?
2) I have tried using a stricter criteria for convergence, but the calculation still shows imaginary frequencies. Does the material having an energy above hull of 0.01 eV/atom a valid reason for this?

I understand that to conclusively answer these questions, we require other criteria, but I ask these questions nonetheless as a starting point because I want to ensure that the methodology is valid. I am still not too familiar with these concepts, hence why I might still lack the intuition of what is right or wrong!

Thank you for your attention!

[manuel_engel1]

Hello,

Thanks for reaching out. This is a very interesting question, and you are certainly right: It's quite difficult to give a general and accurate answer.

Often, imaginary phonon frequencies can hint at instabilities of the crystal. However, there are other situations in which imaginary phonon modes can arise. For example

• Softer materials (such as Van-der-Waals crystals) can exhibit highly anharmonic vibrational modes. In this case, it is often not possible to describe all vibrational modes using (harmonic) phonons. Therefore, it is quite possible to obtain imaginary modes because the methodology (DFPT) is unable to resolve all the physically relevant vibrational modes. In fact, I would say that the primary reason why imaginary phonons arise in unstable crystals is because they become more anharmonic close to a transition state.

• The density-functional or exchange-correlation approximation might fail to produce accurate forces. As a consequence, the phonon spectrum might be wrong. A functional that is quite good at getting accurate phonons in solids is the SCAN functional (see METAGGA).

In order to check whether your system is indeed unstable, you would most likely have to run molecular-dynamics simulations at the conditions that you are interested in. This will tell you more about the dynamics of the crystal and does not restrict you to a purely harmonic treatment of the vibrational properties.

All of that being said, you can still use phonon calculations to test the stability of the crystal by looking for imaginary modes. Just keep in mind that this method is not perfect and might (more likely) hint at an underconverged calculation or one that does not simulate the right physics.

I hope that I was able to answer your question.

Kind regards

[reynaldo.putra]

Dear Manuel,

Thank you very much for your input! Right, I have also considered running MD simulations to check on the dynamics of the crystal. I have look into the tutorial on vasp.at, and is it true to assume that we can use the ICONST file to monitor the changes over time in bond length, angles and dihedral/torsional angles throughout the MD simulation?

Secondly, is it possible for you to explain what you mean by "does not restrict you to a purely harmonic treatment of the vibrational properties"? I apologize, but since I do not have a background in materials science, I might lack the means to understand...

Lastly, what other further analyses to be done to conclusively decide whether a material is stable? Perhaps another DFT relaxation for the final AIMD structure?
If there are any literature references on these protocols, that would be very helpful!

Thank you for your time!
Reynaldo

[reynaldo.putra]

Apologies, I'd like to add something else! I have looked at the tutorial for phonon calculations at https://vasp.at/tutorials/latest/phonon/part2/. I did not see the phonon frequency being observed in any of the steps.

This might be a naive and somewhat confusing question, but is there a reason that observing the phonon frequencies is not considered as an important part of the tutorial?

Thank you again for your time!

[manuel_engel1]

Hi Reynaldo,

I have look into the tutorial on vasp.at, and is it true to assume that we can use the ICONST file to monitor the changes over time in bond length, angles and dihedral/torsional angles throughout the MD simulation?

The ICONST file can indeed be used to monitor the specified degrees of freedom. It can also be used to constrain them in certain ways. You can find the relevant information on the ICONST wiki page.

Secondly, is it possible for you to explain what you mean by "does not restrict you to a purely harmonic treatment of the vibrational properties"?

We have a theory page on phonons on the VASP wiki. It is very condensed, but it might already tell you what you want to know. Essentially, the phonon frequencies calculated in VASP correspond to phonons in the harmonic approximation, meaning that only terms up to second order in the atomic displacements are considered. The "anhormonic" (higher-order terms) are neglected.
Regarding literature, I recommend to pick up any undergraduate-level text book on solid state physics and study the section on lattice vibrations. There should be a nice introduction akin to the VASP wiki page but in much greater detail.

Lastly, what other further analyses to be done to conclusively decide whether a material is stable? Perhaps another DFT relaxation for the final AIMD structure?

This is really difficult to answer in general. I think that MD is probably the way to go here as it covers much more edge cases than a static DFT calculation. However, even in MD you can miss out on things and at the end of the day, the simulation is not always a good match for reality.

To answer your most recent question,

is there a reason that observing the phonon frequencies is not considered as an important part of the tutorial?

The phonon spectrum is plotted in this tutorial. However, the plot also considers which phonon frequencies belong to which atomic species (site-projected phonon dispersion), so the lines in the plot have a width and color that corresponds to the Mg and O atoms. This is not always useful, but the tutorial showcases this functionality. If you mean that we don't look at the actual numbers, you can do that of course. But often a phonon-dispersion plot gives you most of the information you are interested in.

I hope that I was able to help you move forward with your project.