Hi All,

Recently I have been performing NEB calculations to search the transition state between C2H2 to C2H3 adsorbed over a surface. Then I preformed a frequency calculation (IBRION = 5, EDIFFG = -0.02, EDIFF = 1e-7, POTIM=0.015) to ensure that the transition state found is indeed a transition state by freezing all atoms in the surface and only allowing the adsorbate atoms to move.

As a result, I noticed there were two imaginary frequencies. I searched through this forum and the web and learned that if my system can translate or rotate, these low modes should be disregarded. I assumed because the molecules were adsorbed over a surface, it could be possible that the molecules can translate across the surface and therefore the second imaginary frequency calculated was due to a translation frequency.

However, my question is, what is considered a low frequency mode? Is there a "frequency cut-off" in which any imaginary frequency higher than a certain energy is considered to be too high to be a translational frequency mode and the NEB calculation needs to be re-done? (i.e. is an imaginary frequency with energy of 11 meV [89.2 cm-1] considered to be a high or low frequency mode?)

Thank you in advance!

## What is considered a low frequency mode?

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### Re: What is considered a low frequency mode?

This is a good question, but one that I feel is a little difficult to answer. The reason that it is difficult is that it depends upon what information you want to extract from the frequencies. It is also a little complicated because it can depend upon if you have frozen atoms in the system.

In the case that you describe, where there are frozen atoms, you should be able to get a single negative mode at the transition state. If you have floppy modes, this can be a challenge, but try including all degrees of freedom in your frequency calculation that you relaxed in your TS calculation. Also make sure that your TS calculation reduced the forces to below, say, 0.01 eV/Ang before calculating the frequencies.

If you are only interested in zero-point energy (as you mentioned the energy of a low mode) then low modes are less relevant if the harmonic approximation holds. The problem is that low modes that are associated with pure or frustrated translation or rotation can have high entropic contributions to a transition state theory rate. So if you want to extract a prefactor, for example, the lowest modes can be the most important. So the best is to get well-converged frequencies. But even then, some post-analysis can be helpful. For example, if I were looking at a saddle for a reaction in gas phase, it would not be crazy to ignore all rotation and translation(ish) modes, assuming their entropic contributions cancel in the prefactor calculation. For a surface reaction, hindered rotation and translation can be very important to the entropy, but maybe should be considered with a model that goes beyond the harmonic approximation. Someone who has done some nice experimental and theoretical work on this is Charlie Campbell.

So I could say that frequencies around 100 cm^-1 are (or could be) basically zero in a typical DFT calculation, but please consider my previous points before just deciding to ignore them.

In the case that you describe, where there are frozen atoms, you should be able to get a single negative mode at the transition state. If you have floppy modes, this can be a challenge, but try including all degrees of freedom in your frequency calculation that you relaxed in your TS calculation. Also make sure that your TS calculation reduced the forces to below, say, 0.01 eV/Ang before calculating the frequencies.

If you are only interested in zero-point energy (as you mentioned the energy of a low mode) then low modes are less relevant if the harmonic approximation holds. The problem is that low modes that are associated with pure or frustrated translation or rotation can have high entropic contributions to a transition state theory rate. So if you want to extract a prefactor, for example, the lowest modes can be the most important. So the best is to get well-converged frequencies. But even then, some post-analysis can be helpful. For example, if I were looking at a saddle for a reaction in gas phase, it would not be crazy to ignore all rotation and translation(ish) modes, assuming their entropic contributions cancel in the prefactor calculation. For a surface reaction, hindered rotation and translation can be very important to the entropy, but maybe should be considered with a model that goes beyond the harmonic approximation. Someone who has done some nice experimental and theoretical work on this is Charlie Campbell.

So I could say that frequencies around 100 cm^-1 are (or could be) basically zero in a typical DFT calculation, but please consider my previous points before just deciding to ignore them.

### Re: What is considered a low frequency mode?

Thank you so much! This was definitely very informational!