It seems there is a general agreement among the practitioners of Molecular Dynamics that 1fs is a fairly reasonable time step, with shorter time steps being required for materials with higher vibrational frequencies. But I haven't seen much information on how one might derive the highest vibrational frequency of a material.

The following question from this site is related: How should one choose the time step in a molecular dynamics integration?

The question has two great answers referencing Nyquist's Theorem and explaining the reasoning behind choosing a timestep frequency below the highest vibrational frequency, but when it comes to establishing if the timestep you've chosen is appropriate it suggests empirically checking various timesteps for energy drift.

Having read around further it seems there are a few other methods for establishing the correct time step, and they are below along with the empirical method:

  1. Empirically check the time-step is correct by performing NVE simulations and checking for energy drift.

  2. Use the first crossing point of the "Velocity Auto-Correlation Function" to establish an appropriate time step. Seen here on the LAMMPS source forge mailing list: https://sourceforge.net/p/lammps/mailman/message/26183023/

  3. Analyse your Interatomic Pair Potentials to establish what the highest frequency is likely to be and use that as a base for you timestep.

Which method would you recommend as the most mathematically/ physically rigorous, and does anyone know or have a link to the specifics of the latter two methods?

  • $\begingroup$ Do you want an answer about which of these is the most rigorous or which methods are most useful? The latter is more subjective. As you pointed out on mattermodeling.stackexchange.com/questions/498/…, the Nyquist Theorem is rigorous for a model problem but it's not that useful of a guideline in practice. IMO, it would be nice if the linked question had more answers of different methods (e.g. those you mention here). Then it could be left up the reader to determine what is the most suitable for them. $\endgroup$ Commented Sep 3, 2021 at 16:24
  • $\begingroup$ @BrandonBocklund In my mind mathematical rigour and usefulness are reasonably closely intertwined, so either would be completely fine! I suppose realistically the other two methods would be more useful as a "Good First Approximation" which could be confirmed by empirical testing. But an explanation of timestep choice beyond "it gives me what I want" is what I really would like! $\endgroup$
    – Connor
    Commented Sep 3, 2021 at 16:29
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    $\begingroup$ @Connor I agree with Brandon that it would be nice if this prior question could collect answers about the pros/cons of more of these methods that you have mentioned. MD is not my area of expertise, but I expect that there is somewhat of hierarchy of choices from least to most rigorous/unapproximated, but that for a give level/rung, its more a choice of what approximations you choose to make and that this would be fairly system dependent. $\endgroup$
    – Tyberius
    Commented Sep 3, 2021 at 16:33
  • $\begingroup$ whoops! I posted my answer in the related question, but I hope my answer over there is useful! $\endgroup$
    – dwhswenson
    Commented Sep 4, 2021 at 9:50
  • $\begingroup$ @dwhswenson Do you mean that your answer to this question was accidentally written below the related question? We can fix that, if that's the case. $\endgroup$ Commented Sep 5, 2021 at 23:45