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When running a molecular dynamics simulation on a singular water molecule in vacuum to analyze its normal modes of vibration from the NVE (microcanonical) ensemble, the bending mode frequency is almost never present in comparison with the two stretching modes in the power spectrum.

Why do these normal modes not equilibrate the same way? Clearly the all three vibrational modes are not equilibrated equally.

Edit: Realized solution to missing bending mode. In NVE simulations for singular water molecule we rely on initialization of velocities using Maxwell-Boltzmann at a given temperature that is around 2 times the desired temperature. If this initialization of motion was motion strictly a combination of stretching modes, there is no reason for energy to transfer to the bending mode no matter how long you run. It's like saying, if you have three springs connecting two objects between two walls, and you give the initial condition of one of the two normal modes (say in-phase oscillation), in principle you will never see the other normal mode (out-of-phase oscillation) no matter how long you wait...

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  • $\begingroup$ +1. Welcome to our site! We hope to see much more of you, and hopefully your question gets answered quickly !!! $\endgroup$ – Nike Dattani Sep 2 '20 at 1:52
  • $\begingroup$ I'm wondering, what is your step size? $\endgroup$ – Cody Aldaz Sep 2 '20 at 3:05
  • $\begingroup$ thank you @NikeDattani ! $\endgroup$ – Houndbobsaw Sep 2 '20 at 5:48
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    $\begingroup$ +1 Welcome to the site! May I add two comments: (i) if you figure out the answer to your own question, it is fine (in fact better) if you post the answer as an "answer" rather than as an edit to your question (i.e. you are encouraged to answer your own question), and (ii) I am not sure I actually follow your answer: energy transfer between stretching and bending would only not occur if the modes didn't couple, but in an MD simulation you should have anharmonic coupling terms between them. $\endgroup$ – ProfM Sep 2 '20 at 7:28
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    $\begingroup$ Also, I'm doubtful of the explanation you have given. It is actually a notorious problem of molecular dynamics that energy transfers between all normal modes unless you try extremely hard to keep the energy from doing this. For classical simulations, this is the expected behavior, but for quantum simulations, there is the so-called zero-point energy leakage, which essentially manages to transfer ZPE from high-frequency modes to low-frequency modes in order to equilibrate the system. This is virtually unavoidable, so I sort of don't believe your problem is with velocity initialization. $\endgroup$ – jheindel Sep 2 '20 at 21:52