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I've been studying MD and more specifically about Car-Parrinello Molecular Dynamics and I'm not entirely sure if I understood the meaning behind the minimization.

This is the way I understand it: The wave function optimization/minimization of the system at the beginning of a CPMD simulation is to make sure there won't be energy transfer between the nuclei and the electrons. Since the electrons will be on the Born-Oppenheimer surface after the minimization, they will be considered "cold" and then in a different temperature from the ions. And then the dynamics might proceed adiabatically, and a result being that the wavefunction doesn't need to be optimized after each time step in the CP method.

Is this way of thinking correct or am I missing something? I've also thought about it being related to the Kohn-Sham energy functional.

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I explained Car-Parrinello MD here, and a key point is that it approximates BOMD (Born-Oppenheimer Molecular Dynamics) where the electronic state is minimized (i.e. the ground electronic state is found and used) at each step. The reason for the minimization in CPMD at the first step, is the same as the reason in the earlier BOMD method that it approximates. Also, the reason why the electronic state's wavefunction doesn't need to be re-minimized at each step in CPMD, is explained in my answer linked at the beginning of this paragraph: a fictitious force is used to keep the electronic state close to the ground state.

As for why BOMD and CPMD aim to involve the ground electronic state instead of an excited one: First of all, why would you not want to minimize the electronic state when doing molecular dynamics? I can only think of two reasons:

  • (1) it's computationally expensive
  • (2) you might be trying to simulate some system which is not in the ground state for some reason.

If you are not in category (2), then I see no reason not to minimize the electronic state if you have a computer that's capable of doing it accurately enough for it to be worth it, and since DFT is typically used to approximate the minimization of the ground state, quite accurate results can be obtained at quite a low cost. Is the "quite good" accuracy of DFT electronic state minimization worth the "quite low" cost? Well CPMD is an extremely popular method, with the original paper currently having 12704 citations on Google Scholar, so I would hope so!

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Yes your understanding is correct.

It helps to think about BOMD as classical dynamics. The electrons are the springs that hold the masses together and the nuclei are the masses.The two key terms are the internal energy (U) and the kinetic energy of the masses (K).

We seek to calculate the positions of the system as a function of time, which we can do numerically by integrating the equation of motion.

Force-field molecular dynamics is exactly this, where the potential energy is just written as harmonic oscillators with the parameters obtained by fitting. We can also calculate the internal energy from first principles using quantum mechanics/the Schrodinger equation.

In either case, the nuclei are following the potential formed by the electrons. As Nike explained above, CPMD just seeks to get the internal energy faster by taking advantage of numerical tricks.

It is critical that we can solve the motion of the nuclei on a potential that is parametrically dependent on the positions of the nuclei $\psi(r;R)$. This is known as the Born-Oppenheimer approximation.

If the motion of electrons is coupled to the motion of the nuclei this is known as non-adiabatic effects and causes a breakdown of the BOMD. This can happen at places known as conical intersections where two or more potential energy surfaces intersect and the electronic state changes rapidly as a function of nuclear position.

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  • $\begingroup$ +1. I've put in emphasis a part which I really liked, since I think it may directly address one of the thoughts that OP put in their question, which is about energy transfer between electrons and nuclei. Feel free to revert if you feel it would be appropriate! $\endgroup$ Aug 23 at 21:05

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