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Here is a claim about the modeling of chemical systems. I can’t remember if it’s true or not:

Suppose we have a bunch of molecules and we want to know how they interact. Eg we want to look at the physics of two $\ce{CO_2}$ molecules bumping into each other. We can do this by treating the nuclei as classical particles moving in a potential function determined by the ground state electronic wavefunction for a given configuration of nuclei.

Eg, we want to know how hydrogen molecules bounce off each other. We do this by modeling it as two protons with momentums and positions, and we iterate forward through time using a Hamiltonian where the potential energy operator uses the Hartree-Fock method or something to calculate the electronic potential.

This approximation obviously ignores some important things, for example the momentum of electrons. But that’s small compared to the momentum of the nuclei and plausibly doesn’t matter.

Is this approximation good? Is it commonly used?

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The Born-Oppenheimer approximation is very used in ab initio molecular dynamics (AIMD). When the Born-Oppenheimer approximation is used, it is more specifically called Born-Oppenheimer molecular dynamics (BOMD). Various software packages have implemented this method, here is a list of a few of them:

Other types of AIMD is also used, including Car-Parrinello molecular dymanics (CPMD) and Ehrenfest molecular dynamics.

As always it is important to remember that the Born-Oppenheimer approximation is only a good approximation if the relaxation time of the electronic structure is much faster than that of the movement of the nucleus.

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  • $\begingroup$ > the Born-Oppenheimer approxiation is only a good approxmation if the relaxation time of the electronic structure is much faster than that of the movement of the nucleis. In what kind of situations is this condition true? $\endgroup$ – Buck Shlegeris Aug 27 '17 at 17:39
  • $\begingroup$ An example I can think of on the top of my head is a scattering experiment. If two nuclei are sent towards each other at "high" speed, then the electrons will NOT relax fast compared to the motion of the nuclei, thus the Born-Oppenheimer approximation cannot be used. $\endgroup$ – Erik Kjellgren Aug 28 '17 at 22:36

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