If I want to do a very accurate simulation of a molecular system (e.g. 2 hydrogen atoms), then I'll want to use something like diffusion Monte Carlo to determine the energies of these atoms in different configurations.For example, if I want to create a bonding potential like the harmonic$$E = K(r - r_0)^2$$or Morse potential$$E = D[1-e^{-\alpha(r-r_0)}]^2$$then I assume what I would do is perform DMC to find the energies for various separation distances, and then perform a regression to fit one of those equations.However, I was recently thinking perhaps this isn't as accurate as it could be, because you're using quantum mechanics to find energies, and then using classical physics (Newton's laws of motion) to evolve the system.A more accurate alternative, I assume, would be to evolve a system of two hydrogen atoms using the time-dependent Schrdinger equation and then somehow fit this to some easily computable model.What I'm curious though is how the resulting simulations would differ?  I don't know enough about QM to speculate on what kind of effects the classical system evolution would be missing, or exactly how much (numerically speaking), the two approaches would differ.  Does anyone have any idea?I suppose I could always try both methods and see, but that's going to take quite a bit of work...
What is the difference in accuracy between fully QM atomic simulations vs QM + classical?
quantum mechanics;molecular dynamics