Applying the time evolution operator as a form of molecular dynamics

Question

I had a kind of weird idea. In molecular dynamics, long timescale simulations (like protein folding) are a really hard problem because you can't "skip steps" of the simulation without huge approximations. Newton's equations of motion essentially have to be integrated over many time steps to obtain an accurate solution. Anything on the order of more than a few milliseconds is essentially impossible to simulate, and with the leveling off of absolute processing speeds in the last decade, it seems this like this problem isn't going away any time soon.

However, the time evolution operator in quantum mechanics is simply:

$$|\psi(t)\rangle = e^{-iHt/\hbar}|\psi(0)\rangle$$

It is not necessary at all to compute any of the $|\psi(t')\rangle$ for $0 < t' < t$ to find $|\psi(t)\rangle$. Supposing that someone (far) in the future figures out a way to efficiently calculate $|\psi(0)\rangle$ for an atomic system, and also figures out some way to store that giant wavefunction, couldn't one simply apply this analytical operator to essentially skip the entire MD process and go straight to the equilibrium configuration?

Answer 1

This is actually done in the electronic structure communities; probably elsewhere too. We call it ab initio molecular dynamics, and it is based exactly on the time dependent Schrodinger equation.

My lab in particular uses it to probe molecular responses to intense laser fields. We first solve for a ground state through typical electronic structure methods (Hartree-Fock, DFT, etc) and then propagate the system in response to some driving field like a laser. Or we ionize the ground state and watch its time evolution. Or we apply a magnetic field...you get the idea. Sometimes you can ignore the coupling of nuclear and electronic motions if the time scale is short enough.

Coupling electronic motion to nuclear motion to get ab initio molecular dynamics is incredibly demanding, so I doubt you'll see if for proteins anytime soon. But perhaps someone on here has tried it or know of cases where it worked.