I don't know the state of the art but I think that we can't even predict the static crystal structure of simple substances---e.g. when iron is BCC vs FCC. The f

I don't know the state of the art but I think that we can't even predict the static crystal structure of simple substances---e.g. when iron is BCC vs FCC. The first-principles simulation of dynamic properties of large quantum many body systems is just not feasible. It is possible that this may change dramatically when quantum computers arrive---currently we describe quantum systems by modeling them with discrete, classical computers, and quantum computers might turn out to model the relevant quantum processes directly.