How do we predict the properties of the materials we make through chemical reactions? I find chemistry fascinating. I've taken a couple of classes and so am familiar with the rudiments of orbital theory, equilibria, acid/base chemistry, and a small bit of organic chemistry. So I can attempt to make predictions about which reactions might happen, but I'd like to know what the properties of the materials made are ahead of time. Is there a way to do this? I know that there are materials composed of the same elements in different structures that have vastly different properties (melting point, color, conductivity, etc.), so what can we actually do to predict these things (i.e. figure out the structure we'll get, and the properties these structures produce)?
Well, you've described one of the goals of computational chemistry. It turns out that this problem is harder than intuition might predict. I recently read an article on the state of quantum computing that happens to summarize the issue for chemists nicely.


  We do not have enough computing power to do this well.


Computational quantum chemical models have become more and more sophisticated to take advantage of increasing computing power, but there still is not enough computing power. Part of the issue is that at the center of what we are trying to do is a multibody problem, which means that any attempts to optimize the electronic state for one electron in a molecule perturbs the state for other electrons. Then we go and adjust those other electrons, which perturbs our first electrons. This is a certified Really Hard ProblemTM. 

At the end of the day, we currently cannot determine exact solutions to multielectron wavefunctions. So approximations get made, and the approximations are getting better. In fact for smallish molecules, we are getting quite close to a variety of known experimental properties. However, for larger molecules, the algorithms still need trained and calibrated on real experimental data. As the molecules get bigger, or the materials being modeled become more complex, our ability to throw quantum chemical calculations at them diminishes. Modeling of proteins mostly uses molecular mechanics and statistical dynamics.