Which means that you rapidly get into trying to develop a large number of approximation schemes. The validity of each scheme is difficult to determine, and ther

Which means that you rapidly get into trying to develop a large number of approximation schemes. The validity of each scheme is difficult to determine, and there's always the possibility that the atom, molecule or crystal that you're studying relies upon some feature of the full 300 dimensional picture that you waved away as not being significant. Not only that, but there's a disconnect between what we know about chemistry, and what we know how to interpret from the results of the simulation. Everyone knows that carbon can form 4 bonds, we've known this long before we were sure about electrons. However, trying to explain what this means in terms of electron probability densities is a research problem in itself.