I think i found the route to calculating the chemistry of the fourth dimension. There are a number of software packages that calculate the various things about molecules using quantum mechanics, based on the Schrödinger equation and more general equations. Maybe if we can find the source code to one of these programs, we can adjust it for the fourth dimension and try some calculations. According to the Wikipedia, here are some software packages that do computational chemistry:
GAUSSIAN, GAMESS, Q-Chem, ACES, MOLPRO, DALTON, Spartan, and PSI
if you want to know more about quantum mechanics, check out the Wikipedia entry.