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What are the applications to chemistry of quantum mechanics? So far I have only seen the Schrodinger equation being solved for a system with a hydrogen nucleus and 1 electron. Is it possible in theory to find the molecular orbital set, and thus the molecular orbital diagram, for all energetically likely isomers of molecules with a set number and type of atoms and set number of electrons (directly from the information of which and how many atoms there are, and how many electrons there are and which atomic orbitals they originally belonged to)? How do we go about writing the equations to do this (solving them need not be demonstrated, nor the approximations you need to do so, although I don't mind if you care to show these things).

Given two molecules and conditions such as temperature and pressure, can you theoretically calculate a) whether they will react and, if so, what product they will form or b) given the product you expect to be formed, the rate constant for the reaction?