Quantum Chemistry seems like a good topic to check out (thank you). I'm concerned with the quantum mechanical model itself in that, with respect to the Heisenberg Uncertainty Principle, the Schrodinger Wave equation is a probabilistic solution. Instead, maybe seek an equation that is deterministic but when constrained can yield position in one sense and energy in another sense.
Have you read "Hacking Matter" by Wil McCarthy? Artificial atoms are very sensitive to the dimensions of the box that contains them and there seems to be no ability to make exact duplicates of each box. This is not a problem for natural atoms but it shows the severe dependence on the atom's potential well to determine the characteristic of the element in question.