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>
> We have devised a set of mathematical rules that seems to fit the
> observations of chemical properties, with a basis in numerology, if
> that's what you want to call quantum numbers,
That's the wording most people would choose. Quantum
mechanics is science. Numerology is not; it has to
do with the occult, essentially the opposite of science.
> Applying these rules requires a bit of jiggery- pokery too, like
> starting to fill outer shells before inner ones are full, without any
> numerological (mathematical) basis for doing so,
It's not jiggery-pokery. It's physics. It's potential
energy and kinetic energy and the equation of motion.
The mathematical and physical basis is well established.
> Nobody has determined the physics, ab initio at least, why this(non-sequential filling of shells by the aufbau scheme) should occur,
The current state of the art is to calculate _ab initio_
not just atoms but molecules. I've seen papers on things
as big and tricky as benzene. Also molecules with
transition elements in them.
I get 20,000 hits from
http://www.google.com/search?q=ab-initio+quantum-chemistry
> .... the approximation
> based on the H-atom we are currently stuck with,
We aren't stuck with that. Haven't been for decades.
http://www.nobel.se/chemistry/laureates/1998/