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5

The very question you pose is addressed thoroughly in this open access work: https://www.nature.com/articles/ncomms9287 . The short answer to your question is that the electron density can be mapped using a technique akin to diffraction as described in their work. You mentioned a distinction between the electron density and the orbitals, and the orbital is ...

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The answer comes in several layers, as Martin has alluded to. I'll try and give a short summary: each point goes slightly deeper than the previous one. For an isolated atom, the labelling of the orbitals is arbitrary. That is to say, the $p_x$, $p_y$, and $p_z$ orbitals are all interchangeable. More formally, this reflects the isotropy of the system, which ...

1

J is the total angular momentum. L is the orbital angular momentum and S is the intrinsic total electron spin angular momentum. J = L + S L = $\sqrt{L\left(L+1\right)}\frac{h}{2\pi }$ --> L can be n-1 where n is the Principal quantum number S = $\sqrt{S\left(S+1\right)}\frac{h}{2\pi }$ --> S is an integer or half an odd integer, depending on whether ...

1

In quantum chemistry numerical experimentation is the norm and rigorous mathematical proof the rare exception. As a result, not many rigorous results are know, not even for the good-old Hartree-Fock method. For a review of mathematical results I recommend you have a look at these references: Claude Le Bris, Computational chemistry from the perspective of ...

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