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Is there any reduction in size of the orbital for a half-filled orbital? Is the probability at any point of finding an electron doubled if there are two electrons instead of one? Is there any difference at all? I'm trying to understand the quantum mechanical model. Thank you in advance!

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While what ssavec says about not taking orbitals away from a structure is true, it's possible to make some generalisations, particularly for lone atoms where the symmetry constraints make the orbital divisions more clear.

When you generate orbitals for an atom, you get the set of s, p, d, f (and so on) orbitals separated out, and you can generally say that for the same principal quantum number (usually denoted n), a doubly-filled orbital will produce more diffuse orbitals than a singly-filled one. This is an obvious consequence of Coulombic repulsion. But, again, all the other orbitals you generate for the altered wave-function will be affected by the change in occupancy and overall charge.

It would be possible to construct a somewhat artificial pair of calculations in which you kept fixed all but one of the occupied orbitals, and then optimised the wavefunction using one electron in one calculation and two in the other, and I would expect you to find that in the calculation with two electrons, the varied orbital would be more diffuse.

Because the two orbitals would be different in spatial form, you wouldn't expect the value at a given point to be a multiple of the other.

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Orbital is "one electron wavefunction", introduced in order to make the treatment of full wavefunction tractable, see http://en.wikipedia.org/wiki/Slater_determinant. You should not take an orbital away from the complete wavefunction and ask, what-if. Because the complete wave function and therefore all the orbitals will adopt to the new conditions.

Most importantly, by adding electron, you change the overall charge. What the change is depends on the exact nature of the process, so it is different if you start with radical-cation and end up with neutral molecule, or start with neutral radical and end up with anion.

The best option is to just play around with any reasonably simple code for electronic structure calculations, be it semi-empiric for simplicity and speed, e.g. OpenMOPAC.

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