That is, why is the potential energy with the orbitals overlapping less than with the Hydrogen atoms 'independent'. Similarly, why is a noble gas configuration stabler than if an electron were to be removed or added? Is this because pairs of electrons are more stable than single electrons? If so, why?
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The pairs of electrons are more stable if you see the pair as a filled orbital (which can contain maximum of 2 different spin electrons via Pauli's Exclusion Principle).
I think the simplest way of explaining the lower energy of two-nuclei orbital is that the size of the electron's 'playground' grows 2 times, and as the area over which the electron may soar increases, it's kinetic energy decreases.
pafau k.
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