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The fourth principle of Molecular Orbitals state that:

Molecular orbitals are best formed when composed of Atomic orbitals of like energies.

I'm not sure about how I should interpret this; which is the correct?

  • It means that the molecular orbitals that I need to consider are the ones formed by the same orbitals on each atom (like a pair of $2p$, two $3s$, etc).

  • It means that I need to evaluate the actual energy on each orbital using: $$E = \frac{-13.6 z^2}{n^2}$$ And then compare the energies of every orbital, to match each orbital on Atom 1 to the closest one on Atom 2? Meaning that I could possibly have a $2s$ pairing with a $3p$, depending on both atoms? (Note that the formula gives different results for each Atomic Orbital depending on the atom's $z$).

I known that every possible orbital combination exists, but I'm asking about the ones that are more relevant and thus need to be considered.

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Both of the statements have merit. When the orbitals are of the same type, the overlap is maximized. When the orbitals are nearly the same energy, the atoms are closer together (and give better overlap) than when the energy difference is larger. You don't really need to calculate the energies of the orbitals, just look at the size of the ions. The larger the ion, the higher the energy level of the bonding electrons.

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