# What can we learn from the energies of molecular orbitals?

Molecular orbital theory is successful in calculating the structure of molecules (minimizing the total energy with respect to atomic positions). The solutions of an MO calculation are useful in deriving molecular properties such as dipole moment or vibration frequencies. These do not rely on energies of electrons in distinct orbitals, i.e. even though the theory is based on combining atomic orbitals to molecular orbitals, the somewhat arbitrary separation into orbitals is not used in these calculations.

On the other hand, many conceptual explanations of chemical properties and reactivity are based on orbital energies, such as HOMO-LUMO considerations, rationalization of electronic spectra, nucleophilicity etc. This answer suggests that the orbital energies of occupied orbitals are somewhat arbitrary and those of empty orbitals are almost meaningless. In the answer to a different question, there is a claim that you can apply orbital energies in just one way, and there is no guarantee how good the answer will be:

Basically the only interesting quantity that you can get from an orbital energy is the first ionization energy based on Koopmans' theorem, which also is just approximately true.

So, what can you do with the orbital energies (either the numeric values or perhaps the ranking by energy)?

• There is nothing arbitrary about the orbital energies. It is reference point that is arbitrary, but that's not a big deal. Mar 4 '20 at 11:27

But we can extend that idea a little bit: Looking at differences in orbital energies, we can estimate the distribution of the electrons and predict a high-spin or low-spin situation of unpaired electrons (e.g. in transition metal compounds). Or the stability of radicals. Or the stability of bonds, e.g. in $$\ce{C=C}$$ bonds, the $$\sigma$$ bond is more stable than the $$\pi$$ bonds. We can even explain the more stable bonding $$\ce{N2}$$ compared to $$\ce{O2}$$, although we are comparing two systems with different nuclear charges and number of electrons here. But these arguments mostly work without looking at the actual numbers for orbital energies. It is mostly just qualitative.