Why is the HOMO always lower in energy than the LUMO?

We say that increasing the energy of the HOMO of molecules increases their reactivity towards electrophiles while decreasing the energy of the LUMO increases their reactivity towards nucleophiles. However, this seems to be built on the implicit assumption that all molecules will always have a HOMO that is lower in energy relative to all LUMOs in every single other molecule. How can that be justified?




That is by definition.


HOMO means highest occupied MO.


MO are calculated and accommodated by energy, from lowest to highest.


According to the multiplicity of the state of your molecule, it must have N paired electrons and M unpaired electrons.
In the ground state, you need to obtain the electronic state of the state with lowest energy. Then you start filling in MO from those with low energy, using the N paired electrons, two at a time, until you fill the N/2 MO with lowest energy.
Then you place your M electrons (one at a time) in the next MO. The *last* orbital that still gets electrons is your HOMO (by definition), the MO above it (in energy) will not get electrons in the ground state, that is the Lowest Unoccupied MO (LUMO).


Only in excited states, electrons form lower MO can be promoted to MO higher in energy, the most likely transition is from HOMO to LUMO, because their are next in energy, and therefore the energy gap is the smallest possible gap. But that does not mean you cannot promote an electron to a MO above the LUMO, or even make it to leave the molecule realm (ionization). Of course, there are methods to calculate all of these cases.


There is no mystery there.


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There is no such assumption whatsoever. Nucleophile and electrophile are names for the compounds that have higher and lower LUMO/HOMO orbitals in this exact relationship between those two compounds. It is just like oxidizers and reductants - there is no absolutes, it's the relative potentials that matters.


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For a reaction to take place, molecules must:


• overcome their electronic repulsion by charge attraction and/or orbital overlap


• have orbitals of appropriate energy to interact—a filled orbital on the nucleophile and an empty orbital on the electrophile


• approach each other such that these orbitals can overlap to form a bonding interaction.


What does this mean for nucleophiles and electrophiles? Well, in general, filled orbitals tend to be low in energy—that is after all why they are filled! Conversely, empty orbitals tend to be high in energy. So the best interaction (the one that gains the new molecule the most energy) is likely to be between the highest in energy of all the filled orbitals—an orbital we can term the ‘highest occupied molecular orbital’ or HOMO for short—and the lowest in energy of all of the unfilled orbitals—the ‘lowest unoccupied molecular orbital’ or LUMO for short. Nucleophiles are either negatively charged or neutral species with a pair of electrons in a high-energy orbital (the HOMO)Few organic compounds have vacant atomic orbitals and in most organic electrophiles the LUMOs are instead low-energy anti-bonding orbitals associated with electronegative atoms. These anti-bonding orbitals can be either π\* orbitals or σ\* orbitals—in other words, molecules which make good electrophiles might have a double or a single bond to an electronegative atom such as O, N, Cl, or Br.
To conclude a basic albeit arbitrary assumption would be that since HOMO is filled, it has the stabilisation energy as opposed to the LUMO.


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