# HOMO / LUMO energies in a qualitative view

I have a question regarding the HOMO and LUMO energies depending on various effects like substituents and electronegativity. It seems to be a somewhat known topic but I cannot really find a clear answer anywhere that would just summarize those effects. So I started to wrap my head around various qualitative effects that you can attribute to either a large or a small HOMO-LUMO gap.

The easiest approach would therefore be considering Koopman's theorem, where the negative HOMO energy approximates the ionization potential and the negative LUMO energy approximates the electron affinity. If we then move to Mulliken's definition of electronegativity we can see that the sum of both IP and EA (divided by two) serve as a good approximation to the electronegativity. Which means that upon many other effects the electronegativity seems to be a key feature to describe the HOMO and LUMO energy. And this is also what I remember from lectures.

In my memory a more electronegative element will lower the energy of the LUMO. That is why in for example photocatalysis many conjugated heterocyclic (N-substituted) ligands are used. The lower π*-orbitals give rise to MLCT transitions. On the other hand the HOMO energy should be increased as well.

If we move to the Klopman-Salem equation we can derive that according to HSAB concept a large HOMO-LUMO gap will be a pair of a hard acid and a hard base and a small HOMO-LUMO gap will be a soft-soft pair. One simplification to this is the case of a Lewis-acid and a Lewis-base reacting, or an electrophile and a nucleophile. Here the HOMO of the nucleophile will interact with the LUMO of the electrophile. This means that a high nucleophilicity requires a high HOMO energy. Unfortunately there is no good description besides lone-pairs on real nucleophilic strenght.

So I thought I could perhaps find other examples and therefore moved to carbenes and their analogues. We destinguish singulett and triplett carbenes. A singulett carbene has a larger HOMO-LUMO gap. Moving to heavier elements we get more singulett character. But this can't be used here since this effect is due to more complicated effects. As Si-Si-bonds and double bonds tend to be be much more reactive and are easily photo-activated as well the HOMO-LUMO gap should be smaller than in corresponding C-C-bonds. But what about substituents on the carbene? Here we find that electronegative ligands will stabilize the a1-orbital in the carbene and in for example aminocarbenes, the π-donor-function of the $$\ce{NH2}$$-group increases the energy of the b1-orbital.

So from these examples I would summarize that in general the inductive effect of an electronegative substituent will stabilize and therefore descrease the energy of the HOMO. And a π-donor will increase the energy of the LUMO by destabilizing it. Comparing this to ligand field theory I would conclude that having an alkyl group will destabilize and therefore increse the HOMO and a π-acceptor will descrease the energy of the LUMO.

Are my findings and ideas somewhat applicable and true? And are there other very simple effects that I can take into consideration if I want to describe the relative positions of the HOMO and LUMO?