It is well known that for a closed shell (all electrons are paired up) molecule, the HOMO-LUMO gap is related to its stability. However, I often see that the same argument is used for open-shell systems (Unrestricted calculation). In such a case, the authors consider energies of both alpha and beta spin orbitals, and the orbital with the highest energy is considered as SOMO. Similarly, the LUMO is decided among both alpha and beta, and the respective gap is considered as the SOMO-LUMO gap. Next, the authors discuss the stability of the system based on that value.

However, to the best of my understanding, for an unrestricted calculation, three SOMO-LUMO gaps can be calculated (1) Gap between alpha spin HOMO and alpha spin LUMO (2) Gap between beta spin HOMO and beta spin LUMO, and (3). The method I mentioned above (considering both alpha and beta).

So, my questions are the following,

a) Is it technically correct to relate stability with the SOMO-LUMO gap calculated by method 3 for an open-shell system? Is it even possible to draw such a relation? How correct are such value and such correlation? If yes, then is there any reason why we are ignoring the other two gaps?

b) Are the gaps obtained by an unrestricted calculation have any practical significance at all (As argued here: https://joaquinbarroso.com/2018/09/27/the-homo-lumo-gap-in-open-shell-calculations-meaningful-or-meaningless/)

Any insightful response will be welcome. Thank you in advance.

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