# Global reactivity parameters from open shell DFT calculations using Koopman's theorem

Koopmans' theorem is a useful approach to calculate the global reactivity parameters from the HOMO-LUMO energies. My question is, does it apply to the open-shell systems where we get two sets of singly occupied (alpha and beta) HOMO-LUMO energies?

I am working on rare earth systems. Rare earth (RE) elements generally show +3 oxidation states which result in open shell configurations for $$\ce{Ce^3+}$$, $$\ce{Eu^3+}$$, $$\ce{Gd^3+}$$ etc. I am performing unrestricted open shell DFT calculations for these systems, as restricted open shell calculations for RE systems require larger computational time and cost. In unrestricted open shell calculations, we get two sets of alpha and beta HOMO and LUMO. My question is, can I apply Koopmans' theorem here to calculate the global reactivity parameters?

Could anyone help with some literature on the reactivity parameters for open shell systems? Thank you!

• Regarding the literature, it might be worth having a look at the section Books about Computational Chemistry and Quantum Chemistry. I'm no specialist in this field, so probably someone else could help you with the precise textbook for you. Sep 14 '19 at 13:00
• Could you walk us through an example you understand, and then give an example of an open-shell system that you are wondering about? That would make it easier to answer. Sep 18 '19 at 1:56
• Hello @KarstenTheis, I am working on rare earth systems. Rare earth (RE) elements generally show +3 oxidation states which result in open shell configurations for Ce3+, Eu3+, Gd3+ etc. I am performing unrestricted open shell DFT calculations for these systems, as restricted open shell calculations for RE systems require larger computational time and cost. In unrestricted open shell calculations, we get two sets of alpha and beta HOMO and LUMO. My question is, can I apply Koopmans' theorem here to calculate the global reactivity parameters? Sep 19 '19 at 6:53