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I recently ran a calculation using the ROB3LYP/LANL2DZ level of theory for a triplet spin molecule. While analyzing the results, the HOMO is doubly degenerate and the LUMO is singly degenerate. I found that the HOMO is -2.740 eV, whereas the LUMO is -3.551 eV. I have no idea how the energy of the HOMO is greater than the LUMO. My guess is that it has to do with the doubly degeneracy/triplet spin state of the molecule, however my experience working with radicals is extremely limited and I am unsure.

Any help making sense of the results is appreciated!

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It would be better to use the word SOMO (Singly Occupied Molecular Orbital), not HOMO. Now assume that you have two SOMOs (or SOMO and SOMO-1 if you prefer). Here are my suggestions:

The first thing to do is to check the wave function stability of ROB3LYP, and see whether a lower-energy ROB3LYP wave function can be obtained. Quantum chemistry packages PySCF, PSI4, and AMESP support that. If you are not using these packages, you can use MOKIT to transfer MOs into those packages. Here is an example about checking ROHF/RODFT wave function stability (written in Chinese, but you can understand English words therein).

Assuming now you've obtained a stable ROB3LYP wave function, and yet the problem is not solved. The molecule you studied may be complicated in electronic-structure and there may exist multiple stable ROB3LYP SCF solutions. Here are some ways to find them: (1) Perform a triplet UB3LYP calculation and make sure you obtain a stable UB3LYP SCF solution, generate UB3LYP NOs (UNO for short), and use UNO as the initial guess of ROB3LYP calculation. (2) Perform spin population analysis using the current ROB3LYP wave function, visualize orbitals near SOMO, see if the electronic configuration is what you expected (e.g. 3d^6 or 3d^5 4s^1 for Fe); if not, permute/alter orbitals and re-perform SCF.

Assuming you've tried all approaches above, and yet the problem is not solved. The possible reason is that the definition of the Fock operator in ROHF/RODFT method is not unique, this makes the SOMO orbital energy differ in various quantum chemistry packages, although with the same total electronic energy. You can use another package (i.e. change the definition of the Fock operator), the problem may disappear. But in such case, it would be better to use the multiconfigurational/multireference methods (CASSCF, NEVPT2, etc).

By the way, using LANL2DZ for all atoms may be outdated and not a good choice. If you insist on using the LANL2 series, LANL2TZ(f) is recommended. def2-TZVP is also good. It is also possible that your problem disappear after using a good/proper basis set.

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