It is well known that accuracy of HF is quite bad compared to popular DFT functionals due to neglect of Coulomb correlation, so simply ignore HF result.

Notice that sequence of MOs calculated by different functionals may be different, the HF composition has crucial influence. Orbital flip phenomenon is commonly observed among two DFT functionals if their HF compositions are very different with each other. Typically, DFT functionals with about 20% HF composition (such as B3LYP and B3PW91) are relatively ideal for evaluating properties of MOs. PBE0 (also known as PBE1PBE) has 25% HF composition, its MO analysis result can also be used.

   I am a new user of MultiWFN! I'v noticed that if I use the Becke orbital partitioning scheme for single point calculations at the HF or DFT level of theory with the same basis set, I get different atom contributions. For example, a particular atom's contributions to the HOMO-1 and HOMO at the HF/6-31+g(d) level are ~1% and ~4%, but thee percentages are roughly flipped at the PBE1PBE/6-31+g(d) level. Which level of theory--HF or DFT--is more appropriate for orbital decomposition analyses? Also, should I be my qualitative in my interpretation?

Best regards,
Jacob