You see MOs for a molecular system. Which is HOMO and which is LUMO orbital, since we have an half filled MO there? What do you think? 104 to 105 ? or ?
As far as I know, does not matter how many electrons are in the orbital, 104 is already occupied by one electron. Thus, 104 is HOMO and 105 is LUMO. I hope this is useful for you...
More specifically, when there is one or more singly-occupied molecular orbital (SOMO), then the label SOMO is preferred instead of HOMO, since HOMO usually implies the highest doubly-occupied molecular orbital - likewise, LUMO is the lowest completely-unoccupied molecular orbital, so not the SOMO, but the next one
You know HOMO is always used for doubled occupied MO, so in your case it is 103, but 104 is not a HOMO, as it is singly occupied so SOMO (singly occupied MO).
LUMO is always unoccupied so the orbital immediate to HOMO or SOMO (in your case) is a LUMO...
LUMO - Lowest Unoccupied Molecular Orbital, since 105 is first with no electron it must be LUMO, thus HOMO as Highest Occupied Molecular Orbital must be 104.
Özgür Alver I think problem is with understanding . HOMO = Highest Occupied. There is no information about half occupied or fully occupied. Occupied is occupied. If you have house that can be filled up with 10 people it doesn't matter if there is only 1 person. Even if there is 1 person house is occupied. The number of people that can be in the house in one moment doesn't matter.
The same is about LUMO =Lowest Unoccupied. If there is nothing in the molecular orbitals it means it is NOT OCCUPIED so in general UNOCCUPIED.
I think if someone reads with understanding and knows meaning of used words that person has NO PROBLEM to know what is HOMO what is LUMO.
Does not matter how many electrons are in the orbital,therefore, 104 is HOMO (Highest Occupied Molecular Orbital ) and 105 is LUMO (Lowest Unoccupied Molecular Orbital) .
According to the definition of HOMO/LUMO by the International Union of Pure and Applied Chemistry (IUPAC), HOMO is the Highest-energy Occupied Molecular Orbital (filled or partly filled) of a molecular entity and LUMO is the Lowest-energy Unoccupied Molecular Orbital (completely or partly vacant) of a molecular entity.
This definition can be found in the book, Compendium of Chemical Terminology, page 600 of 1622. The electronic version of the book can be download in the website: http://goldbook.iupac.org/
Therefore, the 104th MO, a singly occupied molecular orbital (SOMO), is HOMO and LUMO in this example.