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When you draw your molecular orbital diagram, your lowest molecular orbital that has no electrons in it is the LUMO. Your highest molecular orbital that is occupied by electrons is your HOMO. The HOMO and LUMO orbitals are the most important orbitals for reactivity.
To add to what Rachel said, when light reaches a certain frequency and excites the electron (in the HOMO) then it jumps to the LUMO. We use HOMO/LUMO to measure energy differences between them + it helps predict the strength of the bond between the molecules.
Adding onto what the previous students said, I like to remember the order (HOMO to LUMO instead of the other way around) by the fact that H comes before L in the alphabet and therefore comes first here too. Essentially, HOMO stands for Highest Occupied Molecular Orbital, and LUMO stands for Lowest Unoccupied Molecular Orbital. The HOMO to LUMO concept just states that there is an electron transition from the HOMO to the LUMO, which helps determine reactivity properties.
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