Question

Is the bandgap is equal to the difference between homo and lumo energies?

Answer 1

Answer:

=> HOMO stands for "Highest Occupied Molecular Orbital", and LUMO stands for "Lowest Unoccupied Molecular Orbital". Don't be confused though, because the LUMO is higher in energy than the HOMO. Hence, it is the most important energy gap to consider.

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Answer 2

$\huge\bold\red{HOLA!!}$

HOMO/LUMO are Molecular Orbitals and the energy of them can in principle be calculated exactly, including all particle interactions. Band theory uses approximations based on the periodicity of the lattice in extended systems, and ignores many contributions to the specific energy of individual particles, such as electrons/holes upon optical excitation, requiring corrections to describe such "excitons".

The terms should not be used interchangeably!