It seems that you should take a look on textbooks in quantum chemistry. There are several approaches based on variational techniques and expanding of wave functions in a series using set of basis orbitals (Slater, Gaussian or Gaussian contracted basis). These methods incorporate the many-body effects into the wave function. Also, the software titled Gaussian could be useful.

It seems that you should take a look on textbooks in quantum chemistry. There are several approaches based on variational techniques and expanding of wave functions in a series using set of basis orbitals (Slater, Gaussian or Gaussian contracted basis). These methods incorporate the many-body effects into the wave function. Also, the software titled Gaussian could be useful.

With any available quantum-chemistry software calculate the Hartree-Fock or DFT energy for your molecule, then find the energy of the Highest-Occupied Molecular Orbital (HOMO) and the Lowest-Unoccupied Molecular Orbital (LUMO). Of course, some reading about HF would be useful to understand what you are doing.

Reading of Prof. Koch's books is usefull in any case. But, I think they concern solid-state semiconductor physics and related many-body interactions rather than molecular physics where terms HOMO and LUMO are widely used.

I agree with previous notice. It is very good book to get start in computing of the electronic structure of complicated nanosystems.

A good program for solid state is Crystal (http://www.crystal.unito.it/).

You may calculate molecular orbitals (HOMO,LUMO are frontier MOs) using any quantum chemistry software package (Gaussian, Gamess, NWChem etc). First optimize molecular system and see the energy eigen values correspond to each MOs in output file.

HOMO is highest occupied MO

LUMO is lowest occupied MO (1st virtual MO)