Chemistry - What is the purpose of calculating other orbitals than HOMO and LUMO?
A practical answer: in most of molecular quantum chemistry, the cost of obtaining unoccupied ("virtual") orbitals is next to nothing because of the algorithms involved. In short, one diagonalizes some matrix (i.e. finding eigenvalues and eigenfunctions, which are the orbital energies and orbitals) and the virtual orbitals are usually delivered anyway.
A more theoretical answer: While a lot of chemistry involves only the ground state, there is UV/vis spectroscopy and photochemistry. For those fields, virtual orbitals are immensely useful, because they will be used for the description of the electronic transitions that happen in those fields. These transitions are not necessarily between HOMO and LUMO because of symmetry, energy scales involved etc.
Even orbitals that, I assume, could never be occupied.
That's an incorrect way of thinking. Orbitals are not occupied. You need occupation of those orbitals to describe the electronic density of the transformation you are doing.
This is, in my opinion, the biggest flaw of explaining chemistry transformation at the quantum level. It's explained the other way around.
So what is the purpose of calculating all these orbitals?
- you always get as many molecular orbitals as initial atomic orbitals you put in, and the atomic orbitals you put in depends on the size of the basis set you choose.
Isn't all the chemical information needed (bonding, reactions) coming from the HOMO&LUMO?
- Not at all, but it generally is a reasonably good approximation for some reactions, or some transformations. But for some transformations you do need to involve more of them.