After having studied the LCAO method, it is assumed that the wavefunction of a single electron in a molecule can be written as a linear combination. I have two questions:
- Which electron of the atoms are we describing, only the outermost electron or?
- Molecules are comprised of atoms and these atoms have multiple electrons, how do we model multiple electrons via the LCAO method? Are the electrons assumed to be non-interacting such that each electron can be described by the LCAO method separately?
Thank you in advance for your time and effort.
With kind regards,
Jelle
LCAO applies to any selection of atomic orbitals. In the lectures we considered a single s-orbital, but when people simulate real materials, typically they consider a combination of orbitals that are relevant. For many semiconductors it would be 1 s-orbital and 3 p-orbitals. For graphene, it’s a single p_z-orbital.
Regarding interactions: often people use an effective model, where they consider the Hamiltonian parameters change due to interactions, but the electrons still moving as if they were non-interacting. This approximation is relatively crude, but it still captures a lot of physical phenomena correctly.