how to visualize HOMO/LUMO states in a nanotube structure

[zhySarah]

Hi everyone!

I am wondering how to visualize HOMO/LUMO states in a tio2 nanotube structure. I have read the tutorial where the LUMO state of a H2O molecule is visualized. http://quantumwise.com/publications/tutorials/item/108-visualize-the-lumo-state-of-a-water-molecule However, there are still some confusions when applying the same calculation to my structure.
1. Does the configuration have to be changed to a molecule configuration?
2. Does the calculation have to be Applied to the Whole system, or is there a way to calculate only a quadrant (or 1/8) of the tube (considering such a number of atoms in the system)?
3. When it comes to the Quantum number under the Eigenstate Block, it is not so clear where the final number 4 in the tutorial step8 comes from. So my understanding of step8 translates as follows: water has 8 valence Electrons (2*H 1s¹ + O 2s²2p⁴=8), there will be 4 occupied states (which refer to two 1s states from two H atoms and 2s+2p states from O atom?). Therefore set the quantum number to 4 for the LUMO state. (how is this 4 related to the previous 8 valence Electrons and 4 occupied states?)

Please help me out and correct me where I am wrong. Thanks 

[zh]

1& 2. HOMO and LUMO are used to for a molecule or isolated system, not for a periodic system. If your simulated TiO2 nanotube has periodic along the tube axis, you should consider the Bloch states at the valence band maximum and at the conduction band minimum. If your simulated TiO2 nanotube is just a short and isolated nanotube, you may consider the HOMO and LUMO.

3. Each energy level can be occupied by 2 electrons at most. If the molecule contains 8 valence electrons, there will be only 4 occupied states for the valence electrons. The unoccupied states aren't related to the number of valence electrons in the system.

[zhySarah]

1& 2. HOMO and LUMO are used to for a molecule or isolated system, not for a periodic system. If your simulated TiO2 nanotube has periodic along the tube axis, you should consider the Bloch states at the valence band maximum and at the conduction band minimum. If your simulated TiO2 nanotube is just a short and isolated nanotube, you may consider the HOMO and LUMO.

3. Each energy level can be occupied by 2 electrons at most. If the molecule contains 8 valence electrons, there will be only 4 occupied states. The unoccupied states aren't related to the number of valence electrons in the system.

Thanks zh! I am still confused about your answer to Q3. I understand that each energy Level can be occupied by 2 Electrons at most. But this only means that a molecule containing 8 valence Electrons has at least 4 occupied states, not necessarily to be exactly 4. In the case of a H2O molecule, H 1s contains only 1 Electron, O 2s contains 2e, O 2p_x contains 2 and O 2p_y 2p_z each contains 1. Among all these occupied energy Levels (if I am correct about this), which are the 4 occupied states you referred to?

[zh]

"In the case of a H2O molecule, H 1s contains only 1 Electron, O 2s contains 2e, O 2px contains 2 and O 2py 2pz each contains 1. Among all these occupied energy Levels (if I am correct about this), which are the 4 occupied states you referred to?"

H 1s, O 2s,  O 2p --->  atomic orbitals.
the 4 occupied states --> the molecular orbitals (or states) of a H2O molecule in the case you mentioned.

Please read  the following webpage to understand the basic concept of molecular orbital theory.
https://en.wikipedia.org/wiki/Atomic_orbital
https://en.wikipedia.org/wiki/Molecular_orbital
http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/