The numerical implement about MPSH

[zhangguangping]

As I konw the MPSH is the diagonalization of th Hamiltonian of the subsystem which is from the converged Hamiltonian of the whole tranport system.Now I wonder how to do it in practical?
If I konwn the converged Rho(charge density) for the space grids.Then I abstract the part belong to the subsystem, and the use it to construct the Hamiltonian of the subsystem the diagonalize it.Can this make sense? Or there are better way to do this in atk?
By this, I mean how to do in numerical practice to do MPSH in atk.
Thanks.

[Anders Blom]

See http://quantumwise.com/documents/tutorials/ATKTutorialDevice/XHTML/chap.analysis.html#sect1.mpsh for a detailed description of how to calculate the MPSH spectrum in ATK 10.8.

[Nordland]

Regarding the algorithm you are correct - however there is one catch. Where the full Hamiltonian have interaction with mirror cells,
the MPSH Hamiltonian does not interaction with mirror cells, so it is truly a molecular Hamiltonian that is diagonalized.

[zhangguangping]

See http://quantumwise.com/documents/tutorials/ATKTutorialDevice/XHTML/chap.analysis.html#sect1.mpsh for a detailed description of how to calculate the MPSH spectrum in ATK 10.8.

Thanks, I have read it ,but it instruct how to do MPSH uning ATK in practical.
But I wonder to know the numerical implement in code.
Thanks for your attentions and patient.

[zhangguangping]

Regarding the algorithm you are correct - however there is one catch. Where the full Hamiltonian have interaction with mirror cells,
the MPSH Hamiltonian does not interaction with mirror cells, so it is truly a molecular Hamiltonian that is diagonalized.

Can you give me some hints on how to make the extracted Hamiltonian be a molecular Hamiltonian ?
I only find a paper (please see the attachment) on this but not descibe the implement in details.
Thanks.

[zhangguangping]

Regarding the algorithm you are correct - however there is one catch. Where the full Hamiltonian have interaction with mirror cells,
the MPSH Hamiltonian does not interaction with mirror cells, so it is truly a molecular Hamiltonian that is diagonalized.

Dear Nordland,
Do you mean that, since we know the Hamiltonian of the transport system where the periodic boundary is used. So the Hamiltonian contains the interactions between the unitcell and the  mirror cells. We construct a molecular Hamiltonian by using the Gamma point? And then give all the element outside the subspace we specified to zero or abstract all the element in the subspace and construct the Hamiltonian of the subspace then diagonalized it getting the MPSH. Am I right?

Thanks in advance.