molecular energy spectrum from MPSH calculation

[jjhskang]

Hi!

Do MPSH molecular energied calculated via "calculateProjectedHamiltoninaEnergySpectrum function" correspond to the center of the broadened molecular states? Otherwise, why do they have definte energy even though the scattering region is coupled to the electrode?

[zh]

What is the meaning of "broadened molecular states"? Could give an example? Please see the discussion in this thread:
http://quantumwise.com/forum/index.php?topic=53.0

Once the Hamiltonian for a molecule (or even a segment of the molecule in the center region) is obtained, the eigenvalues (or energy spectrum) can be obtained by diagonalization. The zero of energy for MPSH is referenced to the average of the Fermi levels of the two electrodes.

[jjhskang]

Hai

Thanks for your reply.

It is clearly possible to project the hamiltonian to specific atoms in the representation using localized basis set.

By the way, let me ask two questions in relation to your reply.

In Fig. 10.1 of Page 197 in ATK manual 2008.10, MPSH of H2 molecule is drawn. Red lines are for isolated H2 molecule, while blue lines are for H2 in the two-probe geometry.

(1)   If energy zero correspond to the average Fermi level of the electrode, are the energy level (Ei’) of the H2 molecule in the two probe geometry calculated using MPSH actually correspond to Ei-Ef(electrode)?

(2)   If that is the case, should energy levels (=Ei) of isolated H2 molecule also to be drawn in comparison with those in the two probe geometry be shifted by the Fermi level of the electrode? Namely, should Ei’= Ei-Ef(electrode) be drawn instead of Ei ? 

[zh]

(1)   If energy zero correspond to the average Fermi level of the electrode, are the energy level (Ei’) of the H2 molecule in the two probe geometry calculated using MPSH actually correspond to Ei-Ef(electrode)?

Yes.

(2)   If that is the case, should energy levels (=Ei) of isolated H2 molecule also to be drawn in comparison with those in the two probe geometry be shifted by the Fermi level of the electrode? Namely, should Ei’= Ei-Ef(electrode) be drawn instead of Ei ? 

The absolute value of energy level (i.e., the eigenvalue) is meaningless. You can choose arbitrarily the zero of energy for reference. Of course, you can shift the energy levels of isolated H2 for comparison with the MPSH levels of H2 in a two-probe system. 

[jjhskang]

I mean that how molecular levels Ei of an "isolated molecul" obtained from calculateMolecularEnergySpectrum() canbe compared with the fermi level Ef of the electrode to which it is to be inserted as a scattering region at a later time. Do we simply use Ei - Ef ?

This problem is related to the position or meaning  of energy zero in the molecular calculation.

[Anders Blom]

You are right. However, in addition note that Ef is not zero in a molecular calculation.