Question about molecular energy spectrum in two-probe

[kaypu]

Dear QuantumWise staff:

i calculate the  molecular energy spectrum in two-probe, the energy zero is Fermilevel, i will upload the energy spectrum in the attcherment.

the orbital of 109 is LUMO, but there are still almost one electron? why?

  Au electrode consists of a (5×5) supercell, T=300K, the K-point 3*3*100, it is enough to correctly describe  Fermilevel.

[Anders Blom]

Because the level is very close to the Fermi level.

As for the parameters, it depends strongly on the system. The only real way to find out is to increase the parameters and try. But you don't need to do that for the full device, you can e.g. test the total energy of the electrode alone.

[kaypu]

thank you professor Anders, it is to say if the LUMO near Fermilevel, the electrons occupying of LUMO is not zero

[Anders Blom]

The concept of HOMO and LUMO depends on there being a clear gap and the Fermi level lying in between levels. There is nothing dictating that such a situation should exist, esp. not in a molecule connected to another system. Therefore one cannot really talk about HOMO and LUMO in the device, only "MPSH levels which derive from the molecular HOMO/LUMO levels".

[kaypu]

 my description is not clearly

Generally speaking, in device system, the electrons occupying of LUMO(MPSH) is nearly 0,

whether the LUMO(MPSH) near Fermilevel, the electrons occupying of LUMO(MPSH) is not zero, like this system?

how do we define the MPSH (HOMO or LUMO) in device system? electrons occupying or positive and negative energy(energy zero is Fermilevel of electrode)?

Regards

[Anders Blom]

how do we define the MPSH (HOMO or LUMO) in device system?

As I wrote above, the concepts HOMO/LUMO do not formally apply to device structures, it's a designation used for isolated molecules.

When you perform an MPSH analysis you obtain a set of "molecule-like" eigenstates and eigenenergies, but first of all they are NOT eigenstates of the transport system, and second their energy positions and occupations are simply what they are. The MPSH states also depend strongly on which atoms you choose to include in the projection. So if a state ends up near the Fermi level Ef, it may have a finite but small population, whether it's above or below Ef. If you are able to correlate the state somehow to the HOMO/LUMO or HOMO-3 or LUMO+3 or any other of the isolated molecule (by symmetry, or energy position, or something else), then fine - it gives useful information. But just because an MPSH eigenstate is above the Fermi level doesn't automatically mean it automatically corresponds to the LUMO level of the system, because as mentioned the concept doesn't apply to a device, and it may be a completely different level if the orbitals are strongly shifted by the hybridization with the electrodes.

[kaypu]

thank you professor Anders