Transmission eigenstate and scattering state

[mephisto3142001]

Hello
I have some questions about Transmission eigenstate.
1. Does Transmission eigenstate mean electron scattering state in central region of devices?
2. If the isosurface of Transmission eigenstate at a particular energy point resembles MPSH of quantum number N,
   whether the transmission coefficient at the same energy point is mostly contributed from MPSH of quantum number N?

[Anders Blom]

1. It's rather a superposition of scattering states, in the same way a molecular eigenstate is a superposition of atomic orbitals.
2. Yes, that sounds reasonable.

[mephisto3142001]

Thanks
I calculated TransmissionSpectrum of di-thiol-Benzene device, and the peak near Fermi-level(average Fermi-level) is
at -1.35ev. I also calculated MolecularEnergySpectrum, and the energy level of HOMO is at -1.84eV. I consulted
"Comp. Mat. Sci., 27, 151, 2003" and lots of papers, I found that the energy level of HOMO always corresponds to the
 peak near Fermi-level. The energy level of HOMO is indeed -1.35eV in "Comp. Mat. Sci., 27, 151, 2003". However, my
result showed that the peak is located at region between HOMO and LUMO, which seems unreasonable.
I guessed my problem is due to geometry optimization, but it's just an estimation. I need some advice to solve it.

+------------------------------------------------------------------------------+
| Molecular Energy Spectrum Report                                             |
| ---------------------------------------------------------------------------- |
| Fermi level = -2.451996e+00                                                  |
| Number of electrons = 42.000000                                              |
| Unit = eV                                                                    |
| Eigenenergies given relative to the Fermi Level                              |
+------------------------------------------------------------------------------+
   17  -3.280691e+00   2.000000e+00
   18  -3.141465e+00   2.000000e+00
   19  -2.590715e+00   2.000000e+00
   20  -1.805176e+00   2.000000e+00  HOMO
   21   2.408238e+00   6.989741e-41
   22   2.536180e+00   4.955903e-43

[Anders Blom]

Your results look reasonable, optimization would only change the magnitude of the peaks, at least if you have a reasonable geometry already.

I would advise you to study http://quantumwise.com/documents/tutorials/latest/MolecularDevice carefully. I don't agree that you should have a HOMO peak at the Fermi level, that's not what you see in Fig 2 in the paper you quote - rather that curve is pretty similar to what you have. Just don't forget k-points in A and B!

[mephisto3142001]

According to the statement above, geometry optimization doesn't affect the value of MolecularEnergySpectrum, does it?

State 21(HOMO) is -1.35eV and it corresponds to the transmission peak near Fermi-level in the paper I quote.
However, my calculated HOMO energy level is -1.80eV, which doesn't correspond to the peak near Fermi-level, that's why
I doubted my result. I want to confirm that whether the energy level of HOMO must correspond to the transmission peak near Fermi-level?

[Anders Blom]

No, that's not the statement. I may shift the peaks and their magnitude. But it doesn't usually introduce new peaks or a whole new shape of the transmission spectrum, provided your original geometry is reasonably close to the optimized one.

Differences in the peak position can be affected by the optimization, but also the precise parameters used, like number of k-points (the article uses only Gamma point), exchange-correlation potential, mesh cut-off, etc.

[mephisto3142001]

Thanks! I have clarified some conceptions.
According to your answer, the energy level of HOMO doesn't necessarily correspond to the transmission peak near Fermi-level, does it?
it's what I want to make clear.

[Anders Blom]

I wouldn't presume to make comments on your results without having seen all details. I can only point you to similar studies, and you can compare your results to theirs, and analyze your structure in the same way. I would however agree with the statement by Stokbro et al. in Comp Sci Mater, that the transmission peak around -1.5 eV is not due to a single molecular level, but rather a superposition of several ones.