some questions about MO

[John]

Dear everyone,

      when calculating the spin transport properties of one magnetic  molecule, the MPSH energy spectrum is list
# -----------------------------------------------------------------------------
# Energy Spectrum
# -----------------------------------------------------------------------------
# Spin-Up Energy (eV)  Spin-Down Energy (eV)
               -18.49                 -18.51
               -17.76                 -17.76
               -17.31                 -17.31
-----------------------------------------
                -1.94                  -0.79
                -1.83                  -0.50
                -1.36                  -0.40
                -1.32                   0.02
                -0.01                  1.24
                 0.02                  1.49
                 1.75                   1.92
------------------------------------------
I have some questions that:

(1) Is the Fermi level same for spin up state and spin down state(E_fermi=0?)
(2) Now, how can we decide the quantum numebers to calculate the MPSH HOMO and LUMO, here, for spin up state, the energy -0.01 and 0.02 correspond to HOMO and LUMO, respectively, and for spin down state -0.40 and 0.02 correspond to HOMO and LUMO? Is it alway right?
(3)Due to the smearing effect, whether the Fermi level could be brodened, and results -0.01 and 0.02 could be treated as 0. if so, sometimes it could be difficult to accurately judge the quantum number of HOMO and LUMO, even due to annexation of energy level.   Now, whether it is effective to judge it according to the different spin stats electron occupation.
(4) Usually, whether are there any obvious differences between the spatial distribution of HOMO or LUMO of one isolated molecule   and that of its MPSH MOs when coulped into two electrodes?

thank you!

[zh]

(1) Is the Fermi level same for spin up state and spin down state(E_fermi=0?)

Of course, yes.

(2) Now, how can we decide the quantum numebers to calculate the MPSH HOMO and LUMO, here, for spin up state, the energy -0.01 and 0.02 correspond to HOMO and LUMO, respectively, and for spin down state -0.40 and 0.02 correspond to HOMO and LUMO? Is it alway right?

Yes, you are right. For the eigenvalues of MPSH, their values are given with respect to the Fermi level (which is set as zero) of two-probe system.

(3)Due to the smearing effect, whether the Fermi level could be brodened, and results -0.01 and 0.02 could be treated as 0. if so, sometimes it could be difficult to accurately judge the quantum number of HOMO and LUMO, even due to annexation of energy level.   Now, whether it is effective to judge it according to the different spin stats electron occupation.

For the eigenvalue of MPSH, the smearing technique is not applied.

(4) Usually, whether are there any obvious differences between the spatial distribution of HOMO or LUMO of one isolated molecule   and that of its MPSH MOs when coulped into two electrodes?

Yes, some obvious difference may exist due to the interaction between electrode and molecule (or the charge transfer between electrode and molecule).