what the absolute HOMO and LUMO energies define?

[hejun8035]

On the Tutorial,

To determine the HOMO and the LUMO levels of the molecule, go into the listing of the molecular energy levels,

14  -9.514529e-02   2.000000e+00
   15   9.514485e-02   6.417571e-44
From the occupations, we see that level 14 is the Highest Occupied Molecular Orbital (HOMO), while level 15 is the Lowest Unoccupied Molecular Orbital (LUMO). The energy of the levels are given relative to the Fermi level and in units of Hartree.

The energy of the Fermi level is listed in the beginning of the file.

# Fermi level = -1.219381e-01                              #
# Number of electrons = 30.000000                          #
From these values, we can evaluate the absolute HOMO and LUMO energies

EHOMO=-5.91eV
ELUMO=-0.73eV

I can't understand what the absolute HOMO and LUMO energies define?

   
 

 

[zh]

Caution: The absolute values of energy levels are meaningless in calculations.  The values of molecular energy levels printed out are referred to the zero of energy, which is ill-defined. For a molecule, the zero of energy may be defined as the electronstatic potential at vacuum region.

[hejun8035]

Thank you !
But I can't understand "From these values, we can evaluate the absolute HOMO and LUMO energies " in the tutorial?  Can you tell me the relationship of absolute HOMO and LUMO energies,Fermi level and the molecular energy levels?  I want to know the algorithm.

[zh]

"From these values, we can evaluate the absolute HOMO and LUMO energies " in the tutorial?

I think that this may be a typo.  HOMO is the highest occupied molecular orbital; LUMO is the lowest unoccupied molecular orbital. I think that you may already know these two terms. So the HOMO and LUMO are just two of molecular energy levels, and they are very special and also very important.  The values of all molecular energy levels are given with respect to the zero of energy (which is a reference point.) The Fermi  level is the highest energy where the electron can be filled. As you know, due to the Pauli principle each energy level can be occupied by two electrons, and the electrons fill the energy level from low to high. For a molecule, sometimes the Fermi level may be thought as the HOMO level. But this may be not true if the Fermi-Dirac distribution is introduced for counting the occupation of electrons. So in the case you observed, the value of Fermi level is not same as the one of HOMO level. 

Admin mod: Corrected confusing spelling mistake

[Anders Blom]

zh's answer is very good.

I just want to add, for completeness, that for molecular systems, as referenced several times on this forum already, the absolute zero energy is the vacuum level meaning the effective potential very far away from the molecule.

Moreover, referring to your question about the "algorithm", as zh so correctly points out, the Fermi level is determined in such a way, that when you use the corresponding Fermi-Dirac occupations for all the molecular levels, the total charge sums up to the total number of electrons in the system. The value of the Fermi level, thus determined is numerically unique for a given set of molecular levels. (Note, however, that we have a slightly different set of such levels in each iteration of the SCF cycle, and thus the Fermi level is one of those quantities that needs to be determined self-consistently.)

From a more physical point of view, the Fermi level can be seen as an energy that lies between the occupied and unoccupied states, and thus can lie anywhere in the HOMO-LUMO gap (this is the same for semiconductors, so it's not special for molecules).