Hi.
What is the difference between fermi energy from DOS and Bandgap from HOMO-LUMO? Should they both be same? relatively in my work the fermi energy calculated from DOS is double the bandgap calculated from HOMO-LUMO.For example the bandgap and fermi energy in my case is -3.815 and -6.106.
Can anyone share the reason for such behaviour ?
Dear Rahul Suresh ,
The Fermi level is the energy at which the probability of occupying an electronic state is 0.5. At energies ≤ HOMO, the probability is close to 1. At energies ≥ LUMO, the probability is close to 0. Therefore, by definition, the Fermi level falls between the HOMO and LUMO, i.e. HOMO < Fermi level < LUMO.
The Fermi level is an energy whereas the band gap (LUMO - HOMO ≥ 0) is an energy difference. They are different quantities and, therefore, their values should not be the same (except by coincidence).
Please let me know if you have any further questions. I would be happy to help.
Best,
Rob
Thank you Mr Rob.
In my study, whereas the fermi energy from DOS is -6.10624 eV and for the same the HOMO and LUMO are -5.85213 and -2.03706 eV. Is this even possible?
The fermi energy calculated from the plot is attached here
Dear Rahul Suresh ,
No, it is not possible for Fermi level < HOMO. How have you determined the HOMO and LUMO?
You say that the Fermi energy is calculated from the attached plot. First, the Fermi level is not an energy difference but rather an energy that falls between the HOMO and LUMO (so I'm not sure why you've drawn a bar from approximately -0.28 a.u. to -0.05 a.u.). Does the output from your calculation report the Fermi level to be -6.10624 eV (-0.22 a.u.)? Because, if the plot you've attached does indeed show the correct band gap, then the Fermi level falls slightly above the HOMO (FYI: for solid-state materials, which is what I think you are studying though you haven't explicitly mentioned, the HOMO and LUMO form energy bands and therefore are referred to as the valence band and conduction band, respectively). Therefore, it appears to me that a Fermi level of -6.10624 eV (-0.22 a.u.) is sensible.
With that being said, it is difficult to diagnose your problem without the following information:
- What software are you using?
- What kind of calculation are you running (e.g. Hartree-Fock, density functional theory, etc.)?
- What kind of system are you trying to model (e.g. inorganic or organic)?
- What parameters are you using for your calculations?
- Can you provide your calculation input, output, and the DOS raw data?
Best,
Rob
Hi Mr Rob
Thank you. Sorry that I didn't give you the system details.
The fermi energy is calculated as the difference of the two peaks (for which i have given the bar) (calculated to eV). If fermi energy is not the difference between the two peaks, how to calculate fermi energy from the plot?
Software: DFT calculations are done on gaussian 09 and DOS plot using multiwfn using wb97xd/6-31g*. The system is a modified MOFs of porphyrin. I have attached the DOS data here. The output file cannot be attached due to the file size (800MB)
Dear Rahul Suresh ,
Thank you for providing more information.
The Fermi level is not equal to LUMO - HOMO. For an intrinsic (i.e. pure) semiconductor or insulator, which both possess a band gap, the Fermi level = HOMO + 1/2 * (LUMO - HOMO) = HOMO + 1/2 * Eg, where Eg is the band gap. Therefore, the Fermi level sits at the midpoint of energy between the HOMO and LUMO, i.e. at the center of the band gap.
I'd be surprised if Gaussian doesn't report the Fermi level in its output (but I don't use Gaussian). Try grepping for variations of "Fermi". If it is not reported, then you will have to find the occupations. First, find the highest energy occupied state; that is your HOMO or valence band maximum (VBM). Then, find the lowest energy unoccupied state; that is your LUMO or conduction band minimum (CBM). Since MOFs are periodic, you must have specified a k-point grid. If you doing Gamma-point calculations (1 k-point at the origin of the Brillouin zone), then finding the HOMO/VBM and LUMO/CBM should be relatively straightforward. However, if you are using a denser k-point grid, then you will have to search for the HOMO/VBM and LUMO/CBM across all k-points.
For more information on occupations and k-points, I recommend that you read the papers cited here (https://gaussian.com/dft/).
Best,
Rob
Thank you so much for your valuable information.
Will report on any further clarifications.
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