[DFTB-Plus-User] Fermi energy at DFTB+

Bálint Aradi balint.aradi at bccms.uni-bremen.de
Fri Jun 17 08:13:02 CEST 2011

Dear Robyn,

> does anyone know how DFTB+ calculates the value of the Fermi energy given in "detailed.out"? and WHY does DFTB+ deals with the Fermi energy in this way? I found the Fermi energy given at "detailed.out" does not exactly sit in the middle of HOMO and LUMO for the semi-conductor-like systems from molecular sizes to cluster sizes and to the periodic one. Actually the Fermi energy given by DFTB+ is closer to HOMO in my systems.
> One things I cannot understand in the Fermi energy provided by DFTB+ is that the Fermi energy does not converge CONTINUALLY when the size of the systems increases. Although the Fermi energy converges to the periodic one, there is a jump (~ 0.5 eV in my systems) existing during the converging process. Does anyone have any ideas to explain the jump?

 The Fermi energy is simply calculated by setting it to a value, which
ensures that the number of electrons obtained from the
Fermi-Dirac-distribution is equal to the number of electrons in the
systems. At low temperatures (especially at 0K) and big band gaps this
position is not well defined. Assuming a HOMO-LUMO splitting of 3.0 eV
and a few Kelvin temperature, setting the Fermi level at HOMO + 1.5 eV
or HOMO + 2.0 eV would yield exactly the same occupation of the levels
(at least at an accuracy of 1e-10 electron). While at exakt 0K the
situation is clear (middle gap position), as soon as you have any
temperature (and in DFTB you alway have a certain temperature, even if
very small), it should move accourding to the difference of the density
of states around the HOMO and the LUMO, which we do not calculate. So,
in that case the Fermi energy lies somewhere in the gap. When you raise
the temperature to higher values, where there are electrons in the LUMO
and holes in the HOME, the Fermi energy will be correct again.

 Regarding continual change of the Fermi energy: Our Fermi-level search
algorithm does not warranty contiuity between different system sizes in
the ill defined cases (low temperature without electrons in the LUMO).
Again, at higher temperatures it should be completely fine.

 Best regards,


Dr. Bálint Aradi
Bremen Center for Computational Materials Science, University of Bremen

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