[DFTB-Plus-User] R: DOS and Transmission units

Bálint Aradi aradi at uni-bremen.de
Wed Feb 17 15:39:28 CET 2021


Dear Théo,

> 
> Thank you for these helpful explications. But now what about the DOS
> computed by dp_dos from the band.out file. Can I integrate it to
> obtain the number of electrons in the conduction band for instance?

Yes, you can. The DOS produced by dp_dos is normed such that its
integral gives the right number of electrons. You can easily check it
yourself: Integrate it out from Emin to Emax for an arbitrary system and
you should obtain the total number of electrons in that system.

Best regards,

Bálint


> 
> Best regards,
> 
> T. Giverne
> 
>> Le 17 févr. 2021 à 12:50, Alessandro Pecchia
>> <alessandro.pecchia at cnr.it> a écrit :
>> 
>> Dear  Théo Giverne,
>> 
>> 'Transmission' is already a dimensionless quantity . It is the
>> transmission of all travelling states at a given energy, E. Mind
>> however that, as defined in most literature of transport, T(E) is
>> the quantity entering the Landauer formula for current, J = 2e/h
>> Integral[ T(E) (f1(E) - f2(E)) dE ].  This means that the T(E)
>> contains the number of states. For a perfectly ideal system it
>> counts the number of bands at a given energy. This also means that
>> T(E) is size-dependent. It depends on cross-section of the
>> conductor.
>> 
>> Concerning the density of states computed by TunnelingAndDos, this
>> is the "trace" of the Retarded Green's function on the central
>> region.  DOS(E) = -1/pi Im{Trace[GR(E)]}
>> 
>> The PDOS is the projection on given atoms/orbitals obtained by
>> sub-tracing the matrix on related atoms/orbitals, such that for
>> instance: PDOS(atom==n, E) = -1/pi Im{ Sum_i GR_ii(E)},   where i
>> are the orbitals of atom n.
>> 
>> HOWEVER, it should be noted that integrating this quantity over E
>> does *not* give back exactly the number of electrons in the central
>> region. In order to sum-up to N, the correct formula should be: 
>> PDOS(atom==n, E) = -1/pi Im{ Sum_i Sum_j GR_ij(E) S_ji}, where S_ij
>> is the overlap matrix.
>> 
>> This was not done because internally GR is restricted to the
>> central region, whereas the sum over j should extend to overlapping
>> regions between central and contacts. In order to get the
>> overlapping parts of GR more computations are needed. Note that
>> such an extra work was done for the density matrix in order to
>> compute correct SCC charges.
>> 
>> It should be said that the DOS computed neglecting the overlap
>> reproduces the main information needed to correlate the
>> transmission to the electronic states and localization.
>> 
>> Regards,
>> 
>> A Pecchia
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> -----Messaggio originale----- Da: DFTB-Plus-User
>> [mailto:dftb-plus-user-bounces at mailman.zfn.uni-bremen.de] Per conto
>> di Théo Giverne Inviato: mercoledì 17 febbraio 2021 10:58 A: User
>> list for DFTB+ related questions Oggetto: Re: [DFTB-Plus-User] DOS
>> and Transmission units
>> 
>> Dear users,
>> 
>> Where can I find in what unit are normalised DOS and Transmission.
>> Without this information the DOS and Transmission are practically
>> useless as they can’t be que quantitatively but only
>> qualitatively. Your answer will be greatly appreciate, thank you,
>> 
>> Sincerely,
>> 
>> Théo Giverne
>> 
>> theo.giverne at etu.u-bordeaux.fr
>> 
>> 
>> 
>>> Le 11 févr. 2021 à 11:05, Théo Giverne
>>> <theo.giverne at etu.u-bordeaux.fr> a écrit : Dear users, I am
>>> currently using the DOS and Transmission results from DFTB+ do
>>> obtain some electronic properties. However I need to know in what
>>> units DFTB+ gives the DOS and the Transmission, I couldn’t find
>>> any information on this matter, does anyone have a clue ? Thank
>>> you, Sincerely, Théo Giverne theo.giverne at etu.u-bordeaux.fr 
>>> _______________________________________________ DFTB-Plus-User
>>> mailing list DFTB-Plus-User at mailman.zfn.uni-bremen.de 
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>>
>>
>>> 
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-- 
Dr. Bálint Aradi
Bremen Center for Computational Materials Science, University of Bremen
http://www.bccms.uni-bremen.de/cms/people/b-aradi/


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