[Pw_forum] the unit of DOS

Iurii TIMROV iurii.timrov at polytechnique.edu
Fri May 6 14:12:23 CEST 2011

Dear All,

I would also like to clarify for myself the units of DOS. By definition,

DOS(E) = \sum_n \int delta(E - E_n(k_x,k_y,k_z)) dk_x dk_y dk_z / (4 \pi^3),

where \delta is the Dirac delta function, k_x,k_y,k_z are the 3 components
of the wave vector, n is the band index, E is the energy (Ref. Ashcroft
and Mermin). According to this equation the unit of DOS is
1/(Energy*length^3).

Is the following statement correct?:
"The Density of States of a system is the number of states per interval of
energy -in the unit cell volume-".

Could somebody comment on this? Is there a mistake in the above thinking?

Thanks!

Best,
Iurii

Iurii TIMROV
Doctorant (PhD student)
Ecole Polytechnique
F-91128 Palaiseau
+33 1 69 33 45 08
timrov at theory.polytechnique.fr

> From Doc/INPUT_DOS.txt
>
> :::: Notes
>
>
>    ::: Output
>
>       The total DOS (states/eV plotted vs E in eV) is written to file
> "fildos"
>
>
> So there is no volume in the units, I guess!!!
>
> Giovanni
>
>
>
> On May 6, 2011, at 12:59 PM, Ramesh Kumar wrote:
>
>> Dear Mashiat alaaii,
>>
>>
>> Sorry for previous posting.
>>
>> The unit is 1/Energy.Volume i.e., Energyâˆ’1Volumeâˆ’1
>>
>> On Fri, May 6, 2011 at 4:05 PM, Ramesh Kumar
>> <rameshchitumalla at gmail.com> wrote:
>> Dear Mashiat alaaii,
>>
>> DOS is a number and I feel it doesn't have any unit.
>>
>> On Fri, May 6, 2011 at 3:52 PM, mashiat alaaii <mashiatalaaii at gmail.com>
>> wrote:
>> Hello,
>> what is the unit of DOS?
>> Should I divide the DOS that QE provides to the volume of slab?
>> Thank you
>> Alaaii
>>
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>>
>>
>> -
>>
>> CH. Ramesh Kumar
>> Research Scholar,
>> Computational Chemistry Lab,
>> Indian Institute of Chemical Technology(IICT),
>>
>>
>>
>>
>> --
>> With Best Regards:
>>
>> CH. Ramesh Kumar
>> Senior Research Fellow,
>> Computational Chemistry Lab,
>> Indian Institute of Chemical Technology(IICT),
>>
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>
>
>
> --
>
>
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> CNR-SPIN and Dipartimento di Scienze Fisiche
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Iurii TIMROV
Doctorant (PhD student)