[QE-users] Density of states and Volume

[Salman Zarrini]

So, that means Quantum-Espresso gives an extensive density of states,
right? if so, then it should have a Volume^-1 in its unit.

Regards,
Salman


On Sat, Nov 13, 2021 at 2:46 PM Stefano Baroni <baroni at sissa.it> wrote:

> it depends on the volume of the unit cell. once you divide by it, you get
> an intensive (volume-independent) quantity. sb
>
> ___
> Stefano Baroni, Trieste -- http://stefano.baroni.me
>
> On 13 Nov 2021, at 20:29, Salman Zarrini <salman.zarrini at gmail.com> wrote:
>
> 
>
> Dear Giovanni,
>
> Thanks for your response.
>
> Then, considering the density of states in an electronic system and what
> Quantum-Espresso calculates as the density of states, should we expect to
> have a volume-independent quantity? if I understood you correctly!
>
> Regards,
> Salman
>
>
> On Sat, Nov 13, 2021 at 1:30 PM Giovanni Cantele <
> giovanni.cantele at spin.cnr.it> wrote:
>
>> Dear Salman,
>>
>> Actually, the two definitions are not mutually exclusive. The first you
>> speak about, is the density of states per unit volume and, as you correctly
>> mention, has units Energy^-1 Volume^-1. However, the definition of density
>> of states a system of electrons and has units Energy^-1:
>>
>> DOS(E) = sum_i Dirac_delta(E-E_i)
>>
>> Integral( dE DOS(E) ) = number of electrons
>>
>> What Quantum-Espresso calculates, is the density of states of the
>> electron system in the unit cell of a given Bravais lattice (due to
>> periodicity, you refer to the primitive cell). If you plot it as is, you
>> should give it units eV^-1. However, you could need the density of states
>> per unit volume. In that case, you can easily obtain the unit cell volume
>> of your system, divide the computed density of states by it, and then the
>> resulting density-of-states-per-unit-volume has units eV^-1 au^-3 (if you
>> express the volume in au^3).
>>
>> In this case, if you integrate over the energy, you obtain number of
>> electrons per unit volume, that is, electron density.
>>
>> Giovanni
>>
>> > On 13 Nov 2021, at 19:14, Salman Zarrini <salman.zarrini at gmail.com>
>> wrote:
>> >
>> > Dearl all,
>> >
>> > As the density of states's definition implies, the electronic density
>> of states has a unit of "Number of electronic states per Energy per Volume"
>> or simply Volume^-1 Energy^-1.  However, the "Volume^-1" is apparently
>> missing in the unit of density of states in literatures as well as here in
>> manual/tutorials of Quantum-Espresso. So that the Energy^-1 is used as the
>> unit for total density of states, atomic site projected density of states
>> and orbital projected density of states.
>> >
>> > I guess it is just a misunderstanding from my side, so, I would be
>> thankful if one could elaborate further on that.
>> >
>> > Regards,
>> > Salman
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> _______________________________________________
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