[QE-users] Density of states and Volume

[patrizio.graziosi at cnr.it]

At best of my understanding, the DOS "as is" in units of cell volume,  
that is the unit cell volume is taken as unity, i.e. [ 1 / ( energy *  
UnitCellVolume ) ] where UnitCellVoume=1.

To get it in units of cube meters, you should divide the DOS "as is"  
by the unit cell volume. For example, if the unit cell volume were  
50A^3, then a DOS of 1 in 1/eV becomes 2x10^28 in 1/(eVm^3), makes  
sense?

Patrizio


Salman Zarrini <salman.zarrini at gmail.com> ha scritto:

> 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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>> _______________________________________________
>> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
>> users mailing list users at lists.quantum-espresso.org
>> https://lists.quantum-espresso.org/mailman/listinfo/users
>>
>> _______________________________________________
>> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
>> users mailing list users at lists.quantum-espresso.org
>> https://lists.quantum-espresso.org/mailman/listinfo/users



-- 

Patrizio Graziosi, PhD

Research Scientist

CNR - ISMN
Institute for the Study of Nanostructured Materials