[QE-users] Density of states and Volume

[Giovanni Cantele]

Dear Salman,

if a quantity is extensive, so the larger the volume/mass/size the larger that quantity, it should NOT have Volume^-1 in its units.

Indeed, the DOS as calculated by Quantum-ESPRESSO is in eV^-1. Let us suppose that you calculate the ground state of a given crystal within its primitive cell and obtain a certain DOS. If you now compute the ground state of the SAME crystal  but with twice the unit cell, the number of electrons doubles and as does the DOS. On the other hand, if you divide both DOSs by the respective unit cell volumes, you’ll get a quantity with Volume^-1 in its units that will be the exactly same for both calculations (provided the convergence of both calculations with respect to the used parameters is the same).

Giovanni

> On 13 Nov 2021, at 21:06, Salman Zarrini <salman.zarrini at gmail.com> wrote:
> 
> 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 <mailto: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 <http://stefano.baroni.me/>
> 
>> On 13 Nov 2021, at 20:29, Salman Zarrini <salman.zarrini at gmail.com <mailto: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 <mailto: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 <mailto: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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