[QE-users] Density of states and Volume

[Salman Zarrini]

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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