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 <[email protected]> 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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