[QE-users] Density of states and Volume

[Giovanni Cantele]

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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