# [Pw_forum] DOS per eV/volume

pari shok parishok at gmail.com
Fri May 11 16:07:08 CEST 2012

*Dear Guido,
Thank you very much for your reply to my question on calculating DOS
per eV per volume.
As far as I remember, there is a factor of 4(pi)^3 for calculating the
DOS per volume. Even the following post mentions it.
So, I was wondering whether I should divide DOS just to unit cell or
unit cell/ 4(pi)^3. As I wrote, there is a factor of 100.
Yours
P Shok
Usually:*>* DOS(E) dE = number of energy levels in the energy range
from E and E+dE*>**>* and according to this definition*>* \int_E0^E1
DOS(E) dE = total number of states between E0 and E1*>*
(adimensional).*>**>* This is what the dos.x executable included in
Quantum-ESPRESSO computes.*>**>* According to the above
definition:*>**>* DOS(E) = \sum_n \int delta(E - E_n(k_x,k_y,k_z))
dk_x dk_y dk_z *V / (4*>* \pi^3)*>**>* If you carefully read the
chapter 8 of Ashcroft-Mermin, it says:*>* "....one can define a
density of levels per unit volume (or "density of*>* levels" for
short)....."*>* and Eq. (8.57) (provided we're looking to the same
edition!) is exactly*>* the definition you gave*>* (so,
"per-unit-of-volume" definition).*>**>* Giovanni*
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