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