[QE-users] Density of states and Volume

Sun Nov 14 19:21:01 CET 2021

Dear Salman, to give you an exhaustive response regarding the behaviour of your DOS, outputs and/or plots would be necessary. However, the only thing I would say you can take for sure is that the values you get from the code are in eV. 

The differences of the values you observe just by changing the cell size are due to a change of the physics and chemistry of your system with the cell side. You have made a virtual experiment in which you expand the side of the cell in all three direction by as much as 100%. It would have been strange if you had get very similar values.

Just as a check, verify that the three integrated DOS are the same.

Giovanni

> On 14 Nov 2021, at 16:37, Salman Zarrini <salman.zarrini at gmail.com> wrote:
> 
> Thanks all for your responses.
> 
> @Giovanni:
> Actually, as an example I had considered the FCC Ni in three hypothetical systems with primitive cells with celldm(1) of A0 = 3.511 angstrom, A1 = 1.5*A0 and A2 = 2*A0, respectively. So, only the celldm increases from one system to another one. Please note that they are not super-cell.
> And ran Quantum-Espresso to calculate the density of states for each of the three systems using similar convergence criterias. To avoid any complication regarding the spin, I hypothetically just used the spin--nonpolarized mode in my calculations.
> 
> The results for density of states at the Fermi level (N(E_F)) for each system is as follows:
> A0 :> N(E_F) = 5 
> A1 = 1.5*A0 :> N(E_F) = 33.78
> A2 = 2*A0:> N(E_F) = 159
> 
> And then the ratio of N(E_F) / V where V is the volume of primitive cell of each system is as follows:
> A0 :> N(E_F) / V0 = 0.462
> A1 = 1.5A0 :>  N(E_F) / V1 = 0.924
> A2 = 2*A0:> N(E_F) / V2 = 1.836
> 
> So, comparing the density of states at the Fermi level, which indeed is a critical quantity in some concepts, shows that the N(E_F) / V change from one to another around two times from system A0 to system A1 and foure times from system A0 to system A2. Although the general N(E) / V are not as similar as I plotted them. 
> 
> I understand the chemistry point of view as by enlarging the cell dimension, the overlap of d wave functions decreases so consequently the band width decreases and that increases the N(E_F) ultimately. However, I still have the problem in understanding the unit(s) used for density of states.
> 
> Regards,
> Salman Zarrini
> 
> On Sun, Nov 14, 2021 at 6:23 AM Giovanni Cantele <giovanni.cantele at spin.cnr.it <mailto:giovanni.cantele at spin.cnr.it>> wrote:
> Dear Salman,
> 
> if a quantity is extensive, so the larger the volume/mass/size the larger that quantity, it should NOT have Volume^-1 in its units.
> 
> Indeed, the DOS as calculated by Quantum-ESPRESSO is in eV^-1. Let us suppose that you calculate the ground state of a given crystal within its primitive cell and obtain a certain DOS. If you now compute the ground state of the SAME crystal  but with twice the unit cell, the number of electrons doubles and as does the DOS. On the other hand, if you divide both DOSs by the respective unit cell volumes, you’ll get a quantity with Volume^-1 in its units that will be the exactly same for both calculations (provided the convergence of both calculations with respect to the used parameters is the same).
> 
> Giovanni
> 
>> On 13 Nov 2021, at 21:06, Salman Zarrini <salman.zarrini at gmail.com <mailto:salman.zarrini at gmail.com>> wrote:
>> 
>> So, that means Quantum-Espresso gives an extensive density of states, right? if so, then it should have a Volume^-1 in its unit.
>> 
>> Regards,
>> Salman
>> 
>> 
>> On Sat, Nov 13, 2021 at 2:46 PM Stefano Baroni <baroni at sissa.it <mailto:baroni at sissa.it>> wrote:
>> it depends on the volume of the unit cell. once you divide by it, you get an intensive (volume-independent) quantity. sb
>> 
>> ___
>> Stefano Baroni, Trieste -- http://stefano.baroni.me <http://stefano.baroni.me/>
>> 
>>> On 13 Nov 2021, at 20:29, Salman Zarrini <salman.zarrini at gmail.com <mailto:salman.zarrini at gmail.com>> wrote:
>>> 
>>> 
>>> 
>>> 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 <mailto: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 <mailto: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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