[QE-users] Density of states and Volume

[Salman Zarrini]

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> 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> 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> 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
>>
>> On 13 Nov 2021, at 20:29, Salman Zarrini <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> 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>
>>> 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
>>> > _______________________________________________
>>> > Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
>>> > users mailing list users at lists.quantum-espresso.org
>>> > https://lists.quantum-espresso.org/mailman/listinfo/users
>>>
>>> _______________________________________________
>>> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
>>> users mailing list users at lists.quantum-espresso.org
>>> https://lists.quantum-espresso.org/mailman/listinfo/users
>>>
>> _______________________________________________
>> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
>> users mailing list users at lists.quantum-espresso.org
>> https://lists.quantum-espresso.org/mailman/listinfo/users
>>
>> _______________________________________________
>> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
>> users mailing list users at lists.quantum-espresso.org
>> https://lists.quantum-espresso.org/mailman/listinfo/users
>
> _______________________________________________
> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
> users mailing list users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
>
>
> _______________________________________________
> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
> users mailing list users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20211114/6f0d519b/attachment.html>