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 < [email protected]> 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 <[email protected]> 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 <[email protected]> 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 <[email protected]> >> 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 < >> [email protected]> 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 <[email protected]> >>> 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 [email protected] >>> > https://lists.quantum-espresso.org/mailman/listinfo/users >>> >>> _______________________________________________ >>> Quantum ESPRESSO is supported by MaX (www.max-centre.eu) >>> users mailing list [email protected] >>> https://lists.quantum-espresso.org/mailman/listinfo/users >>> >> _______________________________________________ >> Quantum ESPRESSO is supported by MaX (www.max-centre.eu) >> users mailing list [email protected] >> https://lists.quantum-espresso.org/mailman/listinfo/users >> >> _______________________________________________ >> Quantum ESPRESSO is supported by MaX (www.max-centre.eu) >> users mailing list [email protected] >> https://lists.quantum-espresso.org/mailman/listinfo/users > > _______________________________________________ > Quantum ESPRESSO is supported by MaX (www.max-centre.eu) > users mailing list [email protected] > https://lists.quantum-espresso.org/mailman/listinfo/users > > > _______________________________________________ > Quantum ESPRESSO is supported by MaX (www.max-centre.eu) > users mailing list [email protected] > https://lists.quantum-espresso.org/mailman/listinfo/users
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