Thank you, Giovanni! Best regards, Iurii
Iurii TIMROV Doctorant (PhD student) Laboratoire des Solides Irradies Ecole Polytechnique F-91128 Palaiseau +33 1 69 33 45 08 timrov at theory.polytechnique.fr > > On May 6, 2011, at 2:12 PM, Iurii TIMROV wrote: > >> I would also like to clarify for myself the units of DOS. By definition, >> the DOS reads: >> >> DOS(E) = \sum_n \int delta(E - E_n(k_x,k_y,k_z)) dk_x dk_y dk_z / (4 >> \pi^3), >> >> where \delta is the Dirac delta function, k_x,k_y,k_z are the 3 >> components >> of the wave vector, n is the band index, E is the energy (Ref. Ashcroft >> and Mermin). According to this equation the unit of DOS is >> 1/(Energy*length^3). >> >> Is the following statement correct?: >> "The Density of States of a system is the number of states per interval >> of >> energy -in the unit cell volume-". >> >> Could somebody comment on this? Is there a mistake in the above >> thinking? > > I would say that the correct statement is (of course it is just a matter > of definition!): > > The Density of States per unit volume of a system is the number of states > per interval of > energy -in the unit cell volume- > > > There is just a volume factor difference between the two definitions. > > 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 > > -- > > **** PLEASE NOTICE THE NEW E-MAIL ADDRESS: giovanni.cantele at spin.cnr.it > > Giovanni Cantele, PhD > CNR-SPIN and Dipartimento di Scienze Fisiche > Universita' di Napoli "Federico II" > Complesso Universitario M. S. Angelo - Ed. 6 > Via Cintia, I-80126, Napoli, Italy > Phone: +39 081 676910 - Fax: +39 081 676346 > Skype contact: giocan74 > > ResearcherID: http://www.researcherid.com/rid/A-1951-2009 > Web page: http://people.na.infn.it/~cantele > http://www.nanomat.unina.it > > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum >
