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
