Dear Agostino,
a couple of points - we are dealing with an atom, and for smearings small enough that occupations do not change as a function of temperature - fractional occupations that are there just because of degeneracies. This is a bit different from the ideal case of the free-electron metal - so for an atom as a function of temperature the total energy E and the entropy S do not change (provided the temperature is smaller than the distance to the next set of empty orbitals), E-TS changes only because of T changing, and S is not zero just because of degeneracy. So my previous post re the atom energies should still hold. Regarding the issue of taking (E+F)/2 (a good idea for a metal, not an atom), that was first introduced by Mike Gillan in 1989 (there is a JPcondmatt from then, I believe, and a later one in 1991 with Alessandro de Vita). That suggestion works only for the energy, but not for antyhing else (forces, stresses, etc...). The Methfessel-Paxton or Marzari-Vanderbilt smearings achieve the same goal of taking (E+F)/2 , but do that variationally (i.e. consistently for forces, stresses, etc...). A long discussion is in chap 4 of http://quasiamore.mit.edu/phd/ . nicola Agostino Migliore wrote: > Hello > > Until the smearing is not fully negligible (so that you still have > appreciable fractional occupations) also E=F-(-TS)=(E-TS)-(-TS) (that is > the difference between the two quantities directly provided by the code) > will be a function of the spreading paramater. On the other hand, if you > get the energy with a small enough smearing, a good estimate for the > energy without smearing is given by the equation > > [F(T)+E(T)]/2=E(0)+O(T^n), with n>2, > > which you can find in > O. Grotheer and M. Fa?hnle, PRB (1998), 58, 13459. > > Best, > Agostino Migliore > CMM, Chemistry Department, UPenn > Philadelphia, PA > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum -- --------------------------------------------------------------------- Prof Nicola Marzari Department of Materials Science and Engineering 13-5066 MIT 77 Massachusetts Avenue Cambridge MA 02139-4307 USA tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu
