[Pw_forum] something about Pt.pw91-n-van.UPF

[Nicola Marzari]

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
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