[Wien] specific heat factor

[georg at chem.au.dk]

Seems like I am to blame here:

Checking it I guess the line should read
gamma=N(E_F)*(6.333D-6)**2*pi**2/3.d0*2.6255D3/2.d0
where N(E_F) is in 1/(Ry uc) 
k_b=6.333D-6 Ry/K
and 2.6255D3/2.d0 is the conversion factor between Ry and kJ/mol. The result
will then be in kJ/(mol K**2) and 1 mol refeers to one mol of primitive unit
cells. If spin polarized it is also pr. spin like N(E_F) is.

This is what comes from putting something in and never applying it. Sorry.
Best wishes
  Georg

Quoting Ruben Weht <ruweht at cnea.gov.ar>:

> Dear Peter,
> 
> I think Jan is right and there is an error in the gamma formula.
> 
> I think Gamma is  (1/3).pi^2.kb^2.Na
> 
> where kb is the Bolztmann constant and Na Avogadro's number.
> 
> As Gamma is in general in units of  mJ/k^2.mol
> and density of states in   states/Ry
> you can take one kb in each energy unit.
> 
> In this way   kb = 1.3806503.10^-20  mJ/K 
> and           kb = 6.3336303.10^-6   Ry/K
>               Na = 6.0221.10^23      1/mol
> 
> So   Gamma = 0.17324706  mJ.Ry/K^2/mol
> 
> I hope it helps,
> Best,
> 
>    Ruben
> 
> >> There is the electronic specific heat C_v/T, which is for
> >> non-interacting electrons propotional to the density of states
> >> at Fermi level, printed out in the output of tetra. I find the
> >> convesion factor from N(E_F) in 1/Ry to gamma in mJ/(K^2 mol)
> >> strange:
> >>
> >> gamma=N(E_F)/2.d0*(8.617D-5)
> **2*pi**2)/3.d0*2.6255D6/27.212d0*1000.d0
> >>
> >> does anybody know where the 2.6255D6 comes from? By the way
> >> conversion factor I normally use is
> >> gamma[mJ/K^2/mol]=0.173*N(E_F)[1/Ry] (quite different from wien
> >> value).
> > 
> > Well, Georg seems to have programmed a "secret" here.
> > 
> > To my understanding the conversions require k_B, Avogadros number
> > and E-conversions into J
> > 
> > 2.6255D6:  This factor arises from two (or actually 3) numbers:
> > Avogadros number (6.022 10^23 /mol)
> > the energy conversion from "atomic units" to Joule, which is
> > 
> > 27.212 * 1.60219 10^-19    (first converts hartree into eV, than
> > eV into J)
> > 
> > PS: The (8.617D-5)**2 is k_B in (eV/K)^2   and this leads to this
> > additionl factor of 1/27.212 ....
> > 
> > And somewhere are hidden the factors of 2 from Ry to hartree....
> > 
> > Hope it fits like this. Just check it on a simple case (Cu or
> > so), where the gamma0 is well known.
> > 
> >                                       P.Blaha
> > -------------------------------------------------------------------
> -------
> > Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060
> > Vienna Phone: +43-1-58801-15671             FAX:
> > +43-1-58801-15698
> > Email: blaha at theochem.tuwien.ac.at    WWW:
> > http://info.tuwien.ac.at/theochem/
> > -------------------------------------------------------------------
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-- 
Georg Madsen
Department of Chemistry
Aarhus University
DK-8000 Århus C
Denmark
tlf (+45) 89423885