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[Adam Sorini <asorini@gmail.com>]

The two things you wrote down differ by but a factor of T, it seems...

2sinh(x/2) = e^(x/2)-e^(-x/2) = e^(x/2)(1-e^{-x})

log(2sinh(x/2)) = x/2+log(1-e^{-x})

thus

log(2sinh(w/2T)) = w/2T + log(1-exp(-w/T)) 

or am I missing something? I bet the correct formula is the one with the right units.

On Mon, Feb 2, 2009 at 4:49 AM, matthieu verstraete <matthieu.jean.verstraete@gmail.com> wrote:

Hello everyone,

I have recently found in a paper a formula for calculating the Free energy from the phonon frequencies:

int_w g(w) (w/2 + T log (1 - exp(-w/T)))

cited as Cochrane and Cowley "Handbook der Physik" Springer (1967) - it looks like the 2002 version no longer has this formula... According to PRL 100 095901 this should be more precise (higher order) for anharmonic contributions...

The equation is quite different from that implemented in abinit (from PRB 51 8610):

int_w g(w) log ( 2 sinh (w/2T) )

The resulting 0 point energy is the same, but the higher energy (even just w > 30 cm-1 in the integrand) behavior is very different. For 300K I get a factor of 2 difference between the formulae.

Does anyone know which of these (or other equations for F) is better, or more general? Or which relation there exists between the two? Which cases justify using one or the other?

Cheers,

Matthieu

--
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Dr. Matthieu Verstraete

European Theoretical Spectroscopy Facility (ETSF) 
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