# [Pw_forum] Re : Thermal conductivity and Gruneisen parameters

Stefano Baroni baroni at sissa.it
Sun Aug 21 09:23:24 CEST 2011

```On Aug 20, 2011, at 11:45 AM, Bertrand SITAMTZE wrote:

> Thermal conductivity could be obtained through velocity autocorrelation function
> after running molecular dynamics (CP in QE).( See the book of Frenkel and Smith
> on page 90).
>
I do not have Frenkel & Smith's book handy, but I would be surprised if it stated what you say. The calculation of the thermal conductivity through MD requires a proper definition of the energy current which is well known for classical systems (though it involves something more complicated than just velocities), but not yet available, to the best of my knowledge, in DFT. If I am wring, please correct me.
>
>
> As for Gruneisen parameters, one could calculate the specific heat through QHA and the bulk modulus with PW, then use the relationship between them. (See the book of L. Anderson on equations of state, starting from page 6).
>
Here, I beg to differ as well. First, the calculation of the constant-volume specific heat does not involve any Gruneisen parameters (gamma). The constant-pressure specific heat (Cp) certainly does, but in the sense that you need them in the first place in order to calculate it. Second, It would seem rather innatural to calculate Cp just to estimate some of the parameters used to obtain it! In any case, the expression for Cp in terms of the gammas is an integral from which it would be impossible to obtain back their individual values.
>

All in all, before asking what QE (or any other code, for that matter) can or cannot do, one should stop for a while and ask oneself what are the most elementary pieces of information needed to compute what we are interested in, and only then ask if any specific code can compute those specific pieces of information. This may take some time, but it is much more instructive than hoping that computer codes can ever be a substitute for our own understanding.

In the specific case of the thermal conductivity, one has the choice to follow the quasi-harmonic or the Kubo-Greenwood routes. Nicola Marzari has already given some hints on the former. Dr. Simatze's comments (and my present reply) apply to the latter. As for Gruneisen parameters, you just have just to inspect their definition (gamma = v/omega d (omega) / d (v)), and realize that any code able to compute vibrational frequencies can with little effort calculate them ... QE can calculate phonon frequencies, I will leave the final conclusion to you ...

Hope this helps
Stefano B

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Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
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