# [gmx-users] Ion conductivity: current-current (auto)correlation function

Dommert Florian dommert at icp.uni-stuttgart.de
Mon Apr 30 21:21:12 CEST 2012

On Mon, 2012-04-30 at 13:49 -0400, Andrew DeYoung wrote:
> Hi,
>
> Is it possible to compute the ion conductivity using any of the existing
> Gromacs tools?  Ion conductivity is proportional to the current-current
> (auto)correlation function.
>
> For example, the current J_z(t) along z can be written as the sum of the
> products of charge and z-component of the speed for each atom in the system:
>
> J_z(t) = \sum_{i=1}^N q_i v_{z,i}(t)
>
> Now, by the Green-Kubo formula, ion conductivity is proportional to the
> current-current (auto)correlation function:
>
> \sigma = \frac{1}{3 V k_B T} \int_{0}^{\infty} dt C_{JJ}(t)
>
> where
>
> C_JJ(t) = < J_z(0) \cdot J_z(t) >
>
> and
>
> <...> represents an equilibrium ensemble average.
>
> I know that g_velacc computes velocity autocorrelation functions, but is
> there any way to compute the current and calculate the current-current
> (auto)correlation function?
>
> It seems that g_current calculates the current autocorrelation function, but
> do you know what method it uses?  Also, is it somehow possible to use
> g_current to calculate only the autocorrelation of the current J_z(t) along
> z?
>

Hi,

g_current calculates the ACF for the whole current vector, but it also
gives an output of the current itself. Hence you can choose the z
direction and calculate its ACF with another tool like g_analyze.
However, make sure you save the velocitities frequently enough
(~0.025ps) to obtain a function that is smooth enough for a reasonable
integration.

/Flo

> Thank you so very much for your time!
>
> Andrew DeYoung
> Carnegie Mellon University
>

--
Florian Dommert
Dipl. - Phys.

Institute for Computational Physics
University Stuttgart

Pfaffenwaldring 27
70569 Stuttgart

EMail: dommert at icp.uni-stuttgart.de
Homepage: http://www.icp.uni-stuttgart.de/~icp/Florian_Dommert

Tel.: +49 - (0)711 - 68563613
Fax.: +49 - (0)711 - 68563658
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