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

Mon Apr 30 19:49:29 CEST 2012

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?

Thank you so very much for your time!

Andrew DeYoung
Carnegie Mellon University