# Calculate diffusion coefficients

The diffusion coefficient D of a material can be measured in at least 2
ways using various options in LAMMPS. See the examples/DIFFUSE directory
for scripts that implement the 2 methods discussed here for a simple
Lennard-Jones fluid model.

The first method is to measure the mean-squared displacement (MSD) of
the system, via the [compute msd](compute_msd) command. The slope of the
MSD versus time is proportional to the diffusion coefficient. The
instantaneous MSD values can be accumulated in a vector via the [fix
vector](fix_vector) command, and a line fit to the vector to compute its
slope via the [variable slope](variable) function, and thus extract D.

The second method is to measure the velocity auto-correlation function
(VACF) of the system, via the [compute vacf](compute_vacf) command. The
time-integral of the VACF is proportional to the diffusion coefficient.
The instantaneous VACF values can be accumulated in a vector via the
[fix vector](fix_vector) command, and time integrated via the [variable
trap](variable) function, and thus extract D.