Molecular Simulation/Diffusion Coefficients

Einstein Equation
$$ \langle |r(t) - r(0)|^2 \rangle = 6 D t $$



Green-Kubo Theory
The diffusion coefficient of a liquid can be calculated from the velocity autocorrelation function of an MD simulation in the canonical ensemble,
 * $$D= \int^\infty_0 \langle v(t) \cdot v(t+\tau) \rangle d \tau$$

where v(t) is the velocity of the particle at time t. Note that care must be taken in using an MD simulation with a stochastic thermostat, which introduce an external source of friction and random force.