# softmatter:Velocity autocorrelation function

### From NSDL Materials Digital Library Wiki

The velocity autocorrrelation function, VACF or C_{vv}, is a autocorelation function relating to the dynamics of a system. The VACF shows how closely the velocity of a particle at a time *t* is correlated with the velocity at a reference time.

It is calculated as follows:

where *N* is the number of particles in the system, and **v**_{i}*(0)* is the starting (reference) time.

The diffusion coefficient can be calculated from the VACF by integrating the area under the curve, and multiplying by the temperature, as detailed by the Green-Kubo relation:

For more information and examples refer to the calculating the diffusion coefficient page.