# Structure factor

The **structure factor**, , for a monatomic system is defined by:

where is the scattering wave-vector modulus

The structure factor is basically a Fourier transform of the pair distribution function ,

At zero wavenumber, *i.e.* ,

from which one can calculate the isothermal compressibility.

To calculate in molecular simulations one typically uses:

- ,

where is the number of particles and and are the coordinates of particles and respectively.

The dynamic, time dependent structure factor is defined as follows:

- ,

The ratio between the dynamic and the static structure factor, , is known as the collective (or coherent) intermediate scattering function.

## References

- Related reading