Calculation of the diffusion coefficient in a liquid based on the force covariance function

Methods of optimal use of statistical information on the Brownian motion of molecules in a liquid for calculating the diffusion coefficient are considered. Relationships between covariance functions for the displacement of a molecule, its velocity, and the force acting on the molecule are established. It is proposed the method of calculation of the diffusion coefficient estimates should be made using the force covariance function, which enables to reduce the time of simulation of the molecular motion. The proposed method is used for callculating diffusion coefficients for some systems.