Velocity autocorrelation function and diffusion coefficient in a liquid

A method of calculating the velocity autocorrelation function psi (t) in a monatomic classical liquid is developed, using directly the equation of motion of an atom in a liquid and a procedure which involves decoupling a statistical average. This leads to an equation of the form (d/dt) psi (t)+ integral 0 t d tau K(t- tau ) psi ( tau )=0 and gives a prescription for calculating the 'memory' function K(t) in terms of the interatomic potential, the static pair correlation function and the selfcorrelation function G s . Within the Gaussian approximation, G s depends on psi (t) and the calculation therefore gives an approximately selfconsistent means of determining the latter. The first approximation to the solution, which involves replacing G s by its ideal gas value, leads to the well known linear trajectory approximation for the diffusion coefficient and indicates that the method will give results which supersede this approximation.