The second-order and fourth-order frequency sum rules of the velocity autocorrelation function (VACF) of Rb have been evaluated for six thermodynamic states along the liquid - vapour coexistence curve by using the Ashcroft pseudopotential and corresponding pair distribution function obtained by molecular dynamics (MD) simulation. These sum rules and a model for the self-diffusion coefficient have been used to study the time evolution of the VACF and self-diffusion coefficients. The results obtained have been compared with MD simulation data. It is found that our model provides the first semiquantitative explanation for the density and temperature dependences of the VACF and self-diffusion coefficients of expanded Rb.