The optimized Rouse-Zimm local dynamics (ORZLD) approximation to the Smoluchowski generalized diffusion approach has been used to predict the local dynamics of cis-l,4-polyisoprene in dilute solution. The equilibrium averages needed in the theory are calculated from a time average along a molecular dynamics trajectory. The first and second order orientation autocorrelation functions for C-H, C-C, and virtual bonds in the repeat unit are calculated from the theory and compared to the same quantities calculated directly from the molecular dynamics trajectory. The correlation functions from the simulation and the theory decay on similar time scales (within a factor of two) and have somewhat similar shapes. The theory predicts a universal relationship between P-1 and P-2 correlation functions which is obeyed to a good approximation by the correlation functions from the simulation. Variations in the local dynamics along the chain contour are qualitatively well described by the theory.