An extended rotational isomeric states (RIS) model is used in conjunction with the matrix expansion method for describing the long time dynamics of flexible polymers in solution. The extended RLS model is derived directly from the potential functions that contain hindered torsional potentials, nonbonded interactions, etc. The matrix expansion method for describing the long time dynamics contains equilibrium conformational averages which are evaluated here from the extended RIS model. The theory effectively assumes that the torsional barriers provide the dominant mechanism for the decay of orientational correlations in the polymer chains. The theory is applied to united atom alkane chain dynamics where previous Brownian dynamics simulations with the same potentials are available for an unambiguous, no-parameter test of the theory. The present computation of equilibrium averages with the extended RIS model represents a significant advancement over the prior treatments that evaluate the equilibrium averages using Brownian dynamics simulations. The comparison with the previous approach indicates the degree to which bond angle fluctuations affect the orientational time correlation functions.