We extend the matrix expansion method to study the long time dynamics for all-atom models of alkane chain internal dynamics. In order to focus on the influence of the poorly understood memory (often also termed "internal friction") contributions, the theory is compared with Brownian dynamics simulations in which the molecular solvent is replaced by a white noise source of random and frictional forces on the individual carbon and hydrogen atoms of the alkane molecule. The interaction potentials contain torsional potentials and nonbonded interactions, and the same potentials are used for both the theory and the simulations. Hence, the comparisons between theory and simulations involve no adjustable parameters. The first order theory is equivalent to a generalized Rouse model in which harmonic forces exist, in principle, between every pair of atoms in the alkane chain, with the force constants evaluated in terms of static equilibrium correlations. The first order theory provides a decent representation of the long time (t greater than or equal to 100 ps) portions of the C-C motion time correlation functions (dipole and orientational), but the theory is poor for the C-H correlation functions because they have correlation times much shorter than 100 ps. Various higher order mode coupling basis sets are investigated to include the long time influences of the memory terms, and the computations consider the role of the more rapid hydrogen motions in exerting a frictional drag on the slower C-C bond motions. The truncated second order basis provides a rapidly convergent and accurate representation of the long time dynamics.