Coarse-grained (CG) polymer models are used to extend the time and length scales accessible with molecular simulation, however model coarseness can lead to incorrect polymer structure. We create CG polymer models from all-atom molecular simulations of polyethylene (PE) and polytetrafluoroethylene (PTFE) melts by using decimation or averaging to combine backbone carbon atoms in a CG bead. Coarse graining creates correlations along the polymer backbone that are not reproduced by bond and angle interactions. Simulations of CG polymer models that include nonbonded, bond and angle interactions derived from iterative Boltzmann inversion reproduce local structure, but with increasing model coarseness overestimate the persistence length and end-to-end distance. Including the correlations introduced by coarse graining as a dihedral interaction reproduces the bond-orientation correlation and molecule-scale properties in PE and PTFE. We show that the bond-orientation correlation can be used to systematically check which interactions are needed to reproduce molecule properties before creating CG interactions.