Recently, a new high-coordination lattice model for rotational isomeric state (RIS) chains was introduced, with the motivation of eventually providing a method for the more efficient simulation of dense, multichain systems by using RIS chains. Here that new method has been extended to include short and long range interaction energies, using polyethylene as the example. The short range energies were included via an extended RIS model. The classical statistical weight matrix was expanded in size and coarse-grained. The conditional probabilities derived from this extended RIS model were the basis for the probabilities of the single-bead moves used in Monte Carlo simulations on the 2nnd lattice. The long range energies were introduced by using the lattice representation of the second virial coefficient. The coarse-grained linear chains have the proper mean-square dimensions, and the width of the distribution function for the squared dimensions has the proper value. Coarse-grained polyethylene macrocycles also have the proper mean-square dimensions.