A new Monte Carlo simulation on a coarse-grained tetrahedral lattice was recently developed for rotational isomeric state polyethylene chains. The short-range interaction was included by extending the classical statistical weight matrix. To describe the cohesive nature of realistic polyethylene systems, nonbonded long-range interaction was considered. The second virial coefficient B-2 of two chains under an interparticle potential was suitably written in a discretized form to be analyzed for this new lattice. Utilizing the vanishing B-2 of a Theta chain was previously suggested for the estimation of interaction parameters representing several nearest neighbors. This approach was shown to be sufficient for treatment of dilute solutions, where long-range interactions are relatively infrequent. This study presents an alternative method of parameter estimation which is more appropriate for the bulk state, where long-range interactions are abundant. Interaction parameters were defined from an averaging procedure of the Mayer function in the expression of B-2. In the latter method, the widely used Lennard-Jones potential and associated parameters for the monomeric unit were used to calculated the average Mayer function. The estimated interaction parameters were used to simulate the average neighbor occupancy and the nonbonded energy per monomer. The nonbonded energy showed a minimum when it was plotted as a function of density. The latter method is considered better for the estimation of long-range interaction and yielded the density of minimum energy in a physically reasonable range. The calculated cohesive energy was shown to be close to the range defined by experiment.