We have carried out molecular dynamics simulations of n-hexane, n-decane, n-pentadecane, and 5-decene in order to find an optimal set of parameters for nonbonded interactions between atoms on different molecules. This optimization is necessary because previous parameter sets optimized by fitting to a single n-alkane do not work well when applied to the simulation of a liquid alkane with a chain length different from the fitted value. For the simulation of fluid phase lipid bilayers in which the hydrocarbon environment is different at different depths in the bilayer interior, it is essential to have a robust parameter set for reliable simulations. We have found such a set, and in this paper we describe the optimization procedure and give the results.