A series of liquid-state computer simulations has been performed on the system [(CH4)2]aq at 25 °C as a function of the separation R between the dissolved CH4 molecules. The potential functions for H2O-H2O, CH4-H2O and CH4-CH4 are based on quantum-mechanical calculations of the corresponding intermolecular interactions. The simulation was carried out by the Monte Carlo method augmented with convergence acceleration techniques involving force-bias and the method of preferential sampling. The potential of mean force wss(R) for the interaction of the apolar species in water was determined using umbrella sampling procedures on four windows on the intersolute coordinate. Convergence acceleration was found to be necessary for obtaining satisfactory results. Contact and solvent-separated contributions to the statistical state of the system are discussed in terms of the radial distribution functions, quasi-component distribution functions for coordination number, binding energy and pair interaction energies. Stereographic views of significant structures are presented, and contributions of clathrate structures in the solvent are discussed. The results are discussed in the context of the experimentally observed concentration dependence of hydrophobic effects and related theoretical work on wss(R) by Marcelja, Mitchell, Ninham and Scully, Pratt and Chandler, and Pangali, Rao and Berne. Prospects for quantitative study of the temperature dependence of the hydrophobic interaction and other quantitative extensions of the work are discussed.