We perform molecular dynamics simulations of tetraalkylammonium ionic liquids confined in the interlayer of montmorillonite (MMT). We study the structure and energetics of the systems, which consist of cations with two different alkyl chain lengths and several ionic liquid concentrations. The results we obtained for the structure, namely the presence of a strong layering in all systems and the formation of nonpolar domains with interdigitated alkyl chains in some cases, are largely consistent with previous surface force balance experiments performed on similar systems. Finally, we show that swelling of the organo-modified MMT by a large amount of ionic liquid seems energetically favorable in all cases.