Multifunctional hybrid materials are obtained by modifying zeolite L (ZL) with stopcock molecules, consisting of a tail group that can enter the ZL nanochannels and a head group too large to pass the channel opening. However, to date no microscopic-level structural information on modified ZL materials has been reported. Herein we draw atomistic pictures of channel openings and stopcock-functionalized ZL based on first-principles calculations. We elucidate the interactions of the tail group with the inner surface of ZL channels and the space-filling properties of the stopcocks, revealing cork- or lid-sealing modes. Water is essential to obtain stable modifications. AlOH groups are the preferred modification sites, bipodal modifications suffer from strain, and tripod binding is ruled out. Our results suggest the viability of recursive functionalization by cross-linking.