Donor-acceptor (DA) complexes of noble gases (Ng) of the general type A <-- Ng <-- D (A = Lewis acid, D = Lewis base) have been theoretically studied using ab initio and DFT methods. Chemical bonding in these compounds is realized via a 3-center 4-electron bond, which is formed by a lone pair of the noble gas, a lone pair of the donor molecule and a vacant orbital of the acceptor molecule. Detailed bonding analysis of the model compounds F(3)Al-Ng-NH(3) reveals that Ng-ammonia interaction is repulsive due to Pauli repulsion. Bonding interaction between Ng and N is mostly electrostatic. In contrast, strong orbital interactions are responsible for the attractive interactions between Ng and AlF(3). Due to the repulsive interactions with the donor molecule and a sizable reorganization energy of the acceptor molecule, optimization attempts of the A <-- Ng <-- D compounds, which feature individual donor and acceptor molecules, always lead to the dissociation of the complex and eventual formation of free Ng. To overcome this obstacle, the concept of a rigid C(3v) symmetric cryptand-type ligand, which features spacially separated pyramidalized donor and acceptor fragments, is introduced. Such "push-pull" ligands are predicted to exothermically form complexes with noble gases. These are the first examples of the thermodynamically stable Ar and Kr compounds. Application of the push-pull cryptand ligands featuring multiple (two and three) donor-acceptor induced chemical bonds is expected to yield stable complexes with virtually any electron-rich element in the periodic table.