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The encapsulation of a set of small molecules, H2, CO, CO2, SO2, and SO3, by a circular C18 ring is investigated by quantum calculations. These ligands lie near the center of the ring but, with the exception of H2, are disposed roughly perpendicular to the ring plane. Their binding energies with the C18 vary from 1.5 kcal/mol for H2 up to 5.7 kcal/mol for SO2, and the bonding is dominated by dispersive interactions spread over the entire ring. The binding of these ligands on the outside of the ring is weaker but allows the opportunity for each to bond covalently with the ring. A pair of C18 units lie parallel to one another. This pair can bind each of these ligands in the area between them with only small perturbations of the double ring geometry. The binding energies of these ligands to this double ring configuration are amplified by some 50% compared to the single ring systems. The presented data concerning the trapping of small molecules may have larger implications regarding hydrogen storage or air pollution reduction. 

The halogen bond formed by a series of Lewis acids TF 3 X (T = C, Si, Ge, Sn, Pb; X = Cl, Br, I) with NH 3 is studied by quantum chemical calculations. The interaction energy is closely mimicked by the depth of the σ-hole on the X atom as well as the full electrostatic energy. There is a first trend by which the hole is deepened if the T atom to which X is attached becomes more electron-withdrawing: C > Si > Ge > Sn > Pb. On the other hand, larger more polarizable T atoms are better able to transmit the electron-withdrawing power of the F substituents. The combination of these two opposing factors leaves PbF 3 X forming the strongest XBs, followed by CF 3 X, with SiF 3 X engaging in the weakest bonds. The charge transfer from the NH 3 lone pair into the σ*(TX) antibonding orbital tends to elongate the covalent TX bond, and this force is largest for the heavier X and T atoms. On the other hand, the contraction of this bond deepens the σ-hole at the X atom, which would enhance both the electrostatic component and the full interaction energy. This bond-shortening effect is greatest for the lighter X atoms. The combination of these two opposing forces leaves the T–X bond contracting for X = Cl and Br, but lengthening for I. 

Bonding within the AsF3 crystal is analyzed via quantum chemical methods so as to identify and quantify the pnicogen bonds that are present. The structure of a finite crystal segment containing nine molecules is compared with that of a fully optimized cluster of the same size. The geometries are qualitatively different, with a much larger binding energy within the optimized nonamer. Although the total interaction energy of a central unit with the remaining peripheral molecules is comparable for the two structures, the binding of the peripherals with one another is far larger in the optimized cluster. This distinction of much stronger total binding within the optimized cluster is not limited to the nonamer but repeats itself for smaller aggregates as well. The average binding energy of the cluster rises quickly with size, asymptotically approaching a value nearly triple that of the dimer. 

[PdCl4]2− dianions are oriented within a crystal in such a way that a Cl of one unit approaches the Pd of another from directly above. Quantum calculations find this interaction to be highly repulsive with a large positive interaction energy. The placement of neutral ligands in their vicinity reduces the repulsion, but the interaction remains highly endothermic. When the ligands acquire a unit positive charge, the electrostatic component and the full interaction energy become quite negative, signalling an exothermic association. Raising the charge on these counterions to +2 has little further stabilizing effect, and in fact reduces the electrostatic attraction. The ability of the counterions to promote the interaction is attributed in part to the H-bonds which they form with both dianions, acting as a sort of glue. 

The ability of two anions to interact with one another is tested in the context of pairs of TrX 4 − homodimers, where Tr represents any of the triel atoms B, Al, Ga, In, or Tl, and X refers to a halogen substituent F, Cl, or Br. None of these pairs engage in a stable complex in the gas phase, but the situation reverses in water where the two monomers are held together by Tr⋯X triel bonds, complemented by stabilizing interactions between X atoms. Some of these bonds are quite strong, notably those involving TrF 4 − , with interaction energies surpassing 30 kcal mol −1 . Others are very much weaker, with scarcely exothermic binding energies. The highly repulsive electrostatic interactions are counteracted by large polarization energies. 

Inspection of the arrangement of tetrachloridopalladate( ii ) centers in a crystalline solid places the Cl of one [PdCl 4 ] 2− directly above the Pd center of its neighbor. A survey of the CSD provides 22 more examples of such MX 4 2− ⋯MX 4 2− complexes, with M being a Group 10 metal and X = Cl, Br, or I. Quantum calculations attribute this arrangement to a π-hole bond wherein Cl lone pairs of one unit transfer charge to vacant orbitals above the Pd center of its neighbor. The stabilizing effect of this bond must overcome the strong Coulombic repulsion between the two dianions, which is facilitated by a polarizable environment as would be present in a crystal, but much more so when the effects of the neighboring counterions are factored in. These conclusions are extended to other [MX 4 ] 2− homodimers, where M represents other members of Group 10, namely Ni and Pt. 

Molecules of the type XYT = Ch (T = C, Si, Ge; Ch = S, Se; X,Y = H, CH3, Cl, Br, I) contain a σ-hole along the T = Ch bond extension. This hole can engage with the N lone pair of NCH and NCCH3 so as to form a chalcogen bond. In the case of T = C, these bonds are rather weak, less than 3 kcal/mol, and are slightly weakened in acetone or water. They owe their stability to attractive electrostatic energy, supplemented by dispersion, and a much smaller polarization term. Immersion in solvent reverses the electrostatic interaction to repulsive, while amplifying the polarization energy. The σ-holes are smaller for T = Si and Ge, even negative in many cases. These Lewis acids can nonetheless engage in a weak chalcogen bond. This bond owes its stability to dispersion in the gas phase, but it is polarization that dominates in solution. 

The possibility that MX 3 − anions can interact with one another is assessed via ab initio calculations in gas phase as well as in aqueous and ethanol solution. A pair of such anions can engage in two different dimer types. In the bridged configuration, two X atoms engage with two M atoms in a rhomboid structure with four equal M–X bond lengths. The two monomers retain their identity in the stacked geometry which contains a pair of noncovalent M⋯X interactions. The relative stabilities of these two structures depend on the nature of the central M atom, the halogen substituent, and the presence of solvent. The interaction and binding energies are fairly small, generally no more than 10 kcal mol −1 . The large electrostatic repulsion is balanced by a strong attractive polarization energy. 

Over the last years, scientific interest in noncovalent interactions based on the presence of electron-depleted regions called σ-holes or π-holes has markedly accelerated. Their high directionality and strength, comparable to hydrogen bonds, has been documented in many fields of modern chemistry. The current review gathers and digests recent results concerning these bonds, with a focus on those systems where both σ and π-holes are present on the same molecule. The underlying principles guiding the bonding in both sorts of interactions are discussed, and the trends that emerge from recent work offer a guide as to how one might design systems that allow multiple noncovalent bonds to occur simultaneously, or that prefer one bond type over another.