Attraction versus Repulsion between Methyl and Related Groups: (CH3NHCH3)2 and (CH3SeBr2CH3)2.

The starting point for this work was a set of crystal structures containing the motif of interaction between methyl groups in homodimers. Two structures were selected for which QTAIM, NCI and NBO analyses suggested an attractive interaction. However, the calculated interaction energy was negative for only one of these systems. The ability of methyl groups to interact with one another is then examined by DFT calculations. A series of (CH3PnHCH3)2 homodimers were allowed to interact with each other for a range of Pn atoms N, P, As, and Sb. Interaction energies of these C∙∙∙C tetrel-bonded species were below 1 kcal/mol, but could be raised to nearly 3 kcal/mol if the C atom was changed to a heavier tetrel. A strengthening of the C∙∙∙C intermethyl bonds can also be achieved by introducing an asymmetry via an electron-withdrawing substituent on one unit and a donor on the other. The attractions between the methyl and related groups occur in spite of a coulombic repulsion between σ-holes on the two groups. NBO, AIM, and NCI tools must be interpreted with caution as they can falsely suggest bonding when the potentials are repulsive.

From weak to strong interactions between halogen and noble gas atoms in halonium complexes.

Halonium cations can interact through a halogen bond with individual noble gas atoms. These bonds can vary widely in strength from 1 to 25 kcal mol-1. Quantum chemical analyses consider X to be attached to a propyl group, pyridine N, or Xe atom, with X = Cl, Br, and I, interacting with Ar, Kr, and Xe atoms. The most weakly bound dyads are bound primarily by electrostatics, but charge transfer takes a larger role for the more tightly held complexes.

Wolfium bonds in homodimers of MX4Y (M = Mo, W; X = F, Cl, Br; Y = O, S, Se).

The term "wolfium bond" has been recently introduced to describe the noncovalent attraction between an atom of group 6 and a nucleophile via a σ-hole binding site. Crystal structures commonly contain a motif wherein two MX4Y units are arranged in close proximity, where M represents either Mo or W, and X and Y refer to halogen and chalcogen atoms respectively. DFT calculations were thus applied to a wide range of homodimers of these molecules so as to assess their preferred arrangements, and to characterize the types of bonding that are present in each in a systematic manner. The most stable Dual-X configuration is symmetric and contains a pair of equivalent M⋯X bonds. The interaction energies range from -8 to -29 kcal mol-1, and are largest for X = F, Y = O, and M = W. The X electron donor is replaced by Y, and the two wolfium bonds are reduced to one, in the less stable Mono-Y structure, with interaction energies between -2 and -10 kcal mol-1. There is some question as to whether the weaker bonds of this type constitute true wolfium bonds.

Influence of Internal Angular Arrangement on Pnicogen Bond Strength.

The three Z-X covalent bonds of a ZX3 unit (Z = P, As, Sb, Bi) are normally arranged in a pyramidal structure. Quantum chemical calculations show that pnicogen bonds (ZBs) to the central Z are weakened if ZX3 is flattened, as in the opening of an umbrella. The partial closing of the umbrella has the opposite effect of substantially strengthening these ZBs, even amounting to a 2- or 3-fold magnification in certain cases. The strongest such bonds, wherein Sb and Bi are in a strained configuration within a ZO3CH model system, have interaction energies of 20 kcal/mol with an NH3 base. Most of these systems, whether flattened or more pyramidal, are capable of engaging in three ZBs simultaneously, despite a certain amount of negative cooperativity.

Factors contributing to halogen bond strength and stretch or contraction of internal covalent bond.

The halogen bond formed by a series of Lewis acids TF3X (T = C, Si, Ge, Sn, Pb; X = Cl, Br, I) with NH3 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 PbF3X forming the strongest XBs, followed by CF3X, with SiF3X engaging in the weakest bonds. The charge transfer from the NH3 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.

Pd and Pt metal atoms as electron donors in σ-hole bonded complexes.

Quantum calculations provide a systematic assessment of the ability of Group 10 transition metals M = Pd and Pt to act as an electron donor within the context of pnicogen, chalcogen, and halogen bonds. These M atoms are coordinated in a square planar geometry, attached to two N atoms of a modified phenanthrene unit, as well as two ligand atoms Cl, Br, or I. As the Lewis acid, a series of AFn molecules were chosen, which could form a pnicogen bond (A = P, As, Sb), chalcogen bond (A = S, Se, Te) or halogen bond (A = Cl, Br, I) with M. These noncovalent bonds are fairly strong, varying between 6 and 20 kcal mol-1, with the occupied dz2 orbital of M acting as the origin of charge transferred to the acid. Pt forms somewhat stronger bonds than Pd, and the bond strength rises with the size of the A atom of the acid. Within the context of smaller A atoms, the bond strength rises in the order pnicogen < chalcogen < halogen, but this distinction vanishes for the fifth-row A atoms. The nature of the ligand atoms on M has little bearing on the bond strength. Based on the Harmonic Oscillator Model of Aromaticity (HOMA) index, the ZB, YB and XB bonds were shown to have only a subtle effect on the ring electronic structures.

Unraveling the Nature of Hydrogen Bonds of "Proton Sponges" Based on Car-Parrinello and Metadynamics Approaches.

The nature of intra- and intermolecular non-covalent interactions was studied in four naphthalene derivatives commonly referred to as "proton sponges". Special attention was paid to an intramolecular hydrogen bond present in the protonated form of the compounds. The unsubstituted "proton sponge" served as a reference structure to study the substituent influence on the hydrogen bond (HB) properties. We selected three compounds substituted by methoxy, amino, and nitro groups. The presence of the substituents either retained the parent symmetry or rendered the compounds asymmetric. In order to reveal the non-covalent interaction properties, the Hirshfeld surface (HS) was computed for the crystal structures of the studied compounds. Next, quantum-chemical simulations were performed in vacuo and in the crystalline phase. Car-Parrinello molecular dynamics (CPMD), Path Integral Molecular Dynamics (PIMD), and metadynamics were employed to investigate the time-evolution changes of metric parameters and free energy profile in both phases. Additionally, for selected snapshots obtained from the CPMD trajectories, non-covalent interactions and electronic structure were studied. Quantum theory of atoms in molecules (QTAIM) and the Density Overlap Regions Indicator (DORI) were applied for this purpose. It was found based on Hirshfeld surfaces that, besides intramolecular hydrogen bonds, other non-covalent interactions are present and have a strong impact on the crystal structure organization. The CPMD results obtained in both phases showed frequent proton transfer phenomena. The proton was strongly delocalized in the applied time-scale and temperature, especially in the PIMD framework. The use of metadynamics allowed for tracing the free energy profiles and confirming that the hydrogen bonds present in "proton sponges" are Low-Barrier Hydrogen Bonds (LBHBs). The electronic and topological analysis quantitatively described the temperature dependence and time-evolution changes of the electronic structure. The covalency of the hydrogen bonds was estimated based on QTAIM analysis. It was found that strong hydrogen bonds show greater covalency, which is additionally determined by the proton position in the hydrogen bridge.

Static and Dynamical Quantum Studies of CX3-AlX2 and CSiX3-BX2 (X = F, Cl, Br) Complexes with Hydrocyanic Acid: Unusual Behavior of Strong π-Hole at Triel Center.

The set of TX3-TrX2 (T = C, Si, Ge; Tr = B, Al, Ga; X = F, Cl, Br) molecules offers a rather unique opportunity to study both σ-hole and π-hole dimerization on the tetrel and triel ends, respectively. According to the molecular electrostatic potential (MEP) distribution, the π-hole extrema (acidic sites) were more intense than their σ-hole counterparts. The molecules owning the most (CX3-AlX2) and least (SiX3-BX2) intense π-holes were chosen to evaluate their capacities to attract one and two HCN molecules (Lewis bases). We discovered that the energetic characteristics of π-hole dimers severely conflict with the monomers MEP pattern since the weakest π-hole monomer forms a dimer characterized by interaction energy compared to those created by the monomers with noticeably greater power in the π-hole region. This outcome is due to the deformation of the weakest π-hole donor. Furthermore, the MEP analysis for monomers in the geometry of respective dimers revealed a "residual π-hole" site that was able to drive second ligand attachment, giving rise to the two "unusual trimers" examined further by the NCI and QTAIM analyses. Apart from them, the π-hole/π-hole and σ-hole/π-hole trimers have also been obtained throughout this study and described using energetic and geometric parameters. The SAPT approach revealed details of the bonding in one of the "unusual trimers". Finally, Born-Oppenheimer Molecular Dynamics (BOMD) simulations were carried out to investigate the time evolution of the interatomic distances of the studied complexes as well as their stability.

Trapping of Small Molecules within Single or Double Cyclo[18]carbon Rings.

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.

Competition between Intra and Intermolecular Pnicogen Bonds: Complexes between Naphthalene Derivatives and Neutral or Anionic Bases.

The PnF2 (Pn=P,As,Sb,Bi) on a naphthalene scaffold can engage in an internal pnicogen Pn⋅⋅⋅N bond (PnB) with an NH2 group placed close to it on the adjoining ring. An approaching neutral NH3 molecule can engage in a second PnB with the central Pn, which tends to weaken the intramolecular bond. The presence of the latter in turn weakens the intermolecular PnB with respect to that formed in its absence. Replacement of the external NH3 by a CN- anion causes a fundamental change in the bonding pattern, producing a fourth covalent bond with Pn, which rearranges into a trigonal bipyramidal motif. This addition disrupts the internal Pn⋅⋅⋅N pnicogen bond, recasting the PnF2 ⋅⋅⋅NH2 interaction into an NH⋅⋅⋅F H-bond.

Experimental and Theoretical Evidence of a Pb⋠⋠⋠Pb Ditetrel Bond Without a σ-Hole.

The crystal structure of a newly synthesized compound, [PbL(Ac)]2 , (where L=2 (amino(pyrazin-2-yl) methylene) hydrazinecarbothioamide, Ac=acetate anion) exhibits a close contact between pairs of Pb atoms, suggesting a ditetrel bond, in addition to two Pb⋅⋅⋅O tetrel bonds, and two C-H⋅⋅⋅O H-bonds. The presence of this ditetrel bond as an attractive component is confirmed by various quantum chemical methods. This novelty of this particular bond is its existence even in the absence of a σ-hole on the Pb atom, which is typically considered a prerequisite for a bond of this type. From a wider perspective, a survey of the Cambridge Structural Database suggests this bond may be more common than was hitherto thought, with 44 examples of Pb⋅⋅⋅Pb contacts amongst a total number of 219 examples of T⋅⋅⋅T interactions in general (T=Si, Ge, Sn, Pb).

Chalcogen Bond as a Factor Stabilizing Ligand Conformation in the Binding Pocket of Carbonic Anhydrase IX Receptor Mimic.

It is postulated that the overexpression of Carbonic Anhydrase isozyme IX in some cancers contributes to the acidification of the extracellular matrix. It was proved that this promotes the growth and metastasis of the tumor. These observations have made Carbonic Anhydrase IX an attractive drug target. In the light of the findings and importance of the glycoprotein in the cancer treatment, we have employed quantum-chemical approaches to study non-covalent interactions in the binding pocket. As a ligand, the acetazolamide (AZM) molecule was chosen, being known as a potential inhibitor exhibiting anticancer properties. First-Principles Molecular Dynamics was performed to study the chalcogen and other non-covalent interactions in the AZM ligand and its complexes with amino acids forming the binding site. Based on Density Functional Theory (DFT) and post-Hartree-Fock methods, the metric and electronic structure parameters were described. The Non-Covalent Interaction (NCI) index and Atoms in Molecules (AIM) methods were applied for qualitative/quantitative analyses of the non-covalent interactions. Finally, the AZM-binding pocket interaction energy decomposition was carried out. Chalcogen bonding in the AZM molecule is an important factor stabilizing the preferred conformation. Free energy mapping via metadynamics and Path Integral molecular dynamics confirmed the significance of the chalcogen bond in structuring the conformational flexibility of the systems. The developed models are useful in the design of new inhibitors with desired pharmacological properties.

Involvement of Arsenic Atom of AsF3 in Five Pnicogen Bonds: Differences between X-ray Structure and Theoretical Models.

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.

The Role of Hydrogen Bonds in Interactions between [PdCl4]2- Dianions in Crystal.

[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.

Competition between Inter and Intramolecular Tetrel Bonds: Theoretical Studies Complemented by CSD Survey.

Crystal structures document the ability of a TF3 group (T=Si, Ge, Sn, Pb) situated on a naphthalene system to engage in an intramolecular tetrel bond (TB) with an amino group on the adjoining ring. Ab initio calculations evaluate the strength of this bond and evaluate whether it can influence the ability of the T atom to engage in a second, intermolecular TB with another nucleophile. A very strong CN- anionic base can approach the T either along the extension of a T-C or T-F bond and form a strong TB with an interaction energy approaching 100 kcal/mol, although this bond is weakened a bit by the presence of the internal T⋅⋅⋅N bond. The much less potent NCH base engages in a correspondingly longer and weaker TB, less than 10 kcal/mol. Such an intermolecular TB is weakened by the presence of the internal TB, to the point that it only occurs for the two heavier tetrel atoms Sn and Pb.

Crystallographic and Theoretical Evidences of Anion⋠⋠⋠Anion Interaction.

Planar (HgCl3 )- anions are stacked fairly closely together in a slipped parallel arrangement within several crystal structures. Quantum chemical analysis shows evidence of strong noncovalent spodium bonds between the Hg π-hole of one unit and the Cl atom of an adjacent unit. Anion⋅⋅⋅anion spodium bonds work in tandem with crystal packing forces.

Anionanion (MX3-)2 dimers (M = Zn, Cd, Hg; X = Cl, Br, I) in different environments.

The possibility that MX3- 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 MX 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.

Triel bonds within anion···anion complexes.

The ability of two anions to interact with one another is tested in the context of pairs of TrX4- 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 TrF4-, 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.

Anion-anion and anion-neutral triel bonds.

The ability of a TrCl4- anion (Tr = Al, Ga, In, Tl) to engage in a triel bond with both a neutral NH3 and CN- anion is assessed by ab initio quantum calculations in both the gas phase and in aqueous medium. Despite the absence of a positive σ or π-hole on the Lewis acid, strong triel bonds can be formed with either base. The complexation involves an internal restructuring of the tetrahedral TrCl4- monomer into a trigonal bipyramid shape, where the base can occupy either an axial or equatorial position. Although this rearrangement requires a substantial investment of energy, it aids the complexation by imparting a much more positive MEP to the site that is to be occupied by the base. Complexation with the neutral base is exothermic in the gas phase and even more so in water where interaction energies can exceed 30 kcal mol-1. Despite the long-range coulombic repulsion between any pair of anions, CN- can also engage in a strong triel bond with TrCl4-. In the gas phase, complexation is endothermic, but dissociation of the metastable dimer is obstructed by an energy barrier. The situation is entirely different in solution, with large negative interaction energies of as much as -50 kcal mol-1. The complexation remains an exothermic process even after the large monomer deformation energy is factored in.

Experimental and Theoretical Studies of Dimers Stabilized by Two Chalcogen Bonds in the Presence of a N···N Pnicogen Bond.

The structure of the 5,6-dichloro-2,1,3-benzoselenadiazole homodimer, obtained by adding the ligand, 4,5-dichloro-o-phenylenediamine, to the methanolic solution of SeCl4, was determined by X-ray crystallography, augmented by Fourier transform infrared, Raman, and NMR spectroscopy. The binding motif involves a pair of Se···N chalcogen bonds, with a supplementary N···N pnicogen bond. Quantum calculations provide assessments of the strengths of the individual interactions as well as their contributing factors. All together, these three bonds compose a total interaction energy between 5.4 and 16.8 kcal/mol, with the larger chalcogen atom associated with the strongest interactions. Replacement of the Se atoms by S and Te analogues allows analysis of the dependence of these forces on the nature of the chalcogen atom. Calculations also measure the importance to the binding of the presence of a second N atom on each diazole unit as well as the substituted phenyl ring to which it is fused.