The Relevance of Experimental Charge Density Analysis in Unraveling Noncovalent Interactions in Molecular Crystals

The work carried out by our research group over the last couple of decades in the context of quantitative crystal engineering involves the analysis of intermolecular interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding using experimental charge density methodology is reviewed. The focus is to extract electron density distribution in the intermolecular space and to obtain guidelines to evaluate the strength and directionality of such interactions towards the design of molecular crystals with desired properties. Following the early studies on halogen bonding interactions, several "sigma-hole" interaction types with similar electrostatic origins have been explored in recent times for their strength, origin, and structural consequences. These include interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding. Experimental X-ray charge density analysis has proved to be a powerful tool in unraveling the strength and electronic origin of such interactions, providing insights beyond the theoretical estimates from gas-phase molecular dimer calculations. In this mini-review, we outline some selected contributions from the X-ray charge density studies to the field of non-covalent interactions (NCIs) involving elements of the groups 14-17 of the periodic table. Quantitative insights into the nature of these interactions obtained from the experimental electron density distribution and subsequent topological analysis by the quantum theory of atoms in molecules (QTAIM) have been discussed. A few notable examples of weak interactions have been presented in terms of their experimental charge density features. These examples reveal not only the strength and beauty of X-ray charge density multipole modeling as an advanced structural chemistry tool but also its utility in providing experimental benchmarks for the theoretical studies of weak interactions in crystals.

Elusive hypervalent phosphorus⋯π interactions: evidence for paradigm transformation from hydrogen to phosphorus bonding at low temperatures

A paradigm transformation from hydrogen to phosphorus bonding is found to depend on the proton affinity of the interacting π-systems.

Pentavalent phosphorus as a unique phosphorus donor in POCl3 homodimer and POCl3–H2O heterodimer: matrix isolation infrared spectroscopic and computational studies

Phosphorus, an important element among the pnicogen group, opens up avenues for experimental and computational explorations of its interaction in a variety of compounds.

Comparison of Various Means of Evaluating Molecular Electrostatic Potentials for Noncovalent Interactions

The various heterodimers formed by a series of Lewis acids with NH₃ as Lewis base are identified. Lewis acids include those that can form chalcogen (HSF and HSBr), pnicogen (H₂ PF and H₂ PBr), and tetrel (H₃ SiF and H₃ SiBr) bonds, as well as H-bonds and halogen bonds. The molecular electrostatic potential (MEP) of each Lewis acid is considered in a number of ways. Pictorial versions show broad regions of positive and negative MEP, on surfaces that vary with respect to either the value of the chosen isopotential, or their distance from the nuclei. Specific points are identified where the MEP reaches a maximum on a particular isodensity surface (V_s,max ). The locations and values of V_s,max were evaluated on different isodensity surfaces, and compared to the stabilities of the various equilibrium geometries. As the chosen isodensity is decreased, and the MEP maxima drift away from the molecule, some points maintain their angular positions with respect to the molecule, whereas others undergo a reorientation. The lowering isodensity also causes some of the maxima to disappear. In general, there is a fairly good correlation between the energetic ordering of the equilibrium structures and the values of V_s,max . A number of possible Lewis acid sites on the heteroaromatic imidazole ring were also considered and presents some cautions about application of V_s,max as the principal criterion for predicting equilibrium geometries. © 2017 Wiley Periodicals, Inc.

Modulating of the pnicogen-bonding by a H⋯π interaction: An ab initio study

An ab initio study of the cooperativity in XH₂P⋯NCH⋯Z and XH₂P⋯CNH⋯Z complexes (X=F, Cl, Br, CN, NC; Z=C₂H₂,C₆H₆) connected by pnicogen-bonding and H⋯π interactions is carried out by means of MP2 computational method. A detailed analysis of the structures, interaction energies and bonding properties is performed on these systems. For each set of the complexes considered, a favorable cooperativity is observed, especially in X=F and CN complexes. However, for a given X or Z, the amount of cooperativity effects in XH₂P⋯CNH⋯Z complexes are more important than XH₂P⋯NCH⋯Z counterparts. Besides, the influence of a H⋯π interaction on a P⋯N (C) bond is more pronounced than that of a P⋯N (C) bond on a H⋯π bond. The quantum theory of atoms in molecules shows that ternary complexes have increased electron densities at their bond critical points relative to the corresponding binary systems. The results also indicate that the strength of the P⋯N(C) and H⋯π interactions increases in the presence of the solvent.

The enhancing effect of a cation-π interaction on the cooperativity of halogen bonds: A computational study

In this work, we investigate the effect of a cation-π interaction on the cooperativity of X⋯N halogen bonds in PhX⋯NCX⋯NH₃ complexes, where Ph=phenyl and X=Cl, Br, I. Molecular geometries and interaction energies of the resulting complexes are studied at the MP2/aug-cc-pVDZ(-PP) computational level. The mechanism of the cooperativity between halogen bonds is analyzed using parameters derived from the noncovalent index, quantum theory of atoms in molecules and natural bond orbital methodologies. It is found that the divalent cations (Be²⁺, Mg²⁺) have a larger influence on the cooperativity of halogen bonds than monovalent ones (Li⁺, Na⁺). The formation of a cation-π interaction leads to strengthening of the halogen bonds, hence increases their cooperativity.

Using one halogen bond to change the nature of a second bond in ternary complexes with P⋯Cl and F⋯Cl halogen bonds

Ab initio MP2/aug’-cc-pVTZ calculations have been carried out to determine the effect of the presence of one halogen bond on the nature of the other in ternary complexes H₂XP:ClF:ClH and H₂XP:ClF:ClF, for X = F, Cl, H, NC, and CN. The P⋯Cl bonds remain chlorine-shared halogen bonds in the ternary complexes H₂XP:ClF:ClH, although the degree of chlorine sharing increases relative to the corresponding binary complexes. The F⋯Cl bonds in the ternary complexes remain traditional halogen bonds. The binding energies of the complexes H₂XP:ClF:ClH increase relative to the corresponding binary complexes, and nonadditivities of binding energies are synergistic. In contrast, the presence of two halogen bonds in the ternary complexes H₂XP:ClF:ClF has a dramatic effect on the nature of these bonds in the four most strongly bound complexes. In these, chlorine transfer occurs across the P⋯Cl halogen bond to produce complexes represented as (H₂XP–Cl)⁺:⁻(F:ClF). In the ion-pair, the cation is also halogen bonded to the anion by a Cl⋯F⁻ halogen bond, while the anion is stabilized by an ⁻F⋯Cl halogen bond. The central ClF molecule no longer exists as a molecule. The binding energies of the ternary H₂XP:ClF:ClF complexes are significantly greater than the binding energies of the H₂XP:ClF:ClH complexes, and nonadditivities exhibit large synergistic effects. The Wiberg bond indexes for the complexes H₂XP:ClF, H₂XP:ClF:ClH, and H₂XP:ClF:ClF, and the cations (H₂XP–Cl)⁺ reflect the changes in the P–Cl and Cl–F bonds. Similarly, EOM-CCSD spin–spin coupling constants are also consistent with the changes in these same bonds. In particular, ^1xJ(P–Cl) in H₂XP:ClF complexes becomes ¹J(P–Cl) in the ternary complexes with chlorine-transferred halogen bonds. A plot of these coupling constants shows a change in the curvature of the trendline as chlorine-shared halogen bonds in H₂XP:ClF:ClH become chlorine-transferred halogen bonds in H₂XP:ClF:ClF. ^1xJ(F–Cl) coupling constants also reflect changes in the nature of F⋯Cl halogen bonds.

New equation for calculating total interaction energy in one noncyclic ABC triad and new insights into cooperativity of noncovalent bonds

In this work, a new equation consist of A⋅⋅⋅B, B⋅⋅⋅C, A⋅⋅⋅BC, and AB⋅⋅⋅C interactions is proposed for calculating the total interaction energy of noncyclic ABC triads. New equations are also proposed for calculating the changes in values of A⋅⋅⋅B and B⋅⋅⋅C interactions on the formation of triad from the corresponding dyads. The advantages of equations proposed here in comparison with many-body interaction energy approach are discussed. All proposed equations were tested in F₃ MLi⋅⋅⋅NCH⋅⋅⋅HLH and F₃ MLi⋅⋅⋅HLH⋅⋅⋅HCN (M = C, Si; L = Be, Mg) as well as H₃ N⋅⋅⋅XY⋅⋅⋅HF (X, Y = F, Cl, Br) noncyclic A⋅⋅⋅B⋅⋅⋅C triads. The data show that the total cooperativity of triad correlates well with the sum of the changes in values of A⋅⋅⋅B and B⋅⋅⋅C interactions calculated through new equations proposed here. © 2016 Wiley Periodicals, Inc.

The mutual influence of Y···N and H···H interactions in XHY···NCH···HM complexes (X = F, Cl, Br; Y = S, Se; M = Li, Na, BeH, MgH): tuning of the chalcogen bond by dihydrogen bond interaction

The equilibrium structures, interaction energies, and bonding properties of ternary XHY···NCH···HM complexes are studied by ab initio calculations, where X = F, Cl, Br, Y = S, Se, and M = Li, Na, BeH, MgH. The ab initio calculations are carried out at the MP2/aug-cc-pVTZ level. The results indicate that all optimized Y···N and H···H binding distances in the ternary complexes are smaller than the corresponding values in the binary systems. The calculated cooperative energies (Ecoop) are between −0.20 kcal/mol in BrHS···NCH···HBeH and −3.29 kcal/mol in FHSe···NCH···HNa. For a given Y and M, the estimated Ecoop values increase as X = F > Cl > Br. In addition, the selenium-bonded complexes exibit larger Ecoop values than those of the sulfur-bonded counterparts. The cooperativity between Y···N and H···H interactions is further analyzed by quantum theory of atoms in molecules and natural bond orbital methods. Cooperative effects make an increase in the J(Y–N) and J(H–H) spin–spin coupling constants of the ternary complexes with respect to the binary systems.

Influence of the protonation of pyridine nitrogen on pnicogen bonding: competition and cooperativity

Ab initio MP2/aug-cc-pVTZ calculations were performed to investigate the pnicogen-bonded complexes of PyZX₂ (Py = pyridine, Z = P and As, X = H and F) and their protonated analogues.

Comparison of π-hole tetrel bonding with σ-hole halogen bonds in complexes of XCN (X = F, Cl, Br, I) and NH3

In addition to the standard halogen bond formed when NH₃approaches XCN (X = F, Cl, Br, I) along its molecular axis, a perpendicular approach is also possible, toward a π-hole that is present above the X–C bond.

Theoretical calculations of π-type pnicogen bonds in the triad intermolecular complexes

The pnicogen bonding interactions of PCl3and π-electron systems (acetylene, ethylene, benzene) were calculated by using MP2/aug-cc-pVDZ method and the effect of hydrogen bond on pnicogen bond systems were investigated. It has been indicated that the hydrogen bonding and the pnicogen bonding interactions have influence on each other and the positively cooperative effect has been detected. The interaction energies of pnicogen bonded supramolecular system were also calculated by using DFT method (M06-2X) and some simple comparisons with those by using MP2 method were made. It has been disclosed from natural bond orbitals (NBO) analysis that more the amount of charge transfer of pnicogen bonding interaction, the greater the stability of the corresponding complex. Through AIM topological analysis, it has been revealed that the electron density of pnicogen bond BCP point is positively correlated with the stability of trimeric complex. Electron localization function (ELF) was also adopted to analyze the nature of pnicogen bonding interactions. Furthermore, density difference function (DDF) method was adopted to analyze the variation of electron density of pnicogen bond system because of hydrogen bond.

The dual role of pnicogen as Lewis acid and base and the unexpected interplay between the pnicogen bond and coordination interaction in H3N⋯FH2X⋯MCN (X = P and As; M = Cu, Ag, and Au)

Ternary systems H₃N⋯FH₂X⋯MCN (X = P and As; M = Cu, Ag, and Au) as well as the corresponding pnicogen-bonded and coordination-bonded binary systems have been studied.

Strength of the pnicogen bond in complexes involving group Va elements N, P, and As

A set of 36 pnicogen homo- and heterodimers, R3E···ER3 and R3E···E′R′3, involving differently substituted group Va elements E = N, P, and As has been investigated at the ωB97X-D/aug-cc-pVTZ level of theory to determine the strength of the pnicogen bond with the help of the local E···E′ stretching force constants k(a). The latter are directly related to the amount of charge transferred from an E donor lone pair orbital to an E′ acceptor σ* orbital, in the sense of a through-space anomeric effect. This leads to a buildup of electron density in the intermonomer region and a distinct pnicogen bond strength order quantitatively assessed via k(a). However, the complex binding energy ΔE depends only partly on the pnicogen bond strength as H,E-attractions, H-bonding, dipole-dipole, or multipole-multipole attractions also contribute to the stability of pnicogen bonded dimers. A variation from through-space anomeric to second order hyperonjugative, and skewed π,π interactions is observed. Charge transfer into a π* substituent orbital of the acceptor increases the absolute value of ΔE by electrostatic effects but has a smaller impact on the pnicogen bond strength. A set of 10 dimers obtains its stability from covalent pnicogen bonding whereas all other dimers are stabilized by electrostatic interactions. The latter are quantified by the magnitude of the local intermonomer bending force constants XE···E′. Analysis of the frontier orbitals of monomer and dimer in connection with the investigation of electron difference densities, and atomic charges lead to a simple rationalization of the various facets of pnicogen bonding. The temperature at which a given dimer is observable under experimental conditions is provided.