The Pnicogen Bond in Review: Structures, Binding Energies, Bonding Properties, and Spin-Spin Coupling Constants of Complexes Stabilized by Pnicogen Bonds

Unraveling pnicogen bonding cooperativity: Insights from molecular electrostatic potential analysis

A theoretical investigation on the cooperativity of a series of binary, ternary, and quaternary complexes interconnected by pnicogen bonds has been conducted using calculations at the M06-2X/aug-cc-pVTZ level of density functional theory. By measuring changes in the molecular electrostatic potential (MESP) at the nucleus of interacting atoms in all of the complexes, it is possible to quantify the substantial reorganization of the electron density triggered by the formation of pnicogen bonds. The positive change in MESP, indicating a loss of electron density from the donor molecule in a dimer, facilitates the acceptance of electron density from a third molecule, resulting in the formation of a ternary complex with a stronger pnicogen bond compared to the one present in the binary complex. Similarly, the acceptor molecule in a dimer with a negative change in MESP showed an enhanced tendency to donate electron density to an electron-deficient third molecule. The MESP analysis provided valuable insights into the donor/acceptor characteristics of pnicogen bonds within the quaternary complexes. The proposed MESP hypotheses are consistent with the positive cooperativity observed in the pnicogen-bonded clusters. To quantify the changes in MESP, both at the donor atom (ΔVdonor ) and the acceptor atom (ΔVacceptor ), for all pnicogen bonds in the cluster, the total change in MESP (ΔΔVn ) was measured as ΔΔVn  = ∑(ΔVdonor )-∑(ΔVacceptor ). Remarkably, ΔΔVn exhibited a strong linear relationship with the sum of the bond energies of the pnicogen bonds in the cluster. This establishes the MESP analysis as a robust approach for understanding the strength and cooperative behavior of pnicogen-bonded clusters. Additionally, the MESP features provided clear evidence of pnicogen bond formation, further supporting the reliability of this approach.

Structural, vibrational and electronic properties of some tetrel-bonded complexes of the fluorinated methanes methyl fluoride, difluoromethane and fluoroform: an ab initio study

A search has been conducted, by means of ab initio molecular orbital theory, for potential tetrel-bonded complexes formed between the fluorinated methanes methyl fluoride, difluoromethane and fluoroform, and the related hydrides ammonia, water, hydrogen fluoride, phosphine, hydrogen sulphide and hydrogen chloride. Eleven such complexes have been identified, six containing CH₃F and five CH₂F₂. The complexes are typically less strongly bound than their hydrogen-bonded counterparts, and the interaction energies vary in a consistent way with the periodic trend of the electron donors. The intermolecular separations and changes of the relevant intramolecular bond lengths, the wavenumber shifts of the critical vibrational modes and the extents of charge transfer correlate, by and large, with the strengths of interaction.

The Phosphorus Bond, or the Phosphorus-Centered Pnictogen Bond: The Covalently Bound Phosphorus Atom in Molecular Entities and Crystals as a Pnictogen Bond Donor

The phosphorus bond in chemical systems, which is an inter- or intramolecular noncovalent interaction, occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a covalently or coordinately bonded phosphorus atom in a molecular entity and a nucleophile in another, or the same, molecular entity. It is the second member of the family of pnictogen bonds, formed by the second member of the pnictogen family of the periodic table. In this overview, we provide the reader with a snapshot of the nature, and possible occurrences, of phosphorus-centered pnictogen bonding in illustrative chemical crystal systems drawn from the ICSD (Inorganic Crystal Structure Database) and CSD (Cambridge Structural Database) databases, some of which date back to the latter part of the last century. The illustrative systems discussed are expected to assist as a guide to researchers in rationalizing phosphorus-centered pnictogen bonding in the rational design of molecular complexes, crystals, and materials and their subsequent characterization.

Study of Beryllium, Magnesium, and Spodium Bonds to Carbenes and Carbodiphosphoranes

The aim of this article is to present results of theoretical study on the properties of C⋯M bonds, where C is either a carbene or carbodiphosphorane carbon atom and M is an acidic center of MX2 (M = Be, Mg, Zn). Due to the rarity of theoretical data regarding the C⋯Zn bond (i.e., the zinc bond), the main focus is placed on comparing the characteristics of this interaction with C⋯Be (beryllium bond) and C⋯Mg (magnesium bond). For this purpose, theoretical studies (ωB97X-D/6-311++G(2df,2p)) have been performed for a large group of dimers formed by MX2 (X = H, F, Cl, Br, Me) and either a carbene ((NH2)2C, imidazol-2-ylidene, imidazolidin-2-ylidene, tetrahydropyrymid-2-ylidene, cyclopropenylidene) or carbodiphosphorane ((PH3)2C, (NH3)2C) molecule. The investigated dimers are characterized by a very strong charge transfer effect from either the carbene or carbodiphosphorane molecule to the MX2 one. This may even be over six times as strong as in the water dimer. According to the QTAIM and NCI method, the zinc bond is not very different than the beryllium bond, with both featuring a significant covalent contribution. However, the zinc bond should be definitely stronger if delocalization index is considered.

Relative Strengths of a Pnicogen and a Tetrel Bond and Their Mutual Effects upon One Another

The ability of the T and Z atoms of TR₃ZR₂ to engage in a noncovalent interaction with NH₃ is assessed by DFT calculations, where the T atom refers to C, Si, and Ge; Z = As, Sb, and P; and substituents R = H and F. In most instances, the tetrel bond (TB) is both stronger and shorter than the pnicogen bond (ZB). These two bond strengths can be equalized, or preference shifted to the ZB, if F substituents are placed on the Z and H on the T atoms. Employing C as the T atom results in a very weak TB, with the ZB clearly favored energetically. The simultaneous formation of both TB and ZB weakens both, particularly the latter, but both bonds survive intact. Geometric and spectroscopic perturbations of the subunits reflect the two types of noncovalent bonds.

Mutual Influence of Pnicogen Bonds and Beryllium Bonds: Energies and Structures in the Spotlight

Pnicogen bonds, which are weak noncovalent interactions (NCIs), can be significantly modified by the presence of beryllium bonds, one of the strongest NCIs known. We demonstrate the importance of this influence by studying ternary complexes in which both NCIs are present, that is, the ternary complexes formed by a nitrogen base (NH₃, NHCH₂, and NCH), a phosphine (fluorophosphane, PH₂F) and a beryllium derivative (BeH₂, BeF₂, BeCl₂, BeCO₃, and BeSO₄). Energies, structures, and nature of the chemical bonding in these complexes are studied by means of ab initio computational methods. The pnicogen bond between the nitrogen base and the phosphine and the beryllium bond between the fluorine atom of fluorophosphane and the beryllium derivative show large cooperativity effects both on energies and geometries, with dissociation energies up to 296 kJ mol^-1 and cooperativity up to 104 kJ mol^-1 in the most strongly bound complex, CH₂HN:PH₂F:BeSO₄. In the complexes between the strongest nitrogen bases and the strongest beryllium donors, phosphorus-shared and phosphorus-transfer bonds are found.

Stabilisation of dianion dimers trapped inside cyanostar macrocycles

Interanionic H-bonds (IAHBs) are unfavourable interactions in the gas phase becoming favoured when anions are in solution. Dianion dimers are also susceptible to being trapped inside the cavities of cyanostar (CS) macrocycles, and thus, the formation of 2 : 2 anion : cyanostar aggregates is mainly supported by three kinds of interactions: IAHBs between the dianions, π-π stacking between the confronted cyanostars, and the presence of an intricate network of multiple C(sp²)HO H-bonds between cyanostar ligands and the anionic moieties. An analysis of the interaction energies supported by NBO reveals a slight cooperative effect of the CSs on the IAHB stabilisation.

Regium Bonds between Silver(I) Pyrazolates Dinuclear Complexes and Lewis Bases (N2, OH2, NCH, SH2, NH3, PH3, CO and CNH)

A theoretical study and Cambridge Structural Database (CSD) search of dinuclear Ag(I) pyrazolates interactions with Lewis bases were carried out and the effect of the substituents and ligands on the structure and on the aromaticity were analyzed. A relationship between the intramolecular Ag–Ag distance and stability was found in the unsubstituted system, which indicates a destabilization at longer distances compensated by ligands upon complexation. It was also observed that the asymmetrical interaction with phosphines as ligands increases the Ag–Ag distance. This increase is dramatically higher when two simultaneous PH3 ligands are taken into account. The calculated 109Ag chemical shielding shows variation up to 1200 ppm due to the complexation. Calculations showed that six-membered rings possessed non-aromatic character while pyrazole rings do not change their aromatic character significantly upon complexation.

N…C and S…S Interactions in Complexes, Molecules, and Transition Structures HN(CH)SX:SCO, for X = F, Cl, NC, CCH, H, and CN

Ab initio Møller-Plesset perturbation theory (MP2)/aug'-cc-pVTZ calculations have been carried out in search of complexes, molecules, and transition structures on HN(CH)SX:SCO potential energy surfaces for X = F, Cl, NC, CCH, H, and CN. Equilibrium complexes on these surfaces have C1 symmetry, but these have binding energies that are no more than 0.5 kJ·mol-1 greater than the corresponding Cs complexes which are vibrationally averaged equilibrium complexes. The binding energies of these span a narrow range and are independent of the N-C distance across the tetrel bond, but they exhibit a second-order dependence on the S-S distance across the chalcogen bond. Charge-transfer interactions stabilize all of these complexes. Only the potential energy surfaces HN(CH)SF:SCO and HN(CH)SCl:SCO have bound molecules that have short covalent N-C bonds and significantly shorter S…S chalcogen bonds compared to the complexes. Equation-of-motion coupled cluster singles and doubles (EOM-CCSD) spin-spin coupling constants 1tJ(N-C) for the HN(CH)SX:SCO complexes are small and exhibit no dependence on the N-C distance, while 1cJ(S-S) exhibit a second-order dependence on the S-S distance, increasing as the S-S distance decreases. Coupling constants 1tJ(N-C) and 1cJ(S-S) as a function of the N-C and S-S distances, respectively, in HN(CH)SF:SCO and HN(CH)SCl:SCO increase in the transition structures and then decrease in the molecules. These changes reflect the changing nature of the N…C and S…S bonds in these two systems.

Cyclohexane-Based Scaffold Molecules Acting as Anion Transport, Anionophores, via Noncovalent Interactions

A theoretical study of a variety of cyclohexane-based anion transporters interacting with the chloride anion has been conducted using density functional theory. The calculations have been performed in the gas phase but also, in order to describe the solvation effects on the interaction, two different solvents-chloroform and dimethylsulfoxide-have been taken into account. Gas-phase interaction energies within the complexes are found to be up to 400 kJ/mol, while, when solvent effects are considered, the interaction energy values decreased drastically concomitantly with an elongation in the interatomic distances. Atoms in molecules and natural bond analysis corroborate the trends found for the intermolecular energies and Cl···H distances, suggesting strong donations from the Cl^- anion into the σ*H-N antibonding orbitals, as well as with noncovalent interaction plots showing large areas of electron density overlap within the chloride anion surroundings.

A theoretical investigation on Cu/Ag/Au bonding in XH2P⋯MY(X = H, CH3, F, CN, NO2; M = Cu, Ag, Au; Y = F, Cl, Br, I) complexes

Intermolecular interaction of XH₂P···MY (X = H, CH₃, F, CN, NO₂; M = Cu, Ag, Au; Y = F, Cl, Br, I) complexes was investigated by means of an ab initio method. The molecular interaction energies are in the order Ag < Cu < Au and increased with the decrease of R_P···M. Interaction energies are strengthened when electron-donating substituents X connected to XH₂P, while electron-withdrawing substituents produce the opposite effect. The strongest P···M bond was found in CH₃H₂P···AuF with -70.95 kcal/mol, while the weakest one was found in NO₂H₂P···AgI with -20.45 kcal/mol. The three-center/four-electron (3c/4e) resonance-type of P:-M-:Y hyperbond was recognized by the natural resonance theory and the natural bond orbital analysis. The competition of P:M-Y ↔ P-M:Y resonance structures mainly arises from hyperconjugation interactions; the bond order of b_P-M and b_M-Y is in line with the conservation of the idealized relationship b_P-M + b_M-Y ≈ 1. In all MF-containing complexes, P-M:F resonance accounted for a larger proportion which leads to the covalent characters for partial ionicity of MF. The interaction energies of these Cu/Ag/Au complexes are basically above the characteristic values of the halogen-bond complexes and close to the observed strong hydrogen bonds in ionic hydrogen-bonded species.

Pseudohalide Tectons within the Coordination Sphere of the Uranyl Ion: Experimental and Theoretical Study of C-H···O, C-H···S, and Chalcogenide Noncovalent Interactions

A series of uranyl thiocyanate and selenocyanate of the type [R₄N]₃[UO₂(NCS)₅] (R₄ = ⁿBu₄, Me₃Bz, Et₃Bz), [Ph₄P][UO₂(NCS)₃(NO₃)] and [R₄N]₃[UO₂(NCSe)₅] (R₄ = Me₄, ⁿPr₄, Et₃Bz) have been prepared and structurally characterized. The resulting noncovalent interactions have been examined and compared to other examples in the literature. The nature of these interactions is determined by the cation so that when the alkyl groups are small, chalcogenide···chalcogenide interactions are present, but this "switches off" when R = ⁿPr and charge assisted U═O···H-C and S(e)···H-C hydrogen bonding remain the dominant interaction. Increasing the size of the chain to ⁿBu results in only S···H-C interactions. The spectroscopic implications of these chalcogenide interactions have been explored in the vibrational and photophysical properties of the series [R₄N]₃[UO₂(NCS)₅] (R₄ = Me₄, Et₄, ⁿPr₄, ⁿBu₄, Me₃Bz, Et₃Bz), [R₄N]₃[UO₂(NCSe)₅] (R₄ = Me₄, ⁿPr₄, Et₃Bz) and [Et₄N]₄[UO₂(NCSe)₅][NCSe]. The data suggest that U═O···H-C interactions are weak and do not perturb the uranyl moiety. While the chalcogenide interactions do not influence the photophysical properties, a coupling of the U═O and δ(NCS) or δ(NCSe) vibrational modes is observed in the 77 K solid state emission spectra. A theoretical examination of representative examples of Se···Se, C-H···Se, and C-H···O═U by molecular electrostatic potentials and NBO and AIM methodologies gives a deeper understanding of these weak interactions. C-H···Se are individually weak but C-H···O═U interactions are even weaker, supporting the idea that the -yl oxo's are weak Lewis bases. An Atoms in Molecules study suggests that the chalcogenide interaction is similar to lone pair···π or fluorine···fluorine interactions. An oxidation of the NCS ligands to form [(UO₂)(SO₄)₂(H₂O)₄]·3H₂O was also noted.

Systematic Coupled Cluster Study of Noncovalent Interactions Involving Halogens, Chalcogens, and Pnicogens

The noncovalent interactions of 32 complexes involving pnicogens, chalcogens, and halogens atoms were investigated at the CCSD(T)/aug-cc-pVTZ level of theory. Two different types of complexes could be distinguished on the basis of geometric parameters, electron difference densities, and the charge transfer mechanisms associated with each type. In the type I conformation, the monomers adopt a skewed orientation allowing charge to be transfer between both monomers, whereas in the type II conformation the monomers adopt a linear arrangement, maximizing charge transfer in only one direction. Type I complexes involving the interaction between pnicogens and chalcogens cannot be unambiguously defined as chalcogen or pnicogen bonds, they are an admixture of both. The charge transfer dependence on the conformation adopted by the complexes described in this work can serve as a novel conformationally driven design concept for materials.

Halogen Bonding Involving CO and CS with Carbon as the Electron Donor

MP2/aug'-cc-pVTZ calculations have been carried out to investigate the halogen-bonded complexes formed when CO and CS act as electron-pair donors through C to ClF, ClNC, ClCl, ClOH, ClCN, ClCCH, and ClNH₂. CO forms only complexes stabilized by traditional halogen bonds, and all ClY molecules form traditional halogen-bonded complexes with SC, except ClF which forms only an ion-pair complex. Ion-pair complexes are also found on the SC:ClNC and SC:ClCl surfaces. SC:ClY complexes stabilized by traditional halogen bonds have greater binding energies than the corresponding OC:ClY complexes. The largest binding energies are found for the ion-pair SC-Cl⁺:-Y complexes. The transition structures which connect the complex and the ion pair on SC:ClNC and SC:ClCl potential surfaces provide the barriers for inter-converting these structures. Charge-transfer from the lone pair on C to the σ-hole on Cl is the primary charge-transfer interaction stabilizing OC:ClY and SC:ClY complexes with traditional halogen bonds. A secondary charge-transfer occurs from the lone pairs on Cl to the in-plane and out-of-plane π antibonding orbitals of ClY. This secondary interaction assumes increased importance in the SC:ClNH₂ complex, and is a factor leading to its unusual structure. C-O and C-S stretching frequencies and 13C chemical shieldings increase upon complex formation with ClY molecules. These two spectroscopic properties clearly differentiate between SC:ClY complexes and SC-Cl⁺:-Y ion pairs. Spin-spin coupling constants 1xJ(C-Cl) for OC:ClY complexes increase with decreasing distance. As a function of the C-Cl distance, 1xJ(C-Cl) and ¹J(C-Cl) provide a fingerprint of the evolution of the halogen bond from a traditional halogen bond in the complexes, to a chlorine-shared halogen bond in the transition structures, to a covalent bond in the ion pairs.

Lone-Pair Hole on P: P···N Pnicogen Bonds Assisted by Halogen Bonds

Ab initio MP2/aug'-cc-pVTZ calculations have been performed on the binary complexes XY:PH₃ for XY = ClCl, FCl, and FBr; and PH₃:N-base for N-base = NCH, NH₃, NCF, NCCN, and N₂; and the corresponding ternary complexes XY:PH₃:N-base, to investigate P···N pnicogen bond formation through the lone-pair hole at P in the binary complexes and P···N pnicogen-bond formation assisted by P···Y halogen bond formation through the σ-hole at Y. Although the binary complexes PH₃:N-base that form through the lone-pair hole have very small binding energies, they are not equilibrium structures on their potential surfaces. The presence of the P···Y halogen bond makes PH₃ a better electron-pair acceptor through its lone-pair hole, leading to stable ternary complexes XY:PH₃:N-base. The halogen bonds in ClCl:PH₃ and ClCl:PH₃:NCCN are traditional halogen bonds, but in the remaining binary and ternary complexes, they are chlorine- or bromine-shared halogen bonds. For a given nitrogen base, the P···N pnicogen bond in the ternary complex FCl:PH₃:N-base appears to be stronger than that bond in FBr:PH₃:N-base, which is stronger than the P···N bond in the corresponding ClCl:PH₃:N-base complex. EOM-CCSD spin-spin coupling constants for the binary and ternary complexes with ClCl and FCl are also consistent with the changing nature of the halogen bonds in these complexes. At long P-Cl distances, the coupling constant ^1xJ(P-Cl) increases with decreasing distance but then decreases as the P-Cl distance continues to decrease, and the halogen bonds become chlorine-shared bonds. At the shorter distances, ^1xJ(P-Cl) approaches the value of ¹J(P-Cl) for the cation ⁺(Cl-PH₃). The coupling constants ^1pJ(P-N) are small and, with one exception, are greater in ClCl:PH₃:N-base complexes compared to that in FCl:PH₃:N-base, despite the shorter P-N distances in the latter.

Highly Selective Halide Receptors Based on Chalcogen, Pnicogen, and Tetrel Bonds

The interactions of halides with a number of bipodal receptors were examined by quantum chemical methods. The receptors were based on a dithieno thiophene framework in which two S atoms can engage in a pair of chalcogen bonds with a halide. These two S atoms were replaced by P and As atoms to compare chalcogen with pnicogen bonding, and by Ge which engages in tetrel bonds with the receptor. Zero, one, and two O atoms were added to the thiophene S atom which is not directly involved in the interaction with the halides. Fluoride bound the most strongly, followed by Cl^- , Br^- , and I^- , respectively. Replacing S by the pnicogen bonds of P strengthened the binding, as did moving down to As in the third row of the periodic table. A further large increment is associated with the switch to the tetrel bonds of Ge. Even though the thiophene S atom is remote from the binding site, each additional O atom added to it raises the binding energy, which can be quite large, as much as 63 kcal mol^-1 for the Ge⋅⋅⋅F^- interaction. The receptors have a pronounced selectivity for F^- over the other halides, as high as 27 orders of magnitude. The data suggest that incorporation of tetrel atoms may lead to new and more powerful halide receptors.

A comparative interplay between small heterorings and hypofluorous acids

Through the B3LYP/6-311++G(d,p) calculations, theoretical studies of structural parameters, electronic properties, infrared vibration modes, and charge density topologies on the C2H4O∙∙∙HX and C2H5N∙∙∙HX (X = F or O-F) heterocylic hydrogen complexes are presented. The H-bond distances and high energies point out strong contacts and stable interactions in these complexes, and the relationships between the frequency shifts on the H-F and H-O bonds as well as O-F σ-holes with the interaction strength are the benchmarks of this current work. The computations of charge transfer amounts in light of the ChelpG and NBO approaches revealed a separation of charge density on the O-F σ-holes, whose statement is reinforced by the QTAIM descriptors. Despite that O∙∙∙H and N∙∙∙H H-bonds have been characterized as closed-shell interactions, qualitatively the appearance of a partial covalent profile also was unveiled by the QTAIM protocol.