On the Uselessness of Bond Paths Linking Distant Atoms and on the Violation of the Concept of Privileged Exchange Channels

Extraction of uranyl from spent nuclear fuel wastewater via complexation-a local vibrational mode study

CONTEXT

The efficient extraction of uranyl from spent nuclear fuel wastewater for subsequent reprocessing and reuse is an essential effort toward minimization of long-lived radioactive waste. N-substituted amides and Schiff base ligands are propitious candidates, where extraction occurs via complexation with the uranyl moiety. In this study, we extensively probed chemical bonding in various uranyl complexes, utilizing the local vibrational modes theory alongside QTAIM and NBO analyses. We focused on (i) the assessment of the equatorial O-U and N-U bonding, including the question of chelation, and (ii) how the strength of the axial U = O bonds of the uranyl moiety changes upon complexation. Our results reveal that the strength of the equatorial uranium-ligand interactions correlates with their covalent character and with charge donation from O and N lone pairs into the vacant uranium orbitals. We also found an inverse relationship between the covalent character of the equatorial ligand bonds and the strength of the axial uranium-oxygen bond. In summary, our study provides valuable data for a strategic modulation of N-substituted amide and Schiff base ligands towards the maximization of uranyl extraction.

METHOD

Quantum chemistry calculations were performed under the PBE0 level of theory, paired with the relativistic NESCau Hamiltonian, currently implemented in Cologne2020 (interfaced with Gaussian16). Wave functions were expanded in the cc-pwCVTZ-X2C basis set for uranium and Dunning's cc-pVTZ for the remaining atoms. For the bonding properties, we utilized the package LModeA in the local modes analyses, AIMALL in the QTAIM calculations, and NBO 7.0 for the NBO analyses.

σ-Hole Site-Based Interactions within Hypervalent Pnicogen, Halogen, and Aerogen-Bearing Molecules with Lewis Bases: A Comparative Study

σ-Hole site-based interactions in the trigonal bipyramidal geometrical structure of hypervalent pnicogen, halogen, and aerogen-bearing molecules with pyridine and NCH Lewis bases (LBs) were comparatively examined. In this respect, the ZF5···, XF3O2···, and AeF2O3···LB complexes (where Z = As, Sb; X = Br, I; Ae = Kr, Xe; and LB = pyridine and NCH) were investigated. The electrostatic potential (EP) analysis affirmations outlined the occurrence of σ-holes on the systems under consideration with disparate magnitudes that increased according to the following order: AeF2O3 < XF3O2 < ZF5. In line with EP outcomes, the proficiency of σ-hole site-based interactions increased as the atomic size of the central atom increased with a higher favorability for the pyridine-based complexes over NCH-based ones. The interaction energy showed the most favorable negative values of -35.97, -44.53, and -56.06 kcal/mol for the XeF2O3···, IF3O2···, and SbF5···pyridine complexes, respectively. The preferentiality pattern of the studied interactions could be explained as a consequence of (i) the dramatic rearrangement of ZF5 molecules from the trigonal bipyramid geometry to the square pyramidal one, (ii) the significant and tiny deformation energy in the case of the interaction of XF3O2 molecules with pyridine and NCH, respectively, and (iii) the absence of geometrical deformation within the AeF2O3···pyridine and ···NCH complexes other than the XeF2O3···pyridine one. Quantum theory of atoms in molecules and noncovalent interaction index findings reveal the partially covalent nature of most of the investigated interactions. Symmetry-adapted perturbation theory affirmations declared that the electrostatic component was the driving force beyond the occurrence of the considered interactions. The obtained findings will help in improving our understanding of the effect of geometrical deformation on intermolecular interactions.

Revealing the Role of Noncovalent Interactions on the Conformation of the Methyl Group in Tricyclic Orthoamide

Tricyclic orthoamides are valuable molecules with wide-ranging applications, including organic synthesis and molecular recognition. Their structural properties make them intriguing, particularly the eclipsed all-trans conformer, which is typically less stable than the alternated conformation and is a rare phenomenon in organic chemistry. However, it gains stability in crystalline and hydrated settings, challenging the existing theoretical explanations. This study investigates which factors make eclipsed conformers more stable using experimentally reported anhydrous (ATO) and hydrated (HTO) crystal structures. Employing the quantum theory of atoms in molecules, noncovalent interaction index, and pairwise energy decomposition analysis, we delve into the noncovalent interaction environment surrounding the molecule of interest. In ATO, dispersive interactions dominate, whereas in HTO, both dispersive and electrostatic contributions are observed due to the presence of water molecules. Anchored to the lone pairs of the nitrogen atom in the orthoamide tricycle, water molecules prompt the methyl group's eclipsing through intermolecular and intramolecular interactions. This work resolves the long-standing conflict behind why tricyclic orthoamide has an eclipsed conformation by establishing the stabilization factors. These insights have implications for crystal engineering and design, enhancing our understanding of structural behavior in both crystalline and hydrated environments.

Double Centrosymmetric Si···π Tetrel Bonds as New Synthons─Evidence from Crystal Structures and DFT Calculations

The crystal structure of bis((μ2-ethynylsilyloxo)-dichloro-aluminum), BEDCA, and a few related structures are characterized by the occurrence of tetrel bonds that link molecules. Particularly, centosymmetric dimers in such structures occur that are connected by two equivalent Si···π tetrel bonds. The dimer of BEDCA and dimers of other model species that similarly are linked by two equivalent Si···π tetrel bonds are analyzed theoretically. Some of the complexes calculated here are also characterized by the occurrence of triel bonds. Thus, ωB97XD/aug-cc-pVTZ calculations are performed and these DFT results are further supported by calculations with the use of other theoretical approaches: the quantum theory of atoms in molecules, QTAIM; the natural bond orbital, NBO; the energy decomposition analysis, EDA; and the noncovalent interactions method, NCI. The results show that the tetrel bonds analyzed here are rather weak, and they are not detected by the QTAIM approach; however, they are detected by other approaches, like NBO, for example. On the other hand, the triel bonds that occur in a few complexes discussed here are very strong and possess characteristics of covalent bonds.

Halide Complexes of 5,6-Dicyano-2,1,3-Benzoselenadiazole with 1 : 4 Stoichiometry: Cooperativity between Chalcogen and Hydrogen Bonding

The [M4 -Hal]- (M=the title compound; Hal=Cl, Br, and I) complexes were isolated in the form of salts of [Et4 N]+ cation and characterized by XRD, NMR, UV-Vis, DFT, QTAIM, EDD, and EDA. Their stoichiometry is caused by a cooperative interplay of σ-hole-driven chalcogen (ChB) and hydrogen (HB) bondings. In the crystal, [M4 -Hal]- are connected by the π-hole-driven ChB; overall, each [Hal]- is six-coordinated. In the ChB, the electrostatic interaction dominates over orbital and dispersion interactions. In UV-Vis spectra of the M+[Hal]- solutions, ChB-typical and [Hal]- -dependent charge-transfer bands are present; they reflect orbital interactions and allow identification of the individual [Hal]- . However, the structural situation in the solutions is not entirely clear. Particularly, the UV-Vis spectra of the solutions are different from the solid-state spectra of the [Et4 N]+ [M4 -Hal]- ; very tentatively, species in the solutions are assigned [M-Hal]- . It is supposed that the formation of the [M4 -Hal]- proceeds during the crystallization of the [Et4 N]+ [M4 -Hal]- . Overall, M can be considered as a chromogenic receptor and prototype sensor of [Hal]- . The findings are also useful for crystal engineering and supramolecular chemistry.

Bader's Topological Bond Path Does Not Necessarily Indicate Stabilizing Interaction-Proof Studies Based on the Ng@[3n]cyclophane Endohedral Complexes

According to Bader's quantum theory of atoms in molecules (QTAIM), the simultaneous presence of a bond path and the corresponding bond critical point between any two atoms is both a necessary and sufficient condition for the atoms to be bonded to one another. In principle, this means that this pair of atoms should make a stabilizing contribution to the molecular system. However, the multitude of so-called counterintuitive bond paths strongly suggests that this statement is not necessarily true. Particularly 'troublesome' are endohedral complexes, in which encapsulation-enforced proximity between the trapped guest (e.g., an atom) and the host's cage system usually 'produces' many counterintuitive bond paths. In the author's opinion, the best evidence to demonstrate the repulsive nature of the intra-cage guest⋯host interaction is the use of some trapping systems containing small escape channels and then showing that the initially trapped entity spontaneously escapes outside the host's cage during geometry optimization of the initially built guest@host endohedral complex. For this purpose, a group of 24 Ng@[3n]cyclophane (3≤n≤6) endohedral complexes is used. As a result, arguments are presented showing that Bader's topological bond path does not necessarily indicate a stabilizing interaction.

Insights into structural, spectroscopic, and hydrogen bonding interaction patterns of nicotinamide-oxalic acid (form I) salt by using experimental and theoretical approaches

In the present work, nicotinamide-oxalic acid (NIC-OXA, form I) salt was crystallized by slow evaporation of an aqueous solution. To understand the molecular structure and spectroscopic properties of NIC after co-crystallization with OXA, experimental infrared (IR), Raman spectroscopic signatures, X-ray powder diffraction (XRPD), and differential scanning calorimetry (DSC) techniques were used to characterize and validate the salt. The density functional theory (DFT) methodology was adopted to perform all theoretical calculations by using the B3LYP/6-311++G (d, p) functional/basis set. The experimental geometrical parameters were matched in good correlation with the theoretical parameters of the dimer than the monomer, due to the fact of covering the nearest hydrogen bonding interactions present in the crystal structure of the salt. The IR and Raman spectra of the dimer showed the red (downward) shifting and broadening of bands among (N15-H16), (N38-H39), and (C13=O14) bonds of NIC and (C26=O24), (C3=O1), and (C26=O25) groups of OXA, hence involved in the formation of NIC-OXA salt. The atoms in molecules (AIM) analysis revealed that (N8-H9···O24) is the strongest (conventional) intermolecular hydrogen bonding interaction in the dimer model of salt with the maximum value of interaction energy -12.1 kcal mol-1. Furthermore, the natural bond orbital (NBO) analysis of the Fock matrix showed that in the dimer model, the (N8-H9···O24) bond is responsible for the stabilization of the salt with an energy value of 13.44 kcal mol-1. The frontier molecular orbitals (FMOs) analysis showed that NIC-OXA (form I) salt is more reactive and less stable than NIC, as the energy gap of NIC-OXA (form I) salt is less than that of NIC. The global and local reactivity descriptor parameters were calculated for the monomer and dimer models of the salt. The electrophilic, nucleophilic, and neutral reactive sites of NIC, OXA, monomer, and dimer models of salt were visualized by plotting the molecular electrostatic potential (MESP) surface. The study provides valuable insights into combining both experimental and theoretical results that could define the physicochemical properties of molecules.

The Ultrashort Spike-Ring Interaction in Substituted Iron Maiden Molecules

The in forms of molecular iron maidens are known for their unique ultrashort interaction between the apical hydrogen atom or its small substituent and the surface of the benzene ring. It is generally believed that this forced ultrashort X⋯π contact is associated with high steric hindrance, which is responsible for specific properties of iron maiden molecules. The main aim of this article is to investigate the influence of significant charge enrichment or depletion of the benzene ring on the characteristics of the ultrashort C-X⋯π contact in iron maiden molecules. For this purpose, three strongly electron-donating (-NH2) or strongly electron-withdrawing (-CN) groups were inserted into the benzene ring of in-[34,10][7]metacyclophane and its halogenated (X = F, Cl, Br) derivatives. It is shown that, despite such extremely electron-donating or electron-accepting properties, the considered iron maiden molecules surprisingly reveal quite high resistance to changes in electronic properties.

Dihydrogen Bonding-Seen through the Eyes of Vibrational Spectroscopy

In this work, we analyzed five groups of different dihydrogen bonding interactions and hydrogen clusters with an H3+ kernel utilizing the local vibrational mode theory, developed by our group, complemented with the Quantum Theory of Atoms-in-Molecules analysis to assess the strength and nature of the dihydrogen bonds in these systems. We could show that the intrinsic strength of the dihydrogen bonds investigated is primarily related to the protonic bond as opposed to the hydridic bond; thus, this should be the region of focus when designing dihydrogen bonded complexes with a particular strength. We could also show that the popular discussion of the blue/red shifts of dihydrogen bonding based on the normal mode frequencies is hampered from mode-mode coupling and that a blue/red shift discussion based on local mode frequencies is more meaningful. Based on the bond analysis of the H3+(H2)n systems, we conclude that the bond strength in these crystal-like structures makes them interesting for potential hydrogen storage applications.

Synthesis and Crystal Structure of Adamantylated 4,5,6,7-Tetrahalogeno-1H-benzimidazoles Novel Multi-Target Ligands (Potential CK2, M2 and SARS-CoV-2 Inhibitors); X-ray/DFT/QTAIM/Hirshfeld Surfaces/Molecular Docking Study

A series of new congeners, 1-[2-(1-adamantyl)ethyl]-1H-benzimidazole (AB) and 1-[2-(1-adamantyl)ethyl]-4,5,6,7-tetrahalogeno-1H-benzimidazole (Hal=Cl, Br, I; tClAB, tBrAB, tIAB), have been synthesized and studied. These novel multi-target ligands combine a benzimidazole ring known to show antitumor activity and an adamantyl moiety showing anti-influenza activity. Their crystal structures were determined by X-ray, while intermolecular interactions were studied using topological Bader's Quantum Theory of Atoms in Molecules, Hirshfeld Surfaces, CLP and PIXEL approaches. The newly synthesized compounds crystallize within two different space groups, P-1 (AB and tIAB) and P2₁/c (tClAB and tBrAB). A number of intramolecular hydrogen bonds, C-H⋯Hal (Hal=Cl, Br, I), were found in all halogen-containing congeners studied, but the intermolecular C-H⋯N hydrogen bond was detected only in AB and tIAB, while C-Hal⋯π only in tClAB and tBrAB. The interplay between C-H⋯N and C-H⋯Hal hydrogen bonds and a shift from the strong (C-H⋯Cl) to the very weak (C-H⋯I) attractive interactions upon Hal exchange, supplemented with Hal⋯Hal overlapping, determines the differences in the symmetry of crystalline packing and is crucial from the biological point of view. The hypothesis about the potential dual inhibitor role of the newly synthesized congeners was verified using molecular docking and the congeners were found to be pharmaceutically attractive as Human Casein Kinase 2, CK2, inhibitors, Membrane Matrix 2 Protein, M2, blockers and Severe Acute Respiratory Syndrome Coronavirus 2, SARS-CoV-2, inhibitors. The addition of adamantyl moiety seems to broaden and modify the therapeutic indices of the 4,5,6,7-tetrahalogeno-1H-benzimidazoles.

Nature and Strength of Weak O⋅⋅⋅O Interactions in Nitryl Halide Dimers

The use of real space functions and molecular graphs has pushed some chemists to wonder: Are interactions between negatively charged oxygen atoms possible? In this contribution we analyze whether there is a real interaction between oxygen atoms in nitryl halide dimers (XNO₂ )₂ (X=F, Cl, Br and I) and in tetranitromethane and derivatives. Based on ab-initio and density functional theories (DFT) methods, we show these complexes are weakly stabilized. Energy decomposition analyses based on local molecular orbitals (LMOEDA) and interacting quantum atoms (IQA) reveal both dispersion and exchange play a crucial role in the stabilization of these complexes. Electron charge density and IQA analyses indicate that the oxygen atoms are connected by privileged exchange channels. In addition, electrostatic interactions between O and N atoms are also vital for the stabilization of the complexes. Finally, a reasonable explanation is given for the dynamic behavior of nitryl groups in tetranitromethane and derivatives.

Nature of Beryllium, Magnesium, and Zinc Bonds in Carbene⋯MX2 (M = Be, Mg, Zn; X = H, Br) Dimers Revealed by the IQA, ETS-NOCV and LED Methods

The nature of beryllium−, magnesium− and zinc−carbene bonds in the cyclopropenylidene⋯MX2 (M = Be, Mg, Zn; X = H, Br) and imidazol-2-ylidene⋯MBr2 dimers is investigated by the joint use of the topological QTAIM-based IQA decomposition scheme, the molecular orbital-based ETS-NOCV charge and energy decomposition method, and the LED energy decomposition approach based on the state-of-the-art DLPNO-CCSD(T) method. All these methods show that the C⋯M bond strengthens according to the following order: Zn < Mg << Be. Electrostatics is proved to be the dominant bond component, whereas the orbital component is far less important. It is shown that QTAIM/IQA underestimates electrostatic contribution for zinc bonds with respect to both ETS-NOCV and LED schemes. The σ carbene→MX2 donation appears to be much more important than the MX2→ carbene back-donation of π symmetry. The substitution of hydrogen atoms by bromine (X in MX2) strengthens the metal−carbene bond in all cases. The physical origin of rotational barriers has been unveiled by the ETS-NOCV approach.

Non-covalent interactions from a Quantum Chemical Topology perspective

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter’s role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

The physical nature of the ultrashort spike-ring interaction in iron maiden molecules

The so-called 'iron maiden' molecules belong to one of the most interesting subgroups of cyclophanes due to the presence of the ultrashort interaction between the CX apical bond and the benzene ring. This article presents an in-depth theoretical study of 16 'iron maiden' molecules, in which X = H, F, Cl or Br and the side chains are of various lengths and types: CSC, CSCC, CCC, and CCCC. It is shown that the H → F → Cl → Br substitution leads to a significant expansion of the 'iron maiden' molecule. Shorter chains lead to more pronounced effects, while insertion of sulfur atoms into the side chains lowers them. Structural changes are associated with an increase in energetic destabilization of X. Moreover, unlike for H, in the case of X = halogen, the out → in isomerization is energetically disadvantageous. The 'iron maiden' molecules are characterized by the presence of only three X⋯C_Ar bond paths. Particularly noteworthy are unusually large (even up to 32) values of the X⋯C_Ar bond ellipticity, which results from flat electron density distribution. The X⋯π interaction in each of the investigated 'iron maiden' molecule turned out to be multi-center, stabilizing and almost purely covalent in nature as indicated by the definitely dominant percentage (94.8%-101.6%) of the exchange-correlation energy. The spatial hindrance within the 'iron maiden' molecules appears to be not so much due to the X⋯π repulsion, but due to unfavorable steric interactions between X and the CC side bonds. It is also confirmed that some CH⋯HC interactions in aliphatic chains can be very weakly stabilizing.

Determining Repulsion in Cyclophane Cages

Superphane, i.e., [2.2.2.2.2.2](1,2,3,4,5,6)cyclophane, is a very convenient molecule in studying the nature of guest⋯host interactions in endohedral complexes. Nevertheless, the presence of as many as six ethylene bridges in the superphane molecule makes it practically impossible for the trapped entity to escape out of the superphane cage. Thus, in this article, I have implemented the idea of using the superphane derivatives with a reduced number of ethylene linkers, which leads to the [2n] cyclophanes where n<6. Seven such cyclophanes are then allowed to form endohedral complexes with noble gas (Ng) atoms (He, Ne, Ar, Kr). It is shown that in the vast majority of cases, the initially trapped Ng atom spontaneously escapes from the cyclophane cage, creating an exohedral complex. This is the best proof that the Ng⋯cyclophane interaction in endohedral complexes is indeed highly repulsive, i.e., destabilizing. Apart from the ‘sealed’ superphane molecule, endohedral complexes are only formed in the case of the smallest He atom. However, it has been shown that in these cases, the Ng⋯cyclophane interaction inside the cyclophane cage is nonbonding, i.e., repulsive. This highly energetically unfavorable effect causes the cyclophane molecule to ‘swell’.

Endo- and exohedral complexes of superphane with cations

Quite recently it has been shown in a previous study that superphane, that is, [2.2.2.2.2.2](1,2,3,4,5,6)cyclophane, is a very convenient molecule in the study of endohedral complexes and especially in the study of the influence of the caged entity (i.e., guest) on the structure of the host molecule. This advantage results from the presence of two parallel benzene rings joined together by six quite flexible ethylene bridges (spacers). This article examines the energetic and structural properties of endo- and exohedral complexes of superphane with the following cations: H⁺ , Li⁺ , Na⁺ , K⁺ , Be²⁺ , Mg²⁺ , Ca²⁺ , B³⁺ , Al³⁺ , Ga³⁺ . The stability of endohedral complexes has been shown to be strongly dependent on the charge and radius of the caged cation. The inclusion of the cation inside the superphane molecule causes its 'swelling', which is manifested by an increase in the distance between the benzene rings and elongations of the ring and spacer C-C bonds. In the case of exohedral complexes, three forms are investigated: with the cation above the benzene ring, with the cation interacting with the superphane window in the equatorial position, and with the cation interacting with the center of the C-C spacer bond. The first of these forms has been shown to be preferred. The cation⋯acceptor distance depends on the cation radius. Among the cations investigated, H⁺ and Be²⁺ are particularly reactive and predisposed to induce significant structural changes in the superphane molecule, forming C-H bond or C-Be-C bridges, respectively.

Does the Presence of a Bond Path Really Mean Interatomic Stabilization? The Case of the Ng@Superphane (Ng = He, Ne, Ar, and Kr) Endohedral Complexes

Using a fairly structurally flexible and, therefore, very suitable for this type of research, superphane molecule, we demonstrate that the inclusion of a noble gas atom (Ng = He, Ne, Ar, and Kr) inside it and, thus, the formation of the Ng@superphane endohedral complex, leads to its ‘swelling’. Positive values of both the binding and strain energies prove that encapsulation and in turn ‘swelling’ of the superphane molecule is energetically unfavorable and that the Ng⋯C interactions in the interior of the cage are destabilizing, i.e., repulsive. Additionally, negative Mayer Bond Orders indicate the antibonding nature of Ng⋯C contacts. This result in combination with the observed Ng⋯C bond paths shows that the presence of a bond path in the molecular graph does not necessarily prove interatomic stabilization. It is shown that the obtained conclusions do not depend on the computational methodology, i.e., the method and the basis set used. However, on the contrary, the number of bond paths may depend on the methodology. This is yet another disadvantageous finding that does not favor the treatment of bond paths on molecular graphs as indicators of chemical bonds. The Kr@superphane endohedral complex features one of the longest C–C bonds ever reported (1.753 Å).

Interaction between favipiravir and hydroxychloroquine and their combined drug assessment: in silico investigations

Hydroxychloroquine (HCQ) and favipiravir (FPV) are known to be effective antivirals, and there are reports about their use to fight the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) despite that these are not conclusive. The use of combined drugs is common in drug discovery, and thus, we investigated HCQ and FPV as a combined drug. The density functional theory method was used for the optimization of geometries, spectroscopic analysis and calculation of reactivity parameters. The quantum theory of atoms in molecules was applied to explain the nature of the hydrogen bonds and confirm the higher stability of the combined drug. We also evaluated the absorption, distribution, metabolism and excretion (ADME) parameters to assess their drug actions jointly using SwissADME. The preliminary findings of our theoretical study are promising for further investigations of more potent and selective antiviral drugs.

Theoretical Study of N-Heterocyclic-Carbene-ZnX2 (X = H, Me, Et) Complexes

This article discusses the properties of as many as 30 carbene–ZnX2 (X = H, Me, Et) complexes featuring a zinc bond C⋯Zn. The group of carbenes is represented by imidazol-2-ylidene and its nine derivatives (labeled as IR), in which both hydrogen atoms of N-H bonds have been substituted by R groups with various spatial hindrances, from the smallest Me, iPr, tBu through Ph, Tol, and Xyl to the bulkiest Mes, Dipp, and Ad. The main goal is to study the relationship between type and size of R and X and both the strength of C⋯Zn and the torsional angle of the ZnX2 plane with respect to the plane of the imidazol-2-ylidene ring. Despite the considerable diversity of R and X, the range of dC⋯Zn is quite narrow: 2.12–2.20 Å. On the contrary, D0 is characterized by a fairly wide range of 18.5–27.4 kcal/mol. For the smallest carbenes, the ZnX2 molecule is either in the plane of the carbene or is only slightly twisted with respect to it. The twist angle becomes larger and more varied with the bulkier R. However, the value of this angle is not easy to predict because it results not only from the presence of steric effects but also from the possible presence of various interatomic interactions, such as dihydrogen bonds, tetrel bonds, agostic bonds, and hydrogen bonds. It has been shown that at least some of these interactions may have a non-negligible influence on the structure of the IR–ZnX2 complex. This fact should be taken into account in addition to the commonly discussed R⋯X steric repulsion.

Methyl groups as widespread Lewis bases in noncovalent interactions

It is well known that, under certain conditions, C(sp³) atoms behave, via their σ-hole, as Lewis acids in tetrel bonding. Here, we show that methyl groups, when bound to atoms less electronegative than carbon, can counterintuitively participate in noncovalent interactions as electron density donors. Thousands of experimental structures are found in which methyl groups behave as Lewis bases to establish alkaline, alkaline earth, triel, tetrel, pnictogen, chalcogen and halogen bonds. Theoretical calculations confirm the high directionality and significant strength of the interactions that arise from a common pattern based on the electron density holes model. Moreover, despite the absence of lone pairs, methyl groups are able to transfer charge from σ bonding orbitals into empty orbitals of the electrophile to reinforce the attractive interaction.

Evidence of C-F···H-C Attractive Interaction: Enforced Coplanarity of a Tetrafluorophenylene-Ethynylene-Linked Porphyrin Dimer

The formation of C-F···H-C "hydrogen bonds" has been a controversial subject because, in principle, fluorine is hardly an acceptor for less acidic protons contrasting to the C-F···H-O and C-F···H-N hydrogen bonds. Nevertheless, the interaction is emerging as a powerful implement for confining the torsional rotation in the design of fully coplanar π-conjugated polymers. Heretofore, no evidence of the C-F···H-C interaction has been observed in solutions. We herein disclose comprehensive evidence that the C-F···H-C interaction produces an attractive force. A ¹⁹F-¹H heteronuclear Overhauser effect experiment elucidated the close proximity of the F and H atoms in the doubly edge-facing C-F···H-C interactions of a meso-tetrafluorophenylene-ethynylene-conjugated porphyrin dimer (1). Extensive electronic and photophysical property investigations confirmed that all the aromatic units were torsionally restricted by the C-F···H-C interactions. Moreover, the enforced coplanarity invoked a markedly high π-staking propensity. Thus, we have firmly established the formation of a C-F···H-C interaction that produces a hydrogen-bond-like attractive force in solution.

Noncovalent bond between tetrel π-hole and hydride

The π-hole above the plane of the X2T'Y molecule (T' = Si, Ge, Sn; X = F, Cl, H; Y = O, S) was allowed to interact with the TH hydride of TH(CH3)3 (T = Si, Ge, Sn). The resulting THT' tetrel bond is quite strong, with interaction energies exceeding 30 kcal mol-1. F2T'O engages in the strongest such bonds, as compared to F2T'S, Cl2T'O, or Cl2T'S. The bond weakens as T' grows larger as in Si > Ge > Sn, despite the opposite trend in the depth of the π-hole. The reverse pattern of stronger tetrel bond with larger T is observed for the Lewis base TH(CH3)3, even though the minimum in the electrostatic potential around the H is nearly independent of T. The THT' arrangement is nonlinear which can be understood on the basis of the positions of the extrema in the molecular electrostatic potentials of the monomers. The tetrel bond is weakened when H2O forms an OT' tetrel bond with the second π-hole of F2T'O, and strengthened if H2O participates in an OHO H-bond.

Focal Point Evaluation of Energies for Tautomers and Isomers for 3-Hydroxy-2-Butenamide: Evaluation of Competing Internal Hydrogen Bonds of Types -OH…O=, -OH…N, -NH…O=, and CH…X (X=O and N)

The title compound is a small molecule with many structural variations; it can illustrate a variety of internal hydrogen bonds, among other noncovalent interactions. Here we examine structures displaying hydrogen bonding between carbonyl oxygen and hydroxyl H; between carbonyl oxygen and amino H; hydroxyl H and amino N; hydroxyl O and amino H. We also consider H-bonding in its tautomer 2-oxopropanamide. By extrapolation algorithms applied to Hartree-Fock and correlation energies as estimated in HF, MP2, and CCSD calculations using the cc-pVNZ correlation-consistent basis sets (N = 2, 3, and 4) we obtain reliable relative energies of the isomeric forms. Assuming that such energy differences may be attributed to the presence of the various types of hydrogen bonding, we attempt to infer relative strengths of types of H-bonding. The Atoms in Molecules theory of Bader and the Local Vibrational Modes analysis of Cremer and Kraka are applied to this task. Hydrogen bonds are ranked by relative strength as measured by local stretching force constants, with the stronger =O…HO- > NH…O= > -OH…N well separated from a cluster > NH…O= ≈ >NH…OH ≈ CH…O= of comparable and intermediate strength. Weaker but still significant interactions are of type CH…N which is stronger than CH…OH.

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.

External electric field effects on the σ-hole and lone-pair hole interactions of group V elements: a comparative investigation

σ-hole and lone-pair (lp) hole interactions of trivalent pnicogen-bearing (ZF3) compounds were comparatively scrutinized, for the first time, under field-free and external electric field (EEF) conditions. Conspicuously, the sizes of the σ-hole and lp-hole were increased by applying an EEF along the positive direction, while the sizes of both holes decreased through the reverse EEF direction. The MP2 energetic calculations of ZF3⋯FH/NCH complexes revealed that σ-holes exhibited more impressive interaction energies compared to the lp-holes. Remarkably, the strengths of σ-hole and lp-hole interactions evolved with the increment of the positive value of the considered EEF; i.e., the interaction energy increased as the utilized EEF value increased. Unexpectedly, under field-free conditions, nitrogen-bearing complexes showed superior strength for their lp-hole interactions than phosphorus-bearing complexes. However, the reverse picture was exhibited for the interaction energies of nitrogen- and phosphorus-bearing complexes interacting within lp-holes by applying the high values of a positively directed EEF. These results significantly demonstrate the crucial influence of EEF on the strength of σ-hole and lp-hole interactions, which in turn leads to an omnipresent enhancement for variable fields, including biological simulations and material science.

Towards developing a criterion to characterize non-covalent bonds: a quantum mechanical study

Chemical bonds are central to chemistry, biology, and allied fields, but still, the criterion to characterize an interaction as a non-covalent bond has not been studied rigorously.

A Critical Overview of Current Theoretical Methods of Estimating the Energy of Intramolecular Interactions

This article is probably the first such comprehensive review of theoretical methods for estimating the energy of intramolecular hydrogen bonds or other interactions that are frequently the subject of scientific research. Rather than on a plethora of numerical data, the main focus is on discussing the theoretical rationale of each method. Additionally, attention is paid to the fact that it is very often possible to use several variants of a particular method. Both of the methods themselves and their variants often give wide ranges of the obtained estimates. Attention is drawn to the fact that the applicability of a particular method may be significantly limited by various factors that disturb the reliability of the estimation, such as considerable structural changes or new important interactions in the reference system.

Cooperativity in a cycloalkane-1,2/1,3-polyol corona: Topological hydrogen bonding in 1,2-diol motifs

A corona, consisting of 18 carbon atoms bearing 12 hydroxy groups in a continuous hydrogen-bonded chain, is built up by alternating degenerate conformations of alternating alkane-1,2-diol and 1,3-diol motifs. Geometries, proton nuclear magnetic resonance shifts and interaction energies for the dodecahydroxycyclo-octadecane and selected fragments are determined by density functional calculations at the B3LYP/6-311+G(d,p) level. Cooperative effects of O-H⋯O-H bonding are evident from the simple juxtaposition of these two motifs with a common OH group in butane-1,2,4-triol conformers. Bracketing a 1,2-diol motif with two 1,3-diol motifs in hexane-1,3,4,6-tetrol leads to a structure in which the 1,2-diol motif displays a bond critical point for hydrogen bonding. This is associated with enhancement of the shift of the hydrogen-bonded OH proton and of the corresponding H⋯O interaction energy. The full corona has a complete outer ring of O-H⋯O-H bond paths, and an inner ring of bond paths, due to C-H⋯H-C hydrogen-hydrogen bonding, which result in a central ring critical point. The topological O-H⋯O-H hydrogen bond, never seen in simple alkane-1,2-diols, is associated with cooperative enhancement of the H⋯O interaction energy, but this is not a necessary condition for a bond path: values for topological C-H⋯H-C hydrogen-hydrogen bonds can be as low as -0.4 kcal mol^-1 .

Versatility of the Cyano Group in Intermolecular Interactions

Several cyano groups are added to an alkane, alkene, and alkyne group so as to construct a Lewis acid molecule with a positive region of electrostatic potential in the area adjoining these substituents. Although each individual cyano group produces only a weak π-hole, when two or more such groups are properly situated, they can pool their π-holes into one much more intense positive region that is located midway between them. A NH3 base is attracted to this site, where it forms a strong noncovalent bond to the Lewis acid, amounting to as much as 13.6 kcal/mol. The precise nature of the bonding varies a bit from one complex to the next but typically contains a tetrel bond to the C atoms of the cyano groups or the C atoms of the linkage connecting the C≡N substituents. The placement of the cyano groups on a cyclic system like cyclopropane or cyclobutane has a mild weakening effect upon the binding. Although F is comparable to C≡N in terms of electron-withdrawing power, the replacement of cyano by F substituents substantially weakens the binding with NH3.

Interatomic exchange-correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding-integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)-and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.

Molecular Orbitals Support Energy-Stabilizing "Bonding" Nature of Bader's Bond Paths

Our MO-based findings proved a bonding nature of each density bridge (DB, or a bond path with an associated critical point, CP) on a Bader molecular graph. A DB pinpoints universal physical and net energy-lowering processes that might, but do not have to, lead to a chemical bond formation. Physical processes leading to electron density (ED) concentration in internuclear regions of three distinctively different homopolar H,H atom-pairs as well as classical C-C and C-H covalent bonds were found to be exactly the same. Notably, properties of individual MOs are internuclear-region specific as they (i) concentrate, deplete, or do not contribute to ED at a CP and (ii) delocalize electron-pairs through either in- (positive) or out-of-phase (negative) interference. Importantly, dominance of a net ED concentration and positive e^--pairs delocalization made by a number of σ-bonding MOs is a common feature at a CP. This feature was found for the covalently bonded atoms as well as homopolar H,H atom-pairs investigated. The latter refer to a DB-free H,H atom-pair of the bay in the twisted biphenyl (Bph) and DB-linked H,H atom-pairs (i) in cubic Li₄H₄, where each H atom is involved in three highly repulsive interactions (over +80 kcal/mol), and (ii) in a weak attractive interaction when sterically clashing in the planar Bph.

Cooperativity in alkane-1,2- and 1,3-polyols: NMR, QTAIM, and IQA study of O─H… OH and C─H… OH bonding interactions

Proton nuclear magnetic resonance chemical shifts and atom-atom interaction energies for alkanepolyols with 1,2-diol and 1,3-diol repeat units, and for their 1:1 pyridine complexes, are computed by density functional theory calculations. In the 1,3-polyols, based on a tG'Gg' repeat unit, the only important intramolecular hydrogen bonding interactions are O─H^… OH. By quantum theory of atoms in molecules analysis of the electron density, unstable bond and ring critical points are found for such interactions in 1,2-polyols with tG'g repeat units, from butane-1,2,3,4-tetrol onwards and in their pyridine complexes from propane-1,2,3-triol onwards. Several features (OH proton shifts and charges, and interaction energies computed by the interacting quantum atoms approach) are used to monitor the dependence of cooperativity on chain length: This is much less regular in 1,2-polyols than in 1,3-polyols and by most criteria has a higher damping factor. Well defined C─H^… OH interactions are found in butane-1,2,3,4-tetrol and higher members of the 1,2-polyol series, as well as in their pyridine complexes: There is no evidence for cooperativity with O─H^… OH bonding. For the 1,2-polyols, there is a tenuous empirical relationship between the existence of a bond critical point for O─H^… OH hydrogen bonding and the interaction energies of competing exchange channels, but the primary/secondary ratio is always less than unity.

Naphthyl-Fused Phosphepines: Luminescent Contorted Polycyclic P-Heterocycles

This article presents the synthesis of a new family of naphthyl-fused phosphepines through Ni-mediated C-C coupling. Interestingly, the chlorophosphine oxide intermediate shows strong resistance toward oxidation/hydrolysis owing to a combination of steric hindrance and pnictogen interactions. However, it can undergo substitution reactions under specific conditions. The optical/redox properties and the electronic structure of these new π-systems were studied experimentally (UV/Vis absorption, emission, cyclic voltammetry) and computationally (TD-DFT calculations, NICS investigation). Taking advantage of the luminescence of these derivatives, a blue-emitting OLED has been prepared, highlighting that these novel π-conjugated P-heterocycles appear to be promising building blocks for solid-state lighting applications.

Nature of the Interaction of Pyridines with OCS. A Theoretical Investigation

Ab initio calculations were carried out to investigate the interaction between para-substituted pyridines (X-C₅H₄N, X=NH₂, CH₃, H, CN, NO₂) and OCS. Three stable structures of pyridine.OCS complexes were detected at the MP2=full/aug-cc-pVDZ level. The A structure is characterized by N…S chalcogen bonds and has binding energies between −9.58 and −12.24 kJ/mol. The B structure is bonded by N…C tetrel bond and has binding energies between −10.78 and −11.81 kJ/mol. The C structure is characterized by π-interaction and has binding energies between −10.76 and −13.33 kJ/mol. The properties of the systems were analyzed by AIM, NBO, and SAPT calculations. The role of the electrostatic potential of the pyridines on the properties of the systems is outlined. The frequency shift of relevant vibrational modes is analyzed.

Identifying intermolecular atom⋯atom interactions that are not just bonding but also competitive

This highlight criticises the QTAIM method and discusses algorithms for identifying intermolecular interactions that are both bonding and competitive.

Study of the influence of intermolecular interaction on classical and reverse substituent effects in para-substituted phenylboranes

The substituent effect and the reverse substituent effect in para-substituted phenylboranes and the influence of the intermolecular interaction of H⋯B type with either silane or methylsilane on the latter of these effects are extensively studied.

Metal-Halogen Bonding Seen through the Eyes of Vibrational Spectroscopy

Incorporation of a metal center into halogen-bonded materials can efficiently fine-tune the strength of the halogen bonds and introduce new electronic functionalities. The metal atom can adopt two possible roles: serving as halogen acceptor or polarizing the halogen donor and acceptor groups. We investigated both scenarios for 23 metal–halogen dimers trans-M(Y₂)(NC₅H₄X-3)₂ with M = Pd(II), Pt(II); Y = F, Cl, Br; X = Cl, Br, I; and NC₅H₄X-3 = 3-halopyridine. As a new tool for the quantitative assessment of metal–halogen bonding, we introduced our local vibrational mode analysis, complemented by energy and electron density analyses and electrostatic potential studies at the density functional theory (DFT) and coupled-cluster single, double, and perturbative triple excitations (CCSD(T)) levels of theory. We could for the first time quantify the various attractive contacts and their contribution to the dimer stability and clarify the special role of halogen bonding in these systems. The largest contribution to the stability of the dimers is either due to halogen bonding or nonspecific interactions. Hydrogen bonding plays only a secondary role. The metal can only act as halogen acceptor when the monomer adopts a (quasi-)planar geometry. The best strategy to accomplish this is to substitute the halo-pyridine ring with a halo-diazole ring, which considerably strengthens halogen bonding. Our findings based on the local mode analysis provide a solid platform for fine-tuning of existing and for design of new metal–halogen-bonded materials.