Halogen bonding: the σ-hole

Halogen bonding refers to the non-covalent interactions of halogen atoms X in some molecules, RX, with negative sites on others. It can be explained by the presence of a region of positive electrostatic potential, the σ-hole, on the outermost portion of the halogen’s surface, centered on the R–X axis. We have carried out a natural bond order B3LYP analysis of the molecules CF₃X, with X = F, Cl, Br and I. It shows that the Cl, Br and I atoms in these molecules closely approximate the configuration, where the z-axis is along the R–X bond. The three unshared pairs of electrons produce a belt of negative electrostatic potential around the central part of X, leaving the outermost region positive, the σ-hole. This is not found in the case of fluorine, for which the combination of its high electronegativity plus significant sp-hybridization causes an influx of electronic charge that neutralizes the σ-hole. These factors become progressively less important in proceeding to Cl, Br and I, and their effects are also counteracted by the presence of electron-withdrawing substituents in the remainder of the molecule. Thus a σ-hole is observed for the Cl in CF₃Cl, but not in CH₃Cl. Figure Schematic representation of the atomic charge generation. The molecular electrostatic potential (MEP) is calculated using the AM1* Hamiltonian. The semiempirical MEP is then scaled to DFT or ab initio level and atomic charges are generated from it by the restrained electrostatic potential (RESP) fit method.     

Expansion of the σ-hole concept

The term “σ-hole” originally referred to the electron-deficient outer lobe of a half-filled p (or nearly p) orbital involved in forming a covalent bond. If the electron deficiency is sufficient, there can result a region of positive electrostatic potential which can interact attractively (noncovalently) with negative sites on other molecules (σ-hole bonding). The interaction is highly directional, along the extension of the covalent bond giving rise to the σ-hole. σ-Hole bonding has been observed, experimentally and computationally, for many covalently-bonded atoms of Groups V–VII. The positive character of the σ-hole increases in going from the lighter to the heavier (more polarizable) atoms within a Group, and as the remainder of the molecule becomes more electron-withdrawing. In this paper, we show computationally that significantly positive σ-holes, and subsequent noncovalent interactions, can also occur for atoms of Group IV. This observation, together with analogous ones for the molecules (H₃C)₂SO, (H₃C)₂SO₂ and Cl₃PO, demonstrates a need to expand the interpretation of the origins of σ-holes: (1) While the bonding orbital does require considerable p character, in view of the well-established highly directional nature of σ-hole bonding, a sizeable s contribution is not precluded. (2) It is possible for the bonding orbital to be doubly-occupied and forming a coordinate covalent bond. Figure Two views of the calculated electrostatic potential on the 0.001 au molecular surface of SiCl₄. Color ranges, in kcal/mole, are: purple, negative; blue, between 0 and 8; green, between 8 and 11; yellow, between 11 and 18; red, more positive than 18. The top view shows three of the four chlorines. In the center is the σ-hole due to the fourth Cl−Si bond, its most positive portion (red) being on the extension of that bond. In the bottom view are visible two of the σ-holes on the silicon. In both views can be seen the σ-holes on the chlorines, on the extensions of the Si−Cl bonds; their most positive portions are green     

Discovery of σ-hole interactions involving ylides

The positive electrostatic potentials (σ-hole) have been found in ylides CH₂XH₃ (X = P, As, Sb) and CH₂YH₂ (Y = S, Se, Te), on the outer surfaces of group VA and VIA atoms, approximately along the extensions of the C–X and C–Y bonds, respectively. These electrostatic potentials suggest that the above ylides can interact with nucleophiles to form weak, directional noncovalent interactions similar to halogen bonding interactions. MP2 calculations have confirmed the formation of CH₂XH₃···HM complexes (X = P, As, Sb; M = BeH, ZnH, MgH, Li, Na). The interaction energies, interaction distances, topological properties (electron density and its Laplacian), and energy properties (kinetic electron energy density and potential electron energy density) at the X(1)···H(10) bond critical points are all correlated with the most negative electrostatic potential value of HM, indicating that electrostatic interactions play an important role in these weak X···H interactions. Similar to the halogen bonding interactions, weak interactions involving ylides may be significant in several areas such as organic synthesis, crystal engineering, and design of new materials.     

σ-hole bonding between like atoms; a fallacy of atomic charges

Covalently bonded atoms, at least in Groups V–VII, may have regions of both positive and negative electrostatic potentials on their surfaces. The positive regions tend to be along the extensions of the bonds to these atoms; the origin of this can be explained in terms of the σ-hole concept. It is thus possible for such an atom in one molecule to interact electrostatically with its counterpart in a second, identical molecule, forming a highly directional noncovalent bond. Several examples are presented and discussed. Such “like-like” interactions could not be understood in terms of atomic charges assigned by any of the usual procedures, which view a bonded atom as being entirely positive or negative. Figure Calculated electrostatic potential on the surface of SCl₂. The sulfur is in the foreground, the chlorines are at the back. Color ranges (kcal mol⁻¹): purple negative, blue between 0 and 8, green between 8 and 15, yellow between 15 and 20, red more positive than 20. Note that the sulfur has regions of both positive (red) and negative (purple) electrostatic potential     

Polarization-induced σ-holes and hydrogen bonding

The strong collinear polarizability of the A-H bond in A-H···B hydrogen bonds is shown to lead to an enhanced σ-hole on the donor hydrogen atom and hence to stronger hydrogen bonding. This effect helps to explain the directionality of hydrogen bonds, the well known cooperative effect in hydrogen bonding, and the occurrence of blue-shifting. The latter results when significant additional electron density is shifted into the A-H bonding region by the polarization effect. The shift in the A-H stretching frequency is shown to depend essentially linearly on the calculated atomic charge on the donor hydrogen for all donors in which A belongs to the same row of the periodic table. A further result of the polarization effect, which is also expected for other σ-hole bonds, is that the strength of the non-covalent interaction depends strongly on external electric fields.     

Theoretical description of halogen bonding – an insight based on the natural orbitals for chemical valence combined with the extended-transition-state method (ETS-NOCV)

In the present study we have characterized the halogen bonding in selected molecules H₃N–ICF₃ (1-NH ₃ ), (PH₃)₂C–ICF₃ (1-CPH ₃ ), C₃H₇Br–(IN₂H₂C₃)₂C₆H₄ (2-Br), H₂–(IN₂H₂C₃)₂C₆H₄ (2-H ₂ ) and Cl–(IC₆F₅)₂C₇H₁₀N₂O₅ (3-Cl), containing from one halogen bond (1-NH ₃ , 1-CPH ₃ ) up to four connections in 3-Cl (the two Cl–HN and two Cl–I), based on recently proposed ETS-NOCV analysis. It was found based on the NOCV-deformation density components that the halogen bonding C–X ^… B (X-halogen atom, B-Lewis base), contains a large degree of covalent contribution (the charge transfer to X ^… B inter-atomic region) supported further by the electron donation from base atom B to the empty σ*(C–X) orbital. Such charge transfers can be of similar importance compared to the electrostatic stabilization. Further, the covalent part of halogen bonding is due to the presence of σ-hole at outer part of halogen atom (X). ETS-NOCV approach allowed to visualize formation of the σ-hole at iodine atom of CF₃I molecule. It has also been demonstrated that strongly electrophilic halogen bond donor, [C₆H₄(C₃H₂N₂I)₂][OTf]₂, can activate chemically inert isopropyl bromide (2-Br) moiety via formation of Br–I bonding and bind the hydrogen molecule (2-H ₂ ). Finally, ETS-NOCV analysis performed for 3-Cl leads to the conclusion that, in terms of the orbital-interaction component, the strength of halogen (Cl–I) bond is roughly three times more important than the hydrogen bonding (Cl–HN).

Enhancing effects of hydrogen/halogen bonds on σ-hole interactions involving ylide

PqsD mediates the conversion of anthraniloyl-coenzyme A (ACoA) to 2-heptyl-4-hydroxyquinoline (HHQ), a precursor of the Pseudomonas quinolone signal (PQS) molecule. Due to the role of the quinolone signaling pathway of Pseudomonas aeruginosa in the expression of several virulence factors and biofilm formation, PqsD is a potential target for controlling this nosocomial pathogen, which exhibits a low susceptibility to standard antibiotics. PqsD belongs to the β-ketoacyl-ACP synthase family and is similar in structure to homologous FabH enzymes in E. coli and Mycobacterium tuberculosis. Here, we used molecular dynamics simulations to obtain the structural position of the substrate ACoA in the binding pocket of PqsD, and semiempirical molecular orbital calculations to study the reaction mechanism for the catalytic cleavage of ACoA. Our findings suggest a nucleophilic attack of the deprotonated sulfur of Cys112 at the carbonyl carbon of ACoA and a switch in the protonation pattern of His257 whereby N_δ is protonated and the proton of N_ε is shifted to the sulfur of CoA during the reaction. This is in agreement with the experimentally determined decreased catalytic activity of the Cys112Ser mutant, whereas the Cys112Ala, His257Phe, and Asn287Ala mutants are all inactive. ESI mass-spectrometric measurements of the Asn287Ala mutant show that anthraniloyl remains covalently bound to Cys112, thus further supporting the inference from our computed mechanism that Asn287 does not take part in the cleavage of ACoA. Since this mutant is inactive, we suggest instead that Asn287 must play an essential role in the subsequent formation of HHQ in vitro.     

σ-hole bonding: molecules containing group VI atoms

It has been observed both experimentally and computationally that some divalently-bonded Group VI atoms interact in a noncovalent but highly directional manner with nucleophiles. We show that this can readily be explained in terms of regions of positive electrostatic potential on the outer surfaces of such atoms, these regions being located along the extensions of their existing covalent bonds. These positive regions can interact attractively with the lone pairs of nucleophiles. The existence of such a positive region is attributed to the presence of a “σ-hole.” This term designates the electron-deficient outer lobe of a half-filled p bonding orbital on the Group VI atom. The positive regions become stronger as the electronegativity of the atom decreases and its polarizability increases, and as the groups to which it is covalently bonded become more electron-withdrawing. We demonstrate computationally that the σ-hole concept and the outer regions of positive electrostatic potential account for the existence, directionalities and strengths of the observed noncovalent interactions. Figure Calculated B3PW91/6-31G** electrostatic potential of F₂S, computed on the 0.001 electrons/bohr³ contour of the electronic density. The sulfur atom is toward the reader; the red areas indicate the most positive potentials, reaching +34.4 kcal/mole, along the extensions of the F-S bonds. The purple region (negative) on the left and the one (not totally visible) on the right side of the sulfur are due to its nonbonded s and p electrons. The fluorines (top left and bottom left) also have negative regions of potential (purple areas)     

Blue shifts <Emphasis Type="Italic">vs</Emphasis> red shifts in σ-hole bonding

σ-Hole bonding is a noncovalent interaction between a region of positive electrostatic potential on the outer surface of a Group V, VI, or VII covalently-bonded atom (a σ-hole) and a region of negative potential on another molecule, e.g., a lone pair of a Lewis base. We have investigated computationally the occurrence of increased vibration frequencies (blue shifts) and bond shortening vs decreased frequencies (red shifts) and bond lengthening for the covalent bonds to the atoms having the σ-holes (the σ-hole donors). Both are possible, depending upon the properties of the donor and the acceptor. Our results are consistent with models that were developed earlier by Hermansson and by Qian and Krimm in relation to blue vs red shifting in hydrogen bond formation. These models invoke the derivatives of the permanent and the induced dipole moments of the donor molecule. Figure Computed electrostatic potential on the molecular surface of Cl-NO₂. Color ranges, in kcal mol⁻¹, are: red, greater than 25; yellow, between 10 and 25; green, between 0 and 10; blue, between −4 and 0; purple, more negative than −4. The chlorine is facing the viewer, to the right. Note the yellow region of positive potential on the outer side of the chlorine, along the extension of the N–Cl bond. The blue region shows the sides of the chlorine to have negative potentials. The calculations were at the B3PW91/6–31G(d,p) level.     

The protonated 2-halogenated imidazolium cation as the noncovalent interaction donor: the σ-hole and π-hole interactions

The σ-hole and π-hole of the protonated 2-halogenated imidazolium cation (XC₃H₄N₂ ⁺; X = F, Cl, Br, I) were investigated and analyzed. The monomers of (CH₃)₃SiY(Y=F, Cl, Br, I), considered as the Lewis base, were combined with the σ-hole and π-hole of XC₃H₄N₂ ⁺ to form the σ-hole and π-hole interactions in the bimolecular complexes (CH₃)₃SiY?·?·?·?XC₃H₄N₂ ⁺ and (CH₃)₃SiY?·?·?·?C₃(X)H₄N₂ ⁺(X/Y=F, Cl, Br, I), respectively. For both the σ-hole and π-hole interactions, the equilibrium geometries of complexes show regular changes according to the sequence of heavy sequence of the noncovalent interaction acceptors and donors. The electrostatic energy is the main contribution in the formation of both kinds of interactions, it has linear relations with the V _S,max values of σ-hole and the V′ _S,max values of π-hole. Both the σ-hole and π-hole interactions belong to the closed-shell and noncovalent interactions. The π-hole interactions are stronger than the σ-hole interactions. For the π-hole interactions, the contribution percents of the dispersion energies are somewhat greater than those of the σ-hole interactions, while it is contrary for the polarization energy.

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Graphical Abstract The protonated 2-halogenated imidazolium cation as the noncovalent interaction donor: the σ-hole and π-hole interactions?

     

Stimulation of σ1 Receptors Alleviates Reperfusion-Induced Myocardial Stunning

In vivo or in vitro administration of a ₁ receptor agonist d-SKF 10.047 (1 mg/kg intravenously or 10 mg/l in vitro) promoted an increase in the resistance of isolated perfused rat heart to ischemia/reperfusion injury. Both in vivo and in vitro stimulation of receptors prevents the development of reperfusion contracture and creatine kinase release and increases the developed pressure, double product, +dP/dt, and –dP/dt in the left ventricle. Activation of receptors has no significant effect on the occurrence of reperfusion arrhythmias ex vivo. Stimulation of cardiac sigma receptors is proposed to prevent myocardial stunning.     

Effect of structural modification in the amine portion of substituted aminobutyl-benzamides as ligands for binding σ1 and σ2 receptors

5-Bromo-N-[4-(6,7-dimethoxy-3,4-dihydro-1H-isoquinolin-2-yl)-butyl)]-2,3-dimethoxy-benzamide (1) is one of the most potent and selective σ(2) receptor ligands reported to date. A series of new analogs, where the amine ring fused to the aromatic ring was varied in size (5-7) and the location of the nitrogen in this ring was modified, has been synthesized and assessed for their σ(1)/σ(2) binding affinity and selectivity. The binding affinity of an open-chained variant of 1 was also evaluated. Only the five-membered ring congener of 1 displayed a higher σ(1)/σ(2) selectivity, derived from a higher σ(2) affinity and a lower σ(1) affinity. Positioning the nitrogen adjacent to the aromatic ring in the five-membered and six-membered ring congeners dramatically decreased affinity for both subtypes. Thus, location of the nitrogen within a constrained ring is confirmed to be key to the exceptional σ(2) receptor binding affinity and selectivity for this active series.     

Neural mechanisms of mother–infant bonding and pair bonding: Similarities,differences, and broader implications

This article is part of a Special Issue “Parental Care”.Mother–infant bonding is a characteristic of virtually all mammals. The maternal neural system may have provided the scaffold upon which other types of social bonds in mammals have been built. For example, most mammals exhibit a polygamous mating system, but monogamy and pair bonding between mating partners occur in ~ 5% of mammalian species. In mammals, it is plausible that the neural mechanisms that promote mother–infant bonding have been modified by natural selection to establish the capacity to develop a selective bond with a mate during the evolution of monogamous mating strategies. Here we compare the details of the neural mechanisms that promote mother–infant bonding in rats and other mammals with those that underpin pair bond formation in the monogamous prairie vole. Although details remain to be resolved, remarkable similarities and a few differences between the mechanisms underlying these two types of bond formation are revealed. For example, amygdala and nucleus accumbens–ventral pallidum (NA–VP) circuits are involved in both types of bond formation, and dopamine and oxytocin actions within NA appear to promote the synaptic plasticity that allows either infant or mating partner stimuli to persistently activate NA–VP attraction circuits, leading to an enduring social attraction and bonding. Further, although the medial preoptic area is essential for maternal behavior, its role in pair bonding remains to be determined. Our review concludes by examining the broader implications of this comparative analysis, and evidence is provided that the maternal care system may have also provided the basic neural foundation for other types of strong social relationships, beyond pair bonding, in mammals, including humans.