A halogen bond occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity. Comparison between hydrogen and halogen bonding: Hydrogen bonding A ⋯ H − D Halogen bonding A ⋯ X − D In both cases, A is the atom, group, or molecule that donates electrons to the electron poor species H-D or X-D. H is the hydrogen atom involved in hydrogen bonding, X is the halogen atom involved in halogen bonding. Note the halogen bond donor accepts electrons while the halogen bond acceptor donates electrons. A parallel relationship can be drawn between halogen bonding and hydrogen bonding. In both types of bonding, an electron donor/electron acceptor relationship exists; the difference between the two is. In hydrogen bonding, a hydrogen atom acts as the electron acceptor and forms a non-covalent interaction by accepting electron density from an electron rich site.
In halogen bonding, a halogen atom is the electron acceptor. The normal covalent bond between H or X and D weakens, so the electron density on H or X appears to be reduced. Electron density transfers results in a penetration of the van der Waals volumes. Halogens participating in halogen bonding include: iodine, bromine and sometimes fluorine. All four halogens are capable of acting as XB donors and follow the general trend: F < Cl < Br < I, with iodine forming the strongest interactions. Dihalogens tend to form strong halogen bonds; the strength and effectiveness of chlorine and fluorine in XB formation depend on the nature of the XB donor. If the halogen is bonded to an electronegative moiety, it is more to form stronger halogen bonds. For example, iodoperfluoroalkanes are well-designed for XB crystal engineering. In addition, this is why F2 can act as a strong XB donor, but fluorocarbons are weak XB donors because the alkyl group connected to the fluorine is not electronegative. In addition, the Lewis base tends to be electronegative as well and anions are better XB acceptors than neutral molecules.
Halogen bonds are strong and directional interactions that give rise to well-defined structures. Halogen bond strengths range from 5–180 kJ/mol; the strength of XB allows it to compete with HB. Halogen bonds tend to form at 180° angles, shown in Odd Hassel’s studies with bromine and 1,4-dioxane in 1954. Another contributing factor to halogen bond strength comes from the short distance between the halogen and Lewis base; the attractive nature of halogen bonds result in the distance between the donor and acceptor to be shorter than the sum of van der Waals radii. The XB interaction becomes stronger as the distance decreases between Lewis base. In 1814, Jean-Jacques Colin described the formation of a liquid — with a metallic lustre — when he mixed together dry gaseous ammonia and dry iodine; the precise composition of the resulting I2... NH3 complex was established fifty years by Frederick Guthrie. In his experiment, he added I2 to aqueous ammonia; the true nature of the molecular interaction was first understood only half of a century ago following Robert Mulliken's groundbreaking discoveries on charge-transfer interactions, their detailed description by Odd Hassel.
In 1950s, Robert S. Mulliken developed a detailed theory of electron donor-acceptor complexes, classifying them as being outer or inner complexes. Outer complexes were those in which the intermolecular interaction between the electron donor and acceptor were weak and had little charge transfer. Inner complexes have extensive charge redistribution. Mulliken's theory has been used to describe the mechanism by. Around the same time period that Mulliken developed his theory, crystallographic studies performed by Hassel began to emerge and became a turning point in the comprehension of XB formation and its characteristics; the first X-ray crystallography study from Hassel’s group came in 1954. In the experiment, his group was able to show the structure of bromine 1,4-dioxanate using x-ray diffraction techniques; the experiment revealed that a short intermolecular interaction was present between the oxygen atoms of dioxane and bromine atoms. The O−Br distance in the crystal was measured at 2.71 Å, which indicates a strong interaction between the bromine and oxygen atoms.
In addition, the distance is smaller than the sum of the van der Waals radii of bromine. The angle between the O−Br and Br−Br bond is about 180°; this was the first evidence of the typical characteristics found in halogen bond formation and led Hassel to conclude that halogen atoms are directly linked to electron pair donor with a bond direction that coincides with the axes of the orbitals of the lone pairs in the electron pair donor molecule. In 1969, Hassel was awarded the Nobel Prize in Chemistry for his outstanding discovery that halogens can act as electrophilic, electron acceptors, self-assemble into directionally organised crystalline charge-transfer complexes in presence of electron donors. An early review about electron donor-acceptor was provided by Bent in 1968; the use of the term "halogen bond" was not implemented until 1978 by Dumas and
Three-center two-electron bond
A 3-center 2-electron bond is an electron-deficient chemical bond where three atoms share two electrons. The combination of three atomic orbitals form three molecular orbitals: one bonding, one non-bonding, one anti-bonding; the two electrons go into the bonding orbital, resulting in a net bonding effect and constituting a chemical bond among all three atoms. In many common bonds of this type, the bonding orbital is shifted towards two of the three atoms instead of being spread among all three. An example of a 3c–2e bond is the trihydrogen cation H+3; this type of bond is called banana bond. An extended version of the 3c–2e bond model features in cluster compounds described by the polyhedral skeletal electron pair theory, such as boranes and carboranes; these molecules derive their stability from having a filled set of bonding molecular orbitals as outlined by Wade's rules. The monomer BH3 is unstable. A B−H−B 3-center-2-electron bond is formed when a boron atom shares electrons with a B−H bond on another boron atom.
The two electrons in a B−H−B bonding molecular orbital are spread out across three internuclear spaces. In diborane, there are two such 3c-2e bonds: two H atoms bridge the two B atoms, leaving two additional H atoms in ordinary B−H bonds on each B; as a result, the molecule achieves stability since each B participates in a total of four bonds and all bonding molecular orbitals are filled, although two of the four bonds are 3-centre B−H−B bonds. The reported bond order for each B−H interaction in a bridge is 0.5, so that the bridging B−H−B bonds are weaker and longer than the terminal B−H bonds, as shown by the bond lengths in the structural diagram. This bonding pattern is seen in trimethylaluminium, which forms a dimer Al26 with the carbon atoms of two of the methyl groups in bridging positions; this type of bond occurs in carbon compounds, where it is sometimes referred to as hyperconjugation. The first stable subvalent Be complex observed contains a three-center two-electron π-bond that consists of donor-acceptor interactions over the C-Be-C core of a Be-carbene adduct.
Carbocation rearrangement reactions occur through three-center bond transition states. Because the three center bond structures have about the same energy as carbocations, there is virtually no activation energy for these rearrangements so they occur with extraordinarily high rates. Carbonium ions such as ethanium C2H+7 have three-center two-electron bonds; the best known and studied structure of this sort is the 2-Norbornyl cation. Three-center four-electron bond 2-Norbornyl cation Dihydrogen complex
In organic chemistry, a bent bond known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a similar "bent" structure within small ring molecules, such as cyclopropane or as a representation of double or triple bonds within a compound, an alternative to the sigma and pi bond model. Bent bonds are a special type of chemical bonding in which the ordinary hybridization state of two atoms making up a chemical bond are modified with increased or decreased s-orbital character in order to accommodate a particular molecular geometry. Bent bonds are found in strained organic compounds such as cyclopropane and aziridine. In these compounds, it is not possible for the carbon atoms to assume the 109.5° bond angles with standard sp3 hybridization. Increasing the p-character to sp5 makes it possible to reduce the bond angles to 60°. At the same time, the carbon-to-hydrogen bonds gain more s-character.
In cyclopropane, the maximum electron density between two carbon atoms does not correspond to the internuclear axis, hence the name bent bond. In cyclopropane, the interorbital angle is 104°; this bending can be observed experimentally by X-ray diffraction of certain cyclopropane derivatives: the deformation density is outside the line of centers between the two carbon atoms. The carbon–carbon bond lengths are shorter than in a regular alkane bond: 151 pm versus 153 pm. Cyclobutane still has bent bonds. In this molecule, the carbon bond angles are 90° for the planar conformation and 88° for the puckered one. Unlike in cyclopropane, the C–C bond lengths increase rather than decrease. In terms of reactivity, cyclobutane is inert and behaves like ordinary alkanes. An alternative model utilizes semi-localized Walsh orbitals in which cyclopropane is described as a carbon sp2 sigma bonding and in-plane pi bonding system. Critics of the Walsh orbital theory argue that this model does not represent the ground state of cyclopropane as it cannot be transformed into the localized or delocalized descriptions via a unitary transformation.
Two different explanations for the nature of double and triple covalent bonds in organic molecules were proposed in the 1930s. Linus Pauling proposed that the double bond results from two equivalent tetrahedral orbitals from each atom, which came to be called banana bonds or tau bonds. Erich Hückel proposed a representation of the double bond as a combination of a sigma bond plus a pi bond; the Hückel representation is the better-known one, it is the one found in most textbooks since the late-20th century. Both models represent the same total electron density, with the orbitals related by a unitary transformation. We can construct the two equivalent bent bond orbitals h and h' by taking linear combinations h = c1σ + c2π and h' = c1σ – c2π for an appropriate choice of coefficients c1 and c2. In a 1996 review, Kenneth B. Wiberg concluded that "although a conclusive statement cannot be made on the basis of the available information, it seems that we can continue to consider the σ/π and bent-bond descriptions of ethylene to be equivalent."
Ian Fleming goes further in a 2010 textbook, noting that "the overall distribution of electrons is the same" in the two models. The bent bond theory can explain other phenomena in organic molecules. In fluoromethane, for instance, the experimental F–C–H bond angle is 109°, greater than the calculated value; this is because according to Bent's rule, the C–F bond gains p-orbital character leading to high s-character in the C–H bonds, H–C–H bond angles approaching those of sp2 orbitals – e.g. 120° – leaving less for the F–C–H bond angle. The difference is again explained in terms of bent bonds. Bent bonds come into play in the gauche effect, explaining the preference for gauche conformations in certain substituted alkanes and the alkene cis effect associated with some unusually stable alkene cis isomers. NMR experiment
A hydrogen bond is a electrostatic force of attraction between a hydrogen atom, covalently bound to a more electronegative atom or group the second-row elements nitrogen, oxygen, or fluorine —the hydrogen bond donor —and another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor. Such an interacting system is denoted Dn–H···Ac, where the solid line denotes a covalent bond, the dotted line indicates the hydrogen bond. There is general agreement that there is a minor covalent component to hydrogen bonding for moderate to strong hydrogen bonds, although the importance of covalency in hydrogen bonding is debated. At the opposite end of the scale, there is no clear boundary between a weak hydrogen bond and a van der Waals interaction. Weaker hydrogen bonds are known for hydrogen atoms bound to elements such as chlorine; the hydrogen bond is responsible for many of the anomalous physical and chemical properties of compounds of N, O, F. Hydrogen bonds can be intramolecular.
Depending on the nature of the donor and acceptor atoms which constitute the bond, their geometry, environment, the energy of a hydrogen bond can vary between 1 and 40 kcal/mol. This makes them somewhat stronger than a van der Waals interaction, weaker than covalent or ionic bonds; this type of bond can occur in inorganic molecules such as water and in organic molecules like DNA and proteins. Intermolecular hydrogen bonding is responsible for the high boiling point of water compared to the other group 16 hydrides that have much weaker hydrogen bonds. Intramolecular hydrogen bonding is responsible for the secondary and tertiary structures of proteins and nucleic acids, it plays an important role in the structure of polymers, both synthetic and natural. It was recognized that there are many examples of weaker hydrogen bonding involving donor Dn other than N, O, or F and/or acceptor Ac with close to or the same electronegativity as hydrogen. Though they are quite weak, they are ubiquitous and are recognized as important control elements in receptor-ligand interactions in medicinal chemistry or intra-/intermolecular interactions in materials sciences.
Thus, there is a trend of gradual broadening for the definition of hydrogen bonding. In 2011, an IUPAC Task Group recommended a modern evidence-based definition of hydrogen bonding, published in the IUPAC journal Pure and Applied Chemistry; this definition specifies: The hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X–H in which X is more electronegative than H, an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation. Most introductory textbooks still restrict the definition of hydrogen bond to the "classical" type of hydrogen bond characterized in the opening paragraph. A hydrogen atom attached to a electronegative atom is the hydrogen bond donor. C-H bonds only participate in hydrogen bonding when the carbon atom is bound to electronegative substituents, as is the case in chloroform, CHCl3. In a hydrogen bond, the electronegative atom not covalently attached to the hydrogen is named proton acceptor, whereas the one covalently bound to the hydrogen is named the proton donor.
In the donor molecule, the H center is protic. The donor is a Lewis base. Hydrogen bonds are represented as H · · · Y system. Liquids that display hydrogen bonding are called associated liquids; the hydrogen bond is described as an electrostatic dipole-dipole interaction. However, it has some features of covalent bonding: it is directional and strong, produces interatomic distances shorter than the sum of the van der Waals radii, involves a limited number of interaction partners, which can be interpreted as a type of valence; these covalent features are more substantial when acceptors bind hydrogens from more electronegative donors. Hydrogen bonds can vary in strength from weak to strong. Typical enthalpies in vapor include: F−H···:F, illustrated uniquely by HF2−, bifluoride O−H···:N, illustrated water-ammonia O−H···:O, illustrated water-water, alcohol-alcohol N−H···:N, illustrated by ammonia-ammonia N−H···:O, illustrated water-amide HO−H···:OH+3 The strength of intermolecular hydrogen bonds is most evaluated by measurements of equilibria between molecules containing donor and/or acceptor units, most in solution.
The strength of intramolecular hydrogen bonds can be studied with equilibria between conformers with and without hydrogen bonds. The most important method for the identification of hydrogen bonds in complicated molecules is crystallography, sometimes NMR-spectroscopy. Structural details, in particular distances between donor and acceptor which are smaller than the sum of the van der Waals radii can be taken as indication of the hydrogen bond strength. One scheme gives the following somewhat arbitrary classification: those that are 15 to 40 kcal/mol, 5 to 15 kcal/mol, >0 to 5 kcal/mol are considered strong, moder
Agostic interaction is a term in organometallic chemistry for the interaction of a coordinatively-unsaturated transition metal with a C−H bond, when the two electrons involved in the C−H bond enter the empty d-orbital of a transition metal, resulting in a three-center two-electron bond. Many catalytic transformations, e.g. oxidative addition and reductive elimination, are proposed to proceed via intermediates featuring agostic interactions. Agostic interactions are observed throughout organometallic chemistry in alkyl and polyenyl ligands; the term agostic, derived from the Ancient Greek word for "to hold close to oneself", was coined by Maurice Brookhart and Malcolm Green, on the suggestion of the classicist Jasper Griffin, to describe this and many other interactions between a transition metal and a C−H bond. Such agostic interactions involve alkyl or aryl groups that are held close to the metal center through an additional σ-bond. Short interactions between hydrocarbon substituents and coordinatively unsaturated metal complexes have been noted since the 1960s.
For example, in tris ruthenium dichloride, a short interaction is observed between the ruthenium center and a hydrogen atom on the ortho position of one of the nine phenyl rings. Complexes of borohydride are described as using the three-center two-electron bonding model; the nature of the interaction was foreshadowed in main group chemistry in the structural chemistry of trimethylaluminium. Agostic interactions are best demonstrated by crystallography. Neutron diffraction data has shown that C−H and M┄H bond distances are 5-20% longer than expected for isolated metal hydride and hydrocarbons; the distance between the metal and the hydrogen is 1.8–2.3 Å, the M┄H−C angle falls in the range 90°–140°. The presence of a 1H NMR signal, shifted upfield from that of a normal aryl or alkane to the region assigned to hydride ligands; the coupling constant 1JCH is lowered to 70–100 Hz versus the 125 Hz expected for a normal sp3 carbon–hydrogen bond. On the basis of experimental and computational studies, the stabilization arising from an agostic interaction is estimated to be 10–15 kcal/mol.
Recent calculations using compliance constants point to a weaker stabilisation. Thus, agostic interactions are stronger than most hydrogen bonds. Agostic bonds sometimes play a role in catalysis by increasing'rigidity' in transition states. For instance, in Ziegler–Natta catalysis the electrophilic metal center has agostic interactions with the growing polymer chain; this increased rigidity influences the stereoselectivity of the polymerization process. The term agostic is reserved to describe two-electron, three-center bonding interactions between carbon, a metal. Two-electron three-center bonding is implicated in the complexation of H2, e.g. in W32H2, related to the agostic complex shown in the figure. Silane binds to metal centers via agostic-like, three-centered Si┄H−M interactions; because these interactions do not include carbon, they are not classified as agostic. Certain M ┄ H − C interactions are described by the term anagostic. Anagostic interactions are more electrostatic in character.
In terms of structures of anagostic interactions, the M┄H distances and M┄H−C angles fall into the ranges 2.3–2.9 Å and 110°–170°, respectively. Agostic interactions serve a key function in alkene polymerization and stereochemistry, as well as migratory insertion. Agostic interactions
A dimer is an oligomer consisting of two monomers joined by bonds that can be either strong or weak, covalent or intermolecular. The term homodimer is used when the two molecules are heterodimer when they are not; the reverse of dimerisation is called dissociation. When two oppositely charged ions associate into dimers, they are referred to as Bjerrum pairs. Carboxylic acids form dimers by hydrogen bonding of the acidic hydrogen and the carbonyl oxygen when anhydrous. For example, acetic acid forms a dimer in the gas phase, where the monomer units are held together by hydrogen bonds. Under special conditions, most OH-containing molecules form dimers. Borane occurs as the dimer diborane, due to the high Lewis acidity of the boron center. Excimers and exciplexes are excited structures with a short lifetime. For example, noble gases do not form stable dimers, but do form the excimers Ar2*, Kr2* and Xe2* under high pressure and electrical stimulation. Molecular dimers are formed by the reaction of two identical compounds e.g.: 2A → A-A.
In this example, monomer "A" is said to dimerise to give the dimer "A-A". An example is a diaminocarbene, which dimerise to give a tetraaminoethylene: 2 C2 → 2C=C2Carbenes are reactive and form bonds. Dicyclopentadiene is an asymmetrical dimer of two cyclopentadiene molecules that have reacted in a Diels-Alder reaction to give the product. Upon heating, it "cracks" to give identical monomers: C10H12 → 2 C5H6Many nonmetallic elements occur as dimers: hydrogen, oxygen, the halogens, i.e. fluorine, chlorine and iodine. Noble gases can form dimers linked for example dihelium or diargon. Mercury occurs as a mercury cation, formally a dimeric ion. Other metals may form a proportion of dimers in their vapour. Known metallic dimers include Li2, Na2, K2, Rb2 and Cs2. Many small organic molecules, most notably formaldehyde form dimers; the dimer of formaldehyde is dioxetane. In the context of polymers, "dimer" refers to the degree of polymerization 2, regardless of the stoichiometry or condensation reactions.
This is applicable to disaccharides. For example, cellobiose is a dimer of glucose though the formation reaction produces water: 2C6H12O6 → C12H22O11 + H2OHere, the dimer has a stoichiometry different from the pair of monomers. Amino acids can form dimers, which are called dipeptides. An example is glycylglycine. Other examples are carnosine. Pyrimidine dimers are formed by a photochemical reaction from pyrimidine DNA bases; this cross-linking causes DNA mutations, causing skin cancers. Monomer Trimer Polymer Protein dimer "IUPAC "Gold Book" definition". Retrieved 2009-04-30
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length is a rhombus but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a rhomboid; the term rhomboid is now more used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes. Some crystals are formed in three-dimensional rhomboids; this solid is sometimes called a rhombic prism. The term occurs in science terminology referring to both its two- and three-dimensional meaning. Euclid introduced the term in his Elements in Book I, Definition 22, Of quadrilateral figures, a square is that, both equilateral and right-angled, and let quadrilaterals other than these be called trapezia. Euclid never used the definition of rhomboid again and introduced the word parallelogram in Proposition 31 of Book I.
Heath suggests that rhomboid was an older term in use. The rhomboid has no line of symmetry, but it has rotational symmetry of order 2. In biology, rhomboid may describe a geometric rhomboid or a bilaterally-symmetrical kite-shaped or diamond-shaped outline, as in leaves or cephalopod fins. In a type of arthritis called pseudogout, crystals of calcium pyrophosphate dihydrate accumulate in the joint, causing inflammation. Aspiration of the joint fluid reveals rhomboid-shaped crystals under a microscope. Weisstein, Eric W. "Rhomboid". MathWorld