Bonding Schemes

BONDING SCHEMES

Bond formation between atoms occurs primarily to enable each atom to achieve an inert gas electron configuration in the valence level (a valence octet for all elements except hydrogen which requires only two electrons to achieve the electronic configuration of helium). An atom can achieve an inert-gas electronic configuration by giving up electrons, accepting electrons, or sharing electrons with another atom. An ionic bond is formed when one atom gives up one or more electrons to reach an octet electronic configuration (as a positively charged ion) and a second atom accepts one or more electrons to reach an octet electronic configuration (as a negatively charged ion). For example, the reaction of a cesium atom with a fluorine atom occurs by the transfer of an electron from the cesium atom to the chlorine atom. By doing so, both cesium and chlorine have reached a valence octet electron configuration. The cesium atom has been converted to a positively charged cesium ion with the octet electronic configuration of xenon, and the chlorine has been converted to a negatively charged chloride ion with the octet electronic configuration of argon. The “bond” between cesium and chlorine is due to the electrostatic attraction of the cesium and chloride ions.

The reaction of potassium metal with tert-butanol gives an ionic bond between the tert-butoxy anion and a potassium cation by transfer of electrons from potas-sium to the hydroxyl functional group. Hydrogen is evolved as a by-product. By losing an electron, potassium gains the octet electronic configuration of argon, oxygen has an octet structure (three lone pairs and one pair of shared electrons), and hydrogen has the electronic configuration of helium. (Based on functional group behavior, any other alcohol is predicted to react with potassium in the same way — and they do!)

Most bonds in organic molecules, however, are covalent bonds in which elec-trons are shared between two atoms. Sharing electrons is a way to enable each atom of the bonded pair to reach an octet electronic configuration without having to give up or gain an electron. Covalent bonds are formed by the overlap of singly occupied AOs to form new MOs that contain a pair of electrons. Each atom in essence gains an electron by sharing. The reaction of a chlorine atom with a fluorine atom occurs by the overlap of a singly occupied 3p orbital of chlorine with a singly occupied 2p orbital of fluorine to give a bond between the two atoms that contains two electrons. This is shown both by using Lewis structures and by using orbital pictures. The type of bond formed is called a σ bond because the region of greatest electron density falls on the internuclear axis.

This simple picture is adequate for many diatomic molecules with univa-lent atoms, but it is not sufficient to describe the bonding in most polyatomic molecules. In addition to electron sharing to reach octet electronic configura-tions, other considerations such as the number of bonds to an atom, the number of electron pairs that are shared between two bonded atoms, and repulsion ener-gies that are present between electron pairs require some modification of the picture. These factors can be rationalized by the idea that valence shell atomic orbitals (2s and 2p’s) can combine to form hybrid AOs. These hybrid AOs over-lap with AOs of other atoms in the usual fashion to form covalent bonds. Hybrid AOs have energies, shapes, and geometries which are intermediate between the atomic orbitals from which they are formed. Hybridization of AOs is an out-growth of bond formation that enables atoms to derive the greatest amount of bond energy from electron sharing and to allow bonded atoms to achieve octet electronic configurations.

If four single bonds and/or electron pairs originate from a single atom, then the s orbital and the three p orbitals of the valence shell combine to form four equivalent sp³ hybrid orbitals that are then used in bond formation to other atoms. Depending on the number of electrons in the valence shell of the atom, these sp³ hybrid orbitals can contain either a single unpaired electron which can be shared with another atom by overlap and bond formation or an unshared pair of electrons which is normally not involved in bond formation. Thus alkanes, which have all single bonds, have carbon atoms which are sp³ hybridized. For example, methane has four single C–H bonds originating at carbon, and these bonds are σ bonds produced by the overlap of four sp³ hybrid orbitals of carbon with four 1s AOs of four hydrogens to give four sp³ – 1s σ bonds from carbon to hydrogen. The geometry of the four equivalent sp³ hybrid orbitals (and hence the compound produced by overlap with these orbitals) is tetrahedral. Thus methane has four equivalent C–H σ bonds which point toward the corners of a regular tetrahedron and have H–C–H bond angles of 109.5^◦ :

In a similar fashion each carbon of propane is sp³ hybridized and tetrahedral since each carbon has four single bonds to other atoms originating from it. For example, the central carbon of propane has two equivalent sp³ – 1s C–H σ bonds and two equivalent sp³ – sp³ C–C σ bonds. (Note that sp³ orbitals from one carbon can overlap with sp³ orbitals from another carbon to produce carbon – carbon bonds.) The geometry is very close to tetrahedral, but the C–C–C bond angle is slightly larger (111^◦ ) to accommodate the bigger CH₃ groups.

Other first-row elements can also be sp³ hybridized. The only requirement is that they have a combination of four single bonds and/or electron pairs originating from a single element. Ammonia, which has three N–H bonds and a lone pair on nitrogen, is thus sp³ hybridized and has three equivalent sp³ – 1s N–H σ bonds and a lone pair which occupies an sp³ hybrid orbital. The geometry is close to tetrahedral with an H–N–H bond angle of 107^◦ . Other amines also have sp³-hybridized nitrogen and are close to a tetrahedral geometry around the nitrogen atom.

The oxygen atom in the water molecule has two bonds and two lone pairs so it too is sp³ hybridized. There are two equivalent sp³ – 1s O–H σ bonds and two lone pairs occupying sp³-hybridized orbitals. Electron – electron repulsions of the lone pairs cause greater distortions from a true tetrahedral geometry so that the H–O–H bond angle is 105^◦ . Other singly bonded oxygen functional groups such as alcohols, ethers, and acetals have sp³-hybridized oxygens and nearly tetrahedral geometries.

Second-row elements such as silicon, phosphorus, and sulfur can also have sp³ hybridization of the valence shell orbitals, although hybridization is not necessar-ily required for second-row elements. When second-row elements do hybridize, however, the 3s and 3p AOs combine to form the sp³ hybrid orbitals. Tetra-methylsilane, the standard reference for nuclear magnetic resonance (NMR) spec-tra, has tetrahedral geometry and thus sp³ hybridization of the 3s and 3p valence shell orbitals of silicon. Dimethyl sulfone has nearly tetrahedral bond angles, indi-cating that the sulfur is sp³ hybridized. Although formal charges are present, the two bonds to oxygen can be thought to arise by the overlap of a filled sp³ orbital on sulfur with an unfilled sp³ orbital on oxygen. The resulting σ bond is called a coordinate covalent, or dative, bond because both of the shared electrons in the bond come from only one of the bonded elements. Hydrogen sulfide has an H–S–H bond angle of 92^◦ , which indicates that sulfur is not hybridized in this compound.

When two pairs of electrons are shared between two elements, a different bonding arrangement is required to enable the atoms to reach valence octet elec-tron configurations. Because of the Pauli exclusion principle, only one sigma bond is possible between any two atoms because only one pair of electrons can occupy the space along the internuclear axis. The second pair of electrons that is shared by the two atoms must therefore be located in space someplace other than along the internuclear axis. The second pair of shared electrons is located in a different type of covalent bond, a π bond, which has electron density found on either side of the internuclear axis. The π bonding results from the parallel overlap (or sideways overlap) of atomic p orbitals. To accommodate the need for a singly occupied atomic p orbital available for the formation of a π bond, hybridization of the valence AOs takes place between the s orbital and two of the three p atomic orbitals. Hybridization of one s and two p AOs produces three equivalent sp² hybrid AOs and a p orbital remains unhybridized in order to produce a π bond.

This bonding scheme permits two pairs of electrons to be shared between two atoms so that each pair occupies a different region of space and does not violate the Pauli exclusion principle. Since only two p orbitals are used in the hybridization and they are orthogonal and define a plane, the sp²-hybridized carbon is planar with bond angles of 120^◦ . The remaining p orbital, which is left unhybridized to form the π bond, is perpendicular to the molecular plane. Once formed, the π bond keeps the entire system rigid and planar, because rotation of one end of the π -bonded system relative to the other end requires that the π bond be broken.

Elements other than carbon are also sp² hybridized if they share two electron pairs with another atom. Thus imines have sp²-hybridized nitrogen (and carbon) to account for formation of the C–N double bond. The lone pair on nitrogen occupies an sp² hybrid orbital. The bond angles are all 120^◦ around both carbon and nitrogen since both are sp² hybridized. Similar considerations hold for the oxygen atom of carbonyl groups of all kinds. The two unshared pairs of electrons on oxygen both occupy sp² orbitals. The interorbital angle is 120^◦ , as expected for trigonal hybridization.

The sharing of three pairs of electrons between two atoms can be accomplished by extrapolation of the above considerations. That is, since there can only be one σ bond connecting the atoms, then the other two pairs of shared electrons must be in two different π bonds, each of which is formed by the parallel overlap of a p orbital. Furthermore the π bonds must be mutually orthogonal so as not to violate the Pauli exclusion principle. Hybridization of one s orbital and one p orbital gives two equivalent sp hybrid AOs which are linearly opposite to one another.

The two remaining p atomic orbitals, which are mutually orthogonal, are used to produce two orthogonal π bonds. The geometry of triply bonded systems is thus linear about the triple bond.

Similar considerations apply to the triply bonded nitrogen found in nitriles. The sp-hybridized carbon and nitrogen atoms form an sp – sp σ bond and two 2p – 2p π bonds between carbon and nitrogen. The unshared pair on nitrogen occupies an sp hybrid orbital.

Another instance where sp hybridization is required occurs in molecules with cumulated double bonds such as allenes, ketenes, and carbodiimides. The end atoms of the cumulated units are sp² hybridized because each shares two electron pairs with another element (the central carbon) and there is a σ and a π bond. The structure, however, requires that two π bonds originate from the central carbon — one π bond going toward one end of the cumulated system, the other π bond going toward the other end. Thus two 2p AOs are required for π bonding from the central carbon and sp hybridization is appropriate. Consequently the geometry is linear at the middle atom and trigonal at the end atoms. A further consequence of the orthogonal π bonds is that planar bonds originating at the end carbons lie in two orthogonal planes with a dihedral angle of 90^◦ . (A dihedral angle is the angle made by two intersecting planes.)

Besides providing a theoretical framework by which the structure, geometry, and octet structure of bonded elements can be explained and understood, the concept of hybridization also predicts the ordering of stabilities and energies of bonds and the energy of lone pairs of electrons in hybrid orbitals. Because s AOs are of lower energy than p AOs, hybrid orbitals with a greater proportion of s character should be more stable and thus form stronger bonds. Unshared pairs of electrons in hybrid orbitals with greater s character should also be of lower energy (more stable). As the percentage of s character of hybrid orbitals increases in the order sp³ – 25% s character < sp² – 33% s character < sp – 50% s character, it is found that the strength of bonds formed by overlap with those orbitals increases in a parallel fashion. For example, the bond dissociation ener-gies of primary C–H bonds have been measured and fall in the order that is predicted by the percentage of s character of the hybrid orbitals on carbon: sp³ C–H, 105 kcal/mol; sp² C–H, 111 kcal/mol; and sp C–H, 133 kcal/mol. Elec-tron pairs are more stable in orbitals with more s character; thus the acidities of primary C–H bonds are found to be sp³ C–H, pK_a = 50; sp² C–H, pK_a = 44; and sp C–H, pK_a = 25. This is due to the fact that the anions formed by pro-ton removal give carbanions that have the negative charge in sp³, sp², and sp orbitals, respectively. Because the lone pair is more stable in an orbital of greater s character, the anion formed by removal of an sp C–H proton is more sta-ble (and hence the proton is more easily removed) than the anion formed by removal of an sp² C–H proton, which in turn is more stable (and hence the proton is more easily removed) than the anion formed by removal of an sp³ C–H proton. Other examples of the effects of greater s character in orbitals are encountered routinely.

The concept of hybridization of AOs to give new hybrid AOs involved in the bonding patterns of atoms is a useful and practical way to describe the way in which functional groups are constructed. It provides a rationale for the structure as well as the geometry and electron distribution in functional groups and molecules in which they are found. It can also be used to predict reactivity patterns of functional groups based on these considerations.