If the electron pairs in covalent bonds were donated and shared absolutely evenly there would be no fixed local charges within a molecule. Although this is true for diatomic elements such as H2, N2 and O2, most covalent compounds show some degree of local charge separation, resulting in bond and / or molecular dipoles. A dipole exists when the centers of positive and negative charge distribution do not coincide.
1. Formal Charges
A large local charge separation usually results when a shared electron pair is donated unilaterally. The three Kekulé formulas shown here illustrate this condition.
In the formula for ozone the central oxygen atom has three bonds and a full positive charge while the right hand oxygen has a single bond and is negatively charged. The overall charge of the ozone molecule is therefore zero. Similarly, nitromethane has a positive-charged nitrogen and a negative-charged oxygen, the total molecular charge again being zero. Finally, azide anion has two negative-charged nitrogens and one positive-charged nitrogen, the total charge being minus one. In general, for covalently bonded atoms having valence shell electron octets, if the number of covalent bonds to an atom is greater than its normal valence it will carry a positive charge. If the number of covalent bonds to an atom is less than its normal valence it will carry a negative charge. The formal charge on an atom may also be calculated by the following formula:
2. Polar Covalent Bonds
Because of their differing nuclear charges, and as a result of shielding by inner electron shells, the different atoms of the periodic table have different affinities for nearby electrons. The ability of an element to attract or hold onto electrons is called electronegativity. A rough quantitative scale of electronegativity values was established by Linus Pauling, and some of these are given in the table to the right. A larger number on this scale signifies a greater affinity for electrons. Fluorine has the greatest electronegativity of all the elements, and the heavier alkali metals such as potassium, rubidium and cesium have the lowest electronegativities. It should be noted that carbon is about in the middle of the electronegativity range, and is slightly more electronegative than hydrogen. When two different atoms are bonded covalently, the shared electrons are attracted to the more electronegative atom of the bond, resulting in a shift of electron density toward the more electronegative atom. Such a covalent bond is polar, and will have a dipole (one end is positive and the other end negative). The degree of polarity and the magnitude of the bond dipole will be proportional to the difference in electronegativity of the bonded atoms. Thus a O–H bond is more polar than a C–H bond, with the hydrogen atom of the former being more positive than the hydrogen bonded to carbon. Likewise, C–Cl and C–Li bonds are both polar, but the carbon end is positive in the former and negative in the latter. The dipolar nature of these bonds is often indicated by a partial charge notation (δ+/–) or by an arrow pointing to the negative end of the bond.
Although there is a small electronegativity difference between carbon and hydrogen, the C–H bond is regarded as weakly polar at best, and hydrocarbons usually have small molecular dipoles and are considered to be non-polar compounds.
The shift of electron density in a covalent bond toward the more electronegative atom or group can be observed in several ways. For bonds to hydrogen, acidity is one criterion. If the bonding electron pair moves away from the hydrogen nucleus the proton will be more easily transfered to a base (it will be more acidic). A comparison of the acidities of methane, water and hydrofluoric acid is instructive. Methane is essentially non-acidic, since the C–H bond is nearly non-polar. As noted above, the O–H bond of water is polar, and it is at least 25 powers of ten more acidic than methane. H–F is over 12 powers of ten more acidic than water as a consequence of the greater electronegativity difference in its atoms.Electronegativity differences may be transmitted through connecting covalent bonds by an inductive effect. Replacing one of the hydrogens of water by a more electronegative atom increases the acidity of the remaining O–H bond. Thus hydrogen peroxide, HO–O–H, is ten thousand times more acidic than water, and hypochlorous acid, Cl–O–H is one hundred million times more acidic. This inductive transfer of polarity tapers off as the number of transmitting bonds increases, and the presence of more than one highly electronegative atom has a cumulative effect. For example, trifluoro ethanol, CF3CH2–O–H is about ten thousand times more acidic than ethanol, CH3CH2–O–H.
One way in which the shapes of molecules manifest themselves experimentally is through molecular dipole moments. A molecule which has one or more polar covalent bonds may have a dipole moment as a result of the accumulated bond dipoles. In the case of water, we know that the O-H covalent bond is polar, due to the different electronegativities of hydrogen and oxygen. Since there are two O-H bonds in water, their bond dipoles will interact and may result in a molecular dipole which can be measured. The following diagram shows four possible orientations of the O-H bonds.
The bond dipoles are colored magenta and the resulting molecular dipole is colored blue. In the linear configuration (bond angle 180º) the bond dipoles cancel, and the molecular dipole is zero. For other bond angles (120 to 90º) the molecular dipole would vary in size, being largest for the 90º configuration. In a similar manner the configurations of methane (CH4) and carbon dioxide (CO2) may be deduced from their zero molecular dipole moments. Since the bond dipoles have canceled, the configurations of these molecules must be tetrahedral (or square-planar) and linear respectively. The case of methane provides insight to other arguments that have been used to confirm its tetrahedral configuration. For purposes of discussion we shall consider three other configurations for CH4, square-planar, square-pyramidal & triangular-pyramidal. Models of these possibilities may be examined by Clicking Here.
Substitution of one hydrogen by a chlorine atom gives a CH3Cl compound. Since the tetrahedral, square-planar and square-pyramidal configurations have structurally equivalent hydrogen atoms, they would each give a single substitution product. However, in the trigonal-pyramidal configuration one hydrogen (the apex) is structurally different from the other three (the pyramid base). Substitution in this case should give two different CH3Cl compounds if all the hydrogens react. In the case of disubstitution, the tetrahedral configuration of methane would lead to a single CH2Cl2 product, but the other configurations would give two different CH2Cl2 compounds. These substitution possibilities are shown in the models.
Kekulé structural formulas are essential tools for understanding organic chemistry. However, the structures of some compounds and ions cannot be represented by a single formula. For example, sulfur dioxide (SO2) and nitric acid (HNO3) may each be described by two equivalent formulas (equations 1 & 2). For clarity the two ambiguous bonds to oxygen are given different colors in these formulas.
If only one formula for sulfur dioxide was correct and accurate, then the double bond to oxygen would be shorter and stronger than the single bond. Since experimental evidence indicates that this molecule is bent (bond angle 120º) and has equal length sulfur : oxygen bonds (1.432 Å), a single formula is inadequate, and the actual structure resembles an average of the two formulas. This averaging of electron distribution over two or more hypothetical contributing structures (canonical forms) to produce a hybrid electronic structure is called resonance. Likewise, the structure of nitric acid is best described as a resonance hybrid of two structures, the double headed arrow being the unique symbol for resonance.
The above examples represent one extreme in the application of resonance. Here, two structurally and energetically equivalent electronic structures for a stable compound can be written, but no single structure provides an accurate or even an adequate representation of the true molecule. In cases such as these, the electron delocalization described by resonance enhances the stability of the molecules, and compounds or ions incorporating such systems often show exceptional stability.
The electronic structures of most covalent compounds do not suffer the inadequacy noted above. Thus, completely satisfactory Kekulé formulas may be drawn for water (H2O), methane (CH4) and acetylene C2H2). Nevertheless, the principles of resonance are very useful in rationalizing the chemical behavior of many such compounds. For example, the carbonyl group of formaldehyde (the carbon-oxygen double bond) reacts readily to give addition products. The course of these reactions can be explained by a small contribution of a dipolar resonance contributor, as shown in equation 3. Here, the first contributor (on the left) is clearly the best representation of this molecular unit, since there is no charge separation and both the carbon and oxygen atoms have achieved valence shell neon-like configurations by covalent electron sharing. If the double bond is broken heterolytically, formal charge pairs result, as shown in the other two structures. The preferred charge distribution will have the positive charge on the less electronegative atom (carbon) and the negative charge on the more electronegative atom (oxygen). Therefore the middle formula represents a more reasonable and stable structure than the one on the right. The application of resonance to this case requires a weighted averaging of these canonical structures. The double bonded structure is regarded as the major contributor, the middle structure a minor contributor and the right hand structure a non-contributor. Since the middle, charge-separated contributor has an electron deficient carbon atom, this explains the tendency of electron donors (nucleophiles) to bond at this site.
The stability of a resonance hybrid is always greater than the stability of any canonical contributor. Consequently, if one canonical form has a much greater stability than all others, the hybrid will closely resemble it electronically and energetically. This is the case for the carbonyl group (eq.3). The left hand C=O structure has much greater total bonding than either charge-separated structure, so it describes this functional group rather well. On the other hand, if two or more canonical forms have identical low energy structures, the resonance hybrid will have exceptional stabilization and unique properties. This is the case for sulfur dioxide (eq.1) and nitric acid (eq.2).
To illustrate these principles we shall consider carbon monoxide (eq.4) and azide anion (eq.5). In each case the most stable canonical form is on the left. For carbon monoxide, the additional bonding is a more important stabilizing factor than the destabilizing charge separation. Furthermore, the double bonded structure has an electron deficient carbon atom (valence shell sextet). A similar destabilizing factor is present in the two azide canonical forms on the top row of the bracket (three bonds vs. four bonds in the structure on the far left). The bottom row pair of equivalent structures also have four bonds, but are destabilized by the high charge density on a single nitrogen atom. Consequently, azide anion is best written as shown on the left.
Another kind of resonance description is often used when referring to the p-d double-bonding in compounds of third period elements, particularly phosphorous and sulfur. In addition to sulfuric acid and phosphoric acid, the useful reagent compounds shown in the following diagram display this dualism. The formally charged structure on the left of each example obeys the octet rule, whereas the neutral double-bonded structure on the right requires overlap with 3d orbitals.
The approximate shapes of these three compounds are identified under each. The Cl–S–Cl bond angle in thionyl chloride suggests a nearly pure p-orbital bonding, presumably due to the increased s-orbital character of the non-bonding electron pair. This agrees with the roughly tetrahedral angle of this grouping in sulfuryl chloride, which does not have such a feature. The S=O and P=O bond lengths in these compounds also indicate substantial double bond character.
All the examples on this page demonstrate an important restriction that must be remembered when using resonance: No atoms change their positions within the common structural framework. Only electrons are moved.
Hydrocarbons having a molecular formula CnH2n+2, where n is an integer, constitute a relatively unreactive class of compounds called alkanes. The C–C and C–H bonds that make up alkanes are relatively non-polar and inert to most (but not all) of the reagents used by organic chemists. Functional groups are atoms or small groups of atoms (two to four) that exhibit an enhanced characteristic reactivity when treated with certain reagents. A particular functional group will almost always display its characteristic chemical behavior when it is present in a compound. Because of their importance in understanding organic chemistry, functional groups have characteristic names that often carry over in the naming of individual compounds incorporating specific groups. In the following table the atoms of each functional group are colored red and the characteristic IUPAC nomenclature suffix that denotes some (but not all) functional groups is also colored.
Group Formula
The chemical behavior of each of these functional groups constitutes a major part of the study of organic chemistry. Many of the functional groups are polar, and their behavior with polar or ionic reagents can be summarized by the principle: Opposites Attract. This is a well known factor in electrostatics and electromagnetism, and it applies equally well to polar covalent interactions. Since few functional groups are ionic in nature, organic chemists use the terms nucleophile and electrophile more commonly than anionic (negative) and cationic (positive). The following definitions should be remembered.
A more detailed model of covalent bonding requires a consideration of valence shell atomic orbitals. For second period elements such as carbon, nitrogen and oxygen, these orbitals have been designated 2s, 2px, 2py & 2pz. The spatial distribution of electrons occupying each of these orbitals is shown in the diagram below.
The valence shell electron configuration of carbon is 2s2, 2px1, 2py1 & 2pz0. If this were the configuration used in covalent bonding, carbon would only be able to form two bonds.
1. Hybrid Orbitals In order to explain the structure of methane (CH4), the 2s and three 2p orbitals must be converted to four equivalent hybrid atomic orbitals, each having 25% s and 75% p character, and designated sp3. These hybrid orbitals have a specific orientation, and the four are naturally oriented in a tetrahedral fashion.
The hypervalent compounds described earlier and drawn below require 3d-orbital contributions to the bonding hybridization. PCl5 is a trigonal bipyramid created by sp3d hybridization. The octahedral configurations are formed by sp3d2 hybridization. Click on the table to see these shapes.
2. Molecular Orbitals Just as the valence electrons of atoms occupy atomic orbitals (AO), the shared electron pairs of covalently bonded atoms may be thought of as occupying molecular orbitals (MO). It is convenient to approximate molecular orbitals by combining or mixing two or more atomic orbitals. In general, this mixing of n atomic orbitals always generates n molecular orbitals. The hydrogen molecule provides a simple example of MO formation. In the following diagram, two 1s atomic orbitals combine to give a sigma (σ) bonding (low energy) molecular orbital and a second higher energy MO referred to as an antibonding orbital. The bonding MO is occupied by two electrons of opposite spin, the result being a covalent bond.
The notation used for molecular orbitals parallels that used for atomic orbitals. Thus, s-orbitals have a spherical symmetry surrounding a single nucleus, whereas σ-orbitals have a cylindrical symmetry and encompass two (or more) nuclei. In the case of bonds between second period elements, p-orbitals or hybrid atomic orbitals having p-orbital character are used to form molecular orbitals. For example, the sigma molecular orbital that serves to bond two fluorine atoms together is generated by the overlap of p-orbitals (part A below), and two sp3 hybrid orbitals of carbon may combine to give a similar sigma orbital. When these bonding orbitals are occupied by a pair of electrons, a covalent bond, the sigma bond results. Although we have ignored the remaining p-orbitals, their inclusion in a molecular orbital treatment does not lead to any additional bonding, as may be shown by activating the fluorine correlation diagram below.
Another type of MO (the π orbital) may be formed from two p-orbitals by a lateral overlap, as shown in part A of the following diagram. Since bonds consisting of occupied π-orbitals (pi-bonds) are weaker than sigma bonds, pi-bonding between two atoms occurs only when a sigma bond has already been established. Thus, pi-bonding is generally found only as a component of double and triple covalent bonds. Since carbon atoms involved in double bonds have only three bonding partners, they require only three hybrid orbitals to contribute to three sigma bonds. A mixing of the 2s-orbital with two of the 2p orbitals gives three sp2 hybrid orbitals, leaving one of the p-orbitals unused. Two sp2 hybridized carbon atoms are then joined together by sigma and pi-bonds (a double bond), as shown in part B.
The manner in which atomic orbitals overlap to form molecular orbitals is commonly illustrated by a correlation diagram. Two examples of such diagrams for the simple diatomic elements F2 and N2 will be drawn above when the appropriate button is clicked. The 1s and 2s atomic orbitals do not provide any overall bonding, since orbital overlap is minimal, and the resulting sigma bonding and antibonding components would cancel. In both these cases three 2p atomic orbitals combine to form a sigma and two pi-molecular orbitals, each as a bonding and antibonding pair. The overall bonding order depends on the number of antibonding orbitals that are occupied. The subtle change in the energy of the σ2p bonding orbital, relative to the two degenerate π-bonding orbitals, is due to s-p hybridization that is unimportant to the present discussion. An impressive example of the advantages offered by the molecular orbital approach to bonding is found in the oxygen molecule. A molecular orbital diagram for oxygen may be seen by Clicking Here.
A cartoon of the p and π orbitals of a double bond may be examined by Clicking Here. A model of the π orbitals of ethene may be examined by Clicking Here. The p-orbitals in these models are represented by red and blue colored spheres or ellipses, which represent different phases, defined by the mathematical wave equations for such orbitals.
Finally, in the case of carbon atoms with only two bonding partners only two hybrid orbitals are needed for the sigma bonds, and these sp hybrid orbitals are directed 180º from each other. Two p-orbitals remain unused on each sp hybridized atom, and these overlap to give two pi-bonds following the formation of a sigma bond (a triple bond), as shown below.
The various hybridization states of carbon may be examined by Clicking Here.
The following problems explore many of the concepts discussed above. They include formal charges, polar bonds, hybridization, resonance and identification of functional groups. The last entry leads to a large assortment of multiple choice questions