RESONANCE - ATOMIC ORBITALS (ESPECIALLY FOR IITJEE)
RESONANCE......ATOMIC ORBITALS....ONLY FOR IITResonance
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.
| 1) sulfur dioxide |  |
|
| 2) nitric acid |
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 composed of such molecules often show exceptional stability.
| 3) formaldehyde |  |
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 basic principles of the resonance method may now be summarized.
For a given compound, a set of Lewis / Kekulé structures are written, keeping the relative positions of all the component atoms the same. These are the canonical forms to be considered, and all must have the same number of paired and unpaired electrons.
The following factors are important in evaluating the contribution each of these canonical structures makes to the actual molecule.
For a given compound, a set of Lewis / Kekulé structures are written, keeping the relative positions of all the component atoms the same. These are the canonical forms to be considered, and all must have the same number of paired and unpaired electrons.
The following factors are important in evaluating the contribution each of these canonical structures makes to the actual molecule.
- The number of covalent bonds in a structure. (The greater the bonding, the more important and stable the contributing structure.)
- Formal charge separation. (Other factors aside, charge separation decreases the stability and importance of the contributing structure.)
- Electronegativity of charge bearing atoms and charge density. (High charge density is destabilizing. Positive charge is best accommodated on atoms of low electronegativity, and negative charge on high electronegative atoms.)
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).
| 4) carbon monoxide |  |
|
| 5) azide anion |
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 more important than 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 left most structure). The bottom row pair of structures have four bonds, but are destabilized by the high charge density on a single nitrogen atom.
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.
Orbitals |
|---|
Atomic and Molecular Orbitals
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. Very nice displays of orbitals may be found at the following sites:
J. Gutow, Univ. Wisconsin Oshkosh
R. Spinney, Ohio State
M. Winter, Sheffield University
J. Gutow, Univ. Wisconsin Oshkosh
R. Spinney, Ohio State
M. Winter, Sheffield University
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.
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.
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 (?) 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.
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 (?) 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 ?-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 ? 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 ?-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 p-orbitals in this model are represented by red and blue colored spheres, 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.
