Resonance:

Multiple equivalent structures: resonance

There is a rather large class of molecules for which one has no difficulty writing Lewis structures; in fact, we can write more than one valid structure for a given molecule! Consider, for example, the nitrate ion NO₃^–. We can develop a Lewis dot formula satisfying the octet rule as follows:

Figure 7.66 Resonance of NO₃^–

According to this structure, the ion contains two N–O single bonds and one N–O double bond. But there is no special reason to place the double bond where it is shown in the diagram above; it could equally well go in either of the other two locations. For this molecule, then, we can write three equally valid structures:

Figure 7.67 Resonating structures of NO₃^–

The double-ended arrows indicate that the nitrate ion is a superposition of all three structures, and this is supported by experimental evidence which shows that the three oxygen atoms are chemically identical, that all three bonds have the same length, and that the molecule has trigonal symmetry (meaning that the three oxygens are geometrically equivalent.)

The term resonance was employed to describe this phenomenon in the 1930’s, before chemical bonding became better understood; the three equivalent structures shown above are known as resonance hybrids. The choice of the word “resonance” was unfortunate because it connotes the existence of some kind of dynamic effect that has led to the mistaken idea that the structure is continually alternating between the three possibilities.

Figure 7.68 Effect of resonance on NO₃^– ion

In actual fact, the nitrate ion has only one structure in which the electrons spread themselves evenly so as to make all three N–O links into “1-1/3 bonds”; we describe them as having a bond order of 4/3. The preferred way of depicting a molecule that has more than one equivalent bonding structure is to use dashed lines to indicate the “fractional” bonds as shown here.

Very similar structures can be written for sulfur trioxide SO₃, and for the carbonate ion CO₃^2–.

In writing out resonance structures, it is important to bear in mind that only the electron pairs can be moved around; the atoms must retain the same connectivity. In some cases it is necessary to move electrons to locations that would produce a positive charge on one atom and a negative charge on the other. Since the separation of electric charge always costs energy, such resonance forms will tend to be less stabilizing and will not be as important contributors to the overall structure as those in where there is no charge separation.

Since electrons in molecules tend to arrange themselves into configurations that give the lowest possible energy, it is not surprising that the resonance hybrid represents a more stable (i.e., strongly bound) molecule than does any one of the contributing structures.

There is a good quantum-mechanical rationale for this; according to the Heisenberg uncertainty principle, the energy of the electron will be more uncertain as its position is more exactly specified. Since energies cannot be negative, the more “uncertain” the energy can be, the higher it can be. If an electron is spread out over two or three bonds in the hybrid instead of being confined to the space between only two atoms, its exact location is much less exactly known, and so its energy will be less uncertain, and therefore lower.

Resonance structures of carboxylic acids

This idea is embodied in the statement you will often see, particularly in the older literature, that a given structure “is stabilized by resonance”. This jargon has been used, for example, to explain the acidity of the -COOH group found in organic acids. Dissociation of a carboxylic acid such as formic acid yields a carboxylate ion –COO^– which can be represented by two equivalent structures. These are more realistically interpreted as a single structure in which the C–O bond order is 1.5:

Figure 7.69 Effect of resonance on carboxylate ion

The idea is that resonance is only possible when the proton has been lost, and that the lower energy of the “resonating” structure provides the driving force for the loss of the proton, and thus is the source of the acidity carboxylic group. (By the way, this view of the cause of carboxylic acidity has been criticized; other factors that may well be more important are also involved.)

Resonance structures of the benzene ring

See here for a summary of the various structures that have been proposed for benzene over the years.

Perhaps the most well known molecule whose structure must be represented as a resonance hybrid is benzene, C₆H₆. The structure of this molecule had long been something of a mystery, in that it was difficult to understand how this formula could be consistent with the well-established tetravalence of carbon in organic compounds. The breakthrough came in 1865 when the German chemist August Kekulé proposed that the molecule is based on a hexagonal ring of carbon atoms as shown at the left below.

Figure 7.70 Resonating Structures of Benzene

However, this structure is not consistent with the chemistry of benzene, which does not undergo the reactions that would be expected of a molecule containing carbon-carbon double bonds. Such compounds are normally quite reactive, while benzene, in contrast, tends to be rather inert to all but the most powerful reagents.

This apparent discrepancy disappeared after the resonance hybrid theory was developed; benzene is regarded as a hybrid of the two structures shown in the center above, and it is often depicted by the structure at the right, in which the circle represents a “half bond”, so that the bond order of each C–C bond is 1.5. Bond length measurements are entirely consistent with this interpretation; they are almost exactly halfway between the values found in compounds known to contain single and double bonds.

Figure 7.71 3D shape of Benzene

A more realistic representation of the benzene molecule shows the two components of its bonds. The “sticks” joining adjacent carbons constitute “half” of the carbon-carbon bonding, while the circular charge clouds above and below the ring together make up the other “half”. The details of this bonding arrangement are discussed in the section on the hybrid orbital model of bonding.

Some apparent violations of the Octet Rule

Electron structures without molecules

Although there are many violations of the octet rule, most electron dot structures that one can write down in accordance with this rule and its general scope of validity correspond to molecules that actually exist. Sometimes, however, we are surprised to find that the molecules corresponding to an apparently reasonable Lewis formula are not known.

In some cases, this has been shown to be a consequence of the very high chemical reactivity of the molecules. Thus hypofluorous acid, HOF, has never been isolated, although its chlorine analog is well known. It was not until 1967 that its short-lived presence was detected spectroscopically. It is now believed that the molecule is stable, but that the products obtained when it reacts with itself are so much more stable that it decomposes almost as fast as it is formed:

2HOF(g) → 2HF(g) + O₂(g)

Other molecules having proper Lewis structures but no apparent existence may be stable only at very low temperatures; examples are O₄ and H₂O₄.

The fluorate ion, FO₃^–, has also never been detected, even though analogs containing the other halogen elements are well known. The problem here may well lie with the very small fluorine atom, which would allow the oxygens to approach so closely that they would repel each other.

Small size is also suggested as the reason for the non-existence of the nitrogen analogs of the sulfate and sulfite ions. These would have the formulas NO₄^3– and NO₃^2–. Here, the problem is believed to be the high charge density: it costs a lot of energy to squeeze this much electric charge in such a small volume. Sulfur, having a larger radius, forms larger ions having lower charge densities, and the total charge would also be only –2 instead of –3.

Molecules without proper Lewis electron structures

There are also examples of molecules whose existence is beyond question, but for which no satisfactory Lewis structures can be written. Two examples are the triiodide ion I₃^–, and the bifluoride ion HF₂^–.

The triiodide ion [I–I–I]^– is a well known species found in aqueous solutions containing iodine and iodide ions:

I₂ + I^– → I₃^–

The bifluoride ion [F–H–F]^– is formed in a rather similar way in hydrofluoric acid solutions containing fluoride ion:

HF + F^– →HF₂^–

Try writing electron-dot structures for these two species, and you will see the problem!

Molecules with unpaired electrons

As you know, electrons tend to pair up in atoms and molecules so that their spins cancel out. If this does not happen— either because there is an uneven number of electrons or it is energetically unfavorable, then the species is said to be paramagnetic. Paramagnetic substances are attracted to a magnetic field, but unlike ferromagnetic materials such as iron, they do not retain their magnetic properties (act as magnets) in the absence of an applied field. Most molecules posses an even number of electrons and are diamagnetic.

Dioxygen

Figure 7.72 Lewis Dot structure of Dioxygen

The most abundant paramagnetic molecule in our world is the ordinary oxygen molecule which has twelve electrons. It is easy to write a proper Lewis structure for O₂ that places an octet around each oxygen atom and a double bond between them. However, it takes only a simple experiment to show that the electrons in dioxygen cannot all be arranged in pairs: if you place a magnet near some liquid oxygen, the liquid will be drawn to the magnet. This can only mean one thing: there are at least two unpaired electrons in the O₂ molecule. A more careful experiment shows that this number is exactly two. Are they in the bond or are they non-bonding electrons? You can decide this by sketching out a few possible structures.

The paramagnetism of oxygen is an anomaly in terms of the Lewis theory, although it is predicted by a more comprehensive theory that we will look at later. There are, however, a few other molecules that we would expect to be paramagnetic simply because they contain an odd number of valence electrons.

Nitric oxide and nitrogen dioxide

Figure 7.73 Lewis Dot structure of NO

Nitrogen, having five valence electrons, forms two well-known odd-electron molecules with oxygen. Nitric oxide, NO, a colorless, odorless, paramagnetic gas, is the simplest stable odd-electron molecule known. It is clear that no structure conforming to the octet rule is possible. The Lewis structure shown here is somewhat misleading; chemical and physical evidence suggest that the unpaired electron is not localized on the nitrogen atom, but extends over the entire molecule.

For example, if the structure were really ·NO, then we would expect the molecule to readily form a dimer ON:NO, but this is not observed. Bond-length measurements indicate that the N–O bond order is 2.5.

Nitric oxide has a remarkably rich chemistry. Until recently, its most famous role was as a precursor to photochemical smog. (The oxide is formed when fuels such as gasoline are burned at high temperatures in the presence of air.)

In the 1980s, to the surprise of almost everyone, NO was identified as an essential component of the signalling pathway of the mamallian cardiovascular system. As such, it provides a means by which cells communicate with one another. Other signalling molecules tend to be far more complicated, and no one would have expected a “free radical” molecule to have other than a damaging effect on the body. 

Nitrogen dioxide is also an odd-electron molecule. In contrast to NO, the odd electron in NO₂ appears to be somewhat local to the nitrogen atom. As a consequence, the dimerization equilibrium

2 NO₂  N₂O₄

is so facile that neither gas can be retained in pure form at ordinary temperatures. Because two equivalent Lewis structures can be written, NO₂ is a resonance hybrid in which the N–O bond order is 1.5.

Figure 7.74 Lewis Dot structure of NO₂

Figure 7.75 Resonating structure of NO₂

More than one non-equivalent structure

It sometimes happens that the octet rule can be satisfied by arranging the electrons in different ways. For example, there are three different ways of writing valid electron dot structures for the thiocyanate ion SCN^–. Some of these structures are more realistic than others; to decide among them, you need to know something about the concepts of formal charge and electronegativity. These topics are discussed in the lesson that follows this one, where examples of working out such structures are given.

The video below illustrates this effect:

Key Concepts and Summary

In a Lewis structure, formal charges can be assigned to each atom by treating each bond as if one-half of the electrons are assigned to each atom. These hypothetical formal charges are a guide to determining the most appropriate Lewis structure. A structure in which the formal charges are as close to zero as possible is preferred. Resonance occurs in cases where two or more Lewis structures with identical arrangements of atoms but different distributions of electrons can be written. The actual distribution of electrons (the resonance hybrid) is an average of the distribution indicated by the individual Lewis structures (the resonance forms).