When scientists use a Lewis structure to represent a molecule, they are drawing a diagram that shows the arrangement of atoms and the distribution of valence electrons. This model works well for many compounds, but for others, a single structure fails to accurately represent the molecule’s true nature. This limitation arises because electrons in certain molecules are not confined to a fixed location between two atoms, as a simple line in a drawing would suggest. Instead, the electrons are spread out, or delocalized, across multiple atoms and bonds simultaneously. This phenomenon, where the electron cloud is shared more broadly than a localized bond indicates, necessitates the use of the concept of resonance to provide a more truthful picture of the molecule’s electronic structure.
The Concept of Resonance
The theory of resonance was developed to overcome the limitations of drawing electron configurations that are restricted to whole-number bonds. In reality, the electrons that form pi bonds and lone pairs are often mobile, existing not in a single fixed position but in an extended region across the molecule’s atomic framework. This movement or sharing of electrons is termed delocalization, and it profoundly affects the molecule’s properties, particularly its stability.
To represent this delocalization, chemists draw multiple Lewis structures, called resonance structures or contributing structures, that collectively describe the molecule’s electronic state. None of these individual drawings are correct on their own; they are hypothetical representations of electron arrangements that contribute to the molecule’s actual structure. The true electronic configuration of the molecule is a single, time-averaged structure known as the resonance hybrid.
The resonance hybrid possesses a lower overall energy than any single contributing structure, which is the chemical basis for the added stability that electron delocalization provides. The stability gained is often quantified as the resonance energy, representing the difference between the actual molecule’s energy and the energy of the most stable hypothetical contributing structure. Not all resonance forms contribute equally to the final hybrid, as some structures may be energetically more favorable than others due to factors like minimized formal charges or complete octets.
Defining Equivalent Resonance Structures
Equivalent resonance structures represent a specific and symmetrical situation where all possible contributing structures are perfectly interchangeable and possess identical chemical characteristics. These structures are defined as equivalent because they have the exact same number and type of bonds, and the distribution of formal charges is symmetrical across the same types of atoms. This means that if one structure has a negative charge on a specific atom, the corresponding atom in every other equivalent structure will also have a negative charge of the same magnitude.
Because of this perfect symmetry, all equivalent resonance forms are considered to be at the same energy level and, consequently, contribute equally to the overall resonance hybrid. When contributions are equal, the resulting molecule is highly symmetrical and stable. This equal contribution is the key differentiator from general resonance, where non-equivalent structures exist; in non-equivalent systems, one structure might be a “major” contributor with a lower energy, while others are “minor” contributors with higher energy.
In a molecule with equivalent resonance structures, the true structure is a simple arithmetic average of all the contributing forms. This results in the molecule exhibiting bond lengths and bond strengths that are intermediate between a single and a double bond, and fractional formal charges that are distributed uniformly across the equivalent atoms. This uniform distribution of charge and bond character provides the maximum stabilization energy for the molecule.
Identifying Rules for Equivalence
For a set of resonance structures to be considered equivalent, they must satisfy a specific set of structural and electronic criteria that enforce symmetry. The first requirement is that the placement of all atoms must remain unchanged; only the non-bonding electrons and pi electrons are permitted to move. If atoms are rearranged, the structures are isomers, not resonance contributors.
All equivalent structures must also contain the same total number of valence electrons, the same number of pi bonds, and the same number of lone pairs. This constraint ensures that the overall electron count and the bond order for the molecule remain consistent across all drawings. Crucially, the formal charges must be distributed identically, not just in their sum, but in their magnitude and location relative to chemically identical atoms.
If one structure has a positive formal charge on a nitrogen atom and a negative formal charge on an oxygen atom, the other equivalent forms must also have a positive charge on a nitrogen atom and a negative charge on an oxygen atom. This symmetry in charge distribution ensures that the structures are rotationally identical, leading to the same energy and stability. Therefore, identifying equivalence is often as simple as determining if a symmetry operation can transform one resonance structure into another.
Practical Examples of Equivalence
The carbonate ion (\(CO_3^{2-}\)), with a central carbon bonded to three oxygen atoms, is a classic example of equivalent resonance. It is possible to draw three different Lewis structures, each placing the carbon-oxygen double bond on a different oxygen atom. Because the three oxygen atoms are chemically identical, these three structures are equivalent, and they contribute equally to the resonance hybrid. The result is that the carbonate ion does not have one double bond and two single bonds; instead, all three carbon-oxygen bonds are identical, possessing a bond order of approximately 1.33, which is stronger than a single bond but weaker than a double bond.
Similarly, the nitrate ion (\(NO_3^{-}\)), which is isoelectronic with the carbonate ion, exhibits three equivalent resonance structures where the double bond shifts among the three oxygen atoms. The overall negative charge of -1 is delocalized equally among the three oxygen atoms, giving each a partial formal charge of \(-2/3\). This delocalization explains why experimental measurements show that all nitrogen-oxygen bonds in the nitrate ion are the same length, which is intermediate between a nitrogen-oxygen single bond and a double bond.
Benzene (\(C_6H_6\)), a six-membered ring of carbon atoms, also demonstrates equivalence with its two Kekulé resonance structures. Since the two structures are identical in energy and formal charge distribution, they contribute equally to the hybrid. The actual benzene molecule has six carbon-carbon bonds of equal length and strength, intermediate between a single and a double bond.