Resonance (chemistry)
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- For other uses, see Resonance (disambiguation).
Resonance in chemistry is a tool used (predominately in organic chemistry) to represent certain types of molecular structures. Resonance is a key component of valence bond theory and arises when no single conventional model using only single, double or triple bonds can account for all the observed properties of the molecule. There are two closely related but useful-to-distinguish meanings given to the term resonance. One of these has to do with diagrammatic representation of molecules using Lewis structures while the other has to do with the mathematical description of a molecule using valence bond theory. These are described next.
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[edit] Resonance as a diagrammatic tool
Lewis dot diagrams often cannot represent the true electronic structure of a molecule. While one can only show single, double or triple covalent bonds using these diagrams, one finds that the observed molecule does not match either of these structures but rather has properties in some sense intermediate to these. Resonance structures are then employed to approximate the true electronic structure. Take the example of benzene (shown to the right). In a Lewis diagram, two carbons can be connected by one or two covalent bonds, but in the observed benzene molecule the bond lengths are longer than double bonds yet shorter than single bonds. Therefore one calls the two lewis structures canonical, contributing or resonating structures and the real molecule is considered to be their average, called a resonance hybrid. Resonance structures of the same molecule are connected with a double-headed arrow.
This form of resonance is simply a way of representing the structure graphically. It is only a notation and does not represent a real phenomenon. Nothing "resonates". The individual resonance structures do not exist in reality: the molecule does not interconvert between them. Instead, the molecule exists in a single unchanging state, intermediate between the resonance structures and only partially described by any one of them. This sharply distinguishes resonance from tautomerism. It is also not right to say that resonance occurs because electrons "flow" or change their place within the molecules. Such a thing would produce magnetic effects that are not observed in reality.
[edit] An analogy
An accurate analogy of resonance is given by the algebra of vectors. A vector r is written in component form as xi+yj+zk where x, y, and z are components and i, j, and k are the standard orthogonal cartesian unit vectors. Just as the real vector r is neither x, nor y, nor z, but rather a combination of all three, a resonance hybrid is a conceptual combination of resonance structures. x, y, and z have no independent existence; they are considered only as a decomposition of r into easier-to-handle components, as is the case with resonance structures. In fact this analogy is very close to the reality, as will be made clear in the following section.
[edit] True nature of resonance
Though resonance is often introduced in such a diagrammatic form in elementary chemistry, it actually has a deeper significance in the mathematical formalism of valence bond theory (VB). When a molecule can not be represented by the standard tools of valence bond theory (promotion, hybridisation, orbital overlap, sigma and pi bond formation) because no single structure predicted by VB can account for all the properties of the molecule, one invokes the concept of resonance.
Valence bond theory gives us a model for benzene where each carbon atom makes three sigma bonds with its neighbouring carbon atoms and one hydrogen atom. But since carbon is tetravalent, it has the ability to form one more bond. In VB it can form this extra bond with either of the neighbouring carbon atoms, giving rise to the familiar Kekulé ring structure. But this can not account for all bond lengths being equal. So what we do is write the actual wavefunction of the molecule as a linear superposition of the two possible Kekulé structures (or rather the wavefunctions representing these structures), creating a wavefunction that is neither of its components but rather a superposition of them, just like our vector analogy (which is formally equivalent to this situation). This clarifies the nature of resonance.
In benzene both Kekulé structures have equal weight, but this need not be the case. In general, the superposition is written with undetermined constant coefficients, which are then variationally optimized to find the lowest possible energy for the given set of basis wavefunctions. This is taken to be the best approximation that can be made to the real structure, though a better one may be made with addition of more structures.
In molecular orbital theory, the main alternative to VB, resonance often (but not always) translates to a delocalization of electrons in pi orbitals (which are a separate concept from pi bonds in VB). For example, in benzene, the MO model gives us 6 pi electrons completely delocalised over all 6 carbon atoms, thus contributing something like half-bonds. This MO interpretation has inspired the picture of the benzene ring as a hexagon with a circle inside. Often when describing benzene the VB picture and the MO picture are intermixed, talking both about sigma 'bonds' (a meaningless concept in MO) and 'delocalized' pi electrons (a meaningless concept in VB). This is not a good practice, because mathematically the models are incompatible. In MO such systems are called conjugated.
[edit] Writing resonance structures
Resonance hybrids are generally more stable than any of the canonical structures would be, if they existed. The delocalization of the electrons lowers the orbital energies, imparting this stability. The resonance in benzene gives rise to the property of aromaticity. The gain in stability of the resonance hybrid over the most stable of the (non-existent) canonical structures is called the resonance energy. The resonance energy can be used to calculate electronegativities.
- Position of nuclei must be the same in all structures, otherwise they would be isomers with real existence.
- Total number of electrons and thus total charge must be constant.
- When separating charge (giving rise to ions), usually structures where negative charges are on less electronegative elements have little contribution, but this may not be true if additional bonds are gained.
- Resonance hybrids can not be made to have lower energy than the actual molecules.
- Usually electrons belonging to sigma bonds can not be rearranged, though exceptions are made in hyperconjugated systems.
[edit] History
The concept of resonance was introduced by Linus Pauling in 1928. He was inspired by the quantum mechanical treatment of the H2+ ion in which an electron is located between two hydrogen nuclei. The alternative term mesomerism popular in German and French publications with the same meaning was introduced by Christopher Ingold in 1938 but did not catch on in the English literature. The current concept of mesomeric effect has taken on a related but different meaning. The double headed arrow was introduced by the German chemist Arndt (also responsible for the Arndt-Eistert synthesis) who preferred the German phrase zwischenstufe or intermediate phase.
Due to confusion with the physical meaning of the word resonance, after all no elements do actually appear to be resonating it is suggested to abandon the phrase resonance in favor of delocalization.[1] Resonance energy would become delocalization energy and a resonance structure becomes a contributing structure. The double headed arrows would be replaced by commas.
[edit] Examples
The ozone molecule is represented by two resonance structures in the top of scheme 2. In reality the two terminal oxygen atoms are equivalent and the hybrid structure is drawn on the right with a charge of -1/2 on both oxygen atoms and partial double bonds.
The concept of benzene as a hybrid of two conventional structures (middle scheme 2) was a major breakthrough in chemistry made by Kekulé, and the two forms of the ring which together represent the total resonance of the system are called Kekulé structures. In the hybrid structure on the right the circle replaces three double bonds.
The allyl cation (bottom scheme 2) has two resonance forms and in the hybrid structure the positive charge is delocalized over the terminal methylene groups.
