Essays on Resonance Theory

res-o-nance n. 1. the state or quality of being resonant (resounding). 2. the prolongation of sound by reflection. 3. Phonet. amplification of the range of audibility of any source of speech sounds. 4. Physics. a. the state of a system in which an abnormally large vibration is produced in response to an external stimulus, occurring when the frequency is the same, or nearly the same, as a natural vibration frequency of the system. b. the vibration produced in such a state. 5. Elect. the condition of a circuit with respect to a given frequency or the like in which the net reactance is a minimum and the current flow a maximum. 6. Chem. the condition exhibited by a molecule when the actual arrangement of its valence electrons is intermediate between two or more arrangements having nearly the same energy, and the positions of the atomic nuclei are identical. - The Random House College Dictionary, Revised Edition 1975

As you can tell from this long (and abridged!) set of definitions, nearly everyone in the English-speaking world connects "resonance" with oscillations, vibrations, and frequencies. Only chemists think otherwise. Since you are here to learn chemistry, you must put aside your old ideas about "resonance" and re-learn this word from a chemist's point-of-view.

Forget vibration. Forget sound, forget frequency. From here on, resonance is about molecules with abnormal electron patterns, and how we can approximate these patterns by combining (superpositioning, averaging) normal electron patterns.

  1. Resonance hybrid - Resonance hybrids are "abnormal" molecules in this sense: their geometry and electron pattern cannot be described by a single Lewis structure.
  2. Resonance contributor - A r esonance hybrid can be viewed as a superposition of inaccurate Lewis structures. These structures "contribute" to our mental picture of the hybrid, but none of them provide a complete or accurate picture.
  3. Resonance form - A resonance hybrid can be viewed as a superposition of inaccurate Lewis structures. These structures help "form" our mental picture of the hybrid, but none of them provide a complete or accurate picture.
  4. Localized vs. delocalized electrons (or bond, or charge) - Delocalized electrons move beyond the regions prescribed by Lewis' bonding theory. A pair of electrons might be spread (delocalize) its bonding influence over two or more atom pairs. Charge imbalances may also be spread over several atoms.
  5. Dashed-line formulas - A resonance hybrid can be viewed as a collection of partial bonds, lone pairs, and/or partial charges. This picture is convenient because it saves us the trouble of combining resonance forms, but is hard to work with in other respects.
  6. Major vs. minor contributors - Resonance hybrids with unsymmetric electron patterns are a superposition of major and minor resonance contributors. The major contributor fits the expt'l data better, arranges electrons in a lower energy pattern, or satisfies resonance rules better than the minor contributor
  7. Superposition of wave functions (Revisions planned) - Most chemists treat a resonance hybrid as a superposition of drawings. This practice is useful, but incorrect (example: it does not explain why the hybrid's electron pattern is more stable than the patterns found in the contributors). A resonance hybrid should be treated as a superposition of wave functions instead.
  8. Resonance affects molecular geometry (Revisions planned) - Distorted bond distances may indicate delocalized partial bonds. Distorted bond angles may indicated delocalized lone pairs. Benzene is a resonance hybrid, but its symmetric geometry is not due to resonance.
  9. Resonance affects energy (Revisions planned) - The electron pattern in a resonance hybrid is more stable than the electron patterns in its contributors, but the amount of stabilization depends on the relative energies of the contributors. Energy also determines the relative role of each contributor in describing the hybrid.
  10. Is everything a resonance hybrid? (Revisions planned) - Practically any wave function can be viewed as a superposition of simpler wave functions. A polar covalent bond can be treated as a superposition of a covalent (nonpolar) contributor and an ionic contributor. Even a covalent bond can be treated as a superposition of two "nonbonding" contributors, and this explains why electron sharing is stabilizing.