Lewis Structures: Resonance
(May 17, 2000, early AM)
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Resonance:  Any valid lewis structure can contribute to the overall electronic structure of a molecule or molecular ion.  The sum of all valid Lewis structures is termed a "resonance hybrid."  Key Points:
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    1) the "best" Lewis Structure(s) will contribute the most... in some cases nearly 100% to the "resonance hybrid"
    2) higher energy structures contribute much less...  sometimes approaching 0%
    3) equivalent structures, those which, by symmetry, must be identical in energy, contribute equally to the resonance hybrid.
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Note 1:  resonance is not a "flip-flop" from one version to another...  the molecule is considered to be all of the structures SIMULTANEOUSLY.
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Note 2: different Lewis structures can be considered "in resonance" if and only if they differ in the arrangement of the elctron pairs.  Movement of atoms is not permitted.  Structures which involve different organization of atoms are termed isomers, and are not resonance forms.

Example 1:  benzene
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Are the two structures in resonance?  Yes.  They differ only in the way electrons are distributed.  No atoms move in generating structure II versus structure I.  I have labelled two of the carbon atoms as "a" and "b" so you can appreciate the distinction between "rotating" the molecule versus redistributing the electrons.
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Which one is the "real" structure?  I.e. what is the "bond order" between Ca and Cb?
In structure I there is a single bond between Ca and Cb while in structure II there is a double bond.  Since the two structures are identical in energy, they contribute equally to the resonance hybrid which describes the overall electronic structure of the molecule.  Since resonance occurs simultaneously, there is an "apparent" bond order of 1.5 between Ca and Cb.

Example 2: Acetone and keto-enol tautomers
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Are I and II in resonance?  No.  Note that the two structures differ in the way the atoms are arranged.  Once the skeltal structure is drawn, then we can appropriate electons in the best manner.  Moving atoms creates a different molecule termed an isomer since it has the same formula.

Example 3: N2O
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    Below are shown 4 Lewis structures for dinitrogen monoxide (a.k.a nitrous oxide).
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Since all of the above structures are acceptible (i.e. do not violate octet rule, electron count, or involve movement of atoms), they can all contribute to the resonance hybrid.  Note, however, that they are all fundamentally different, and thus will not contribute equally.  We can say that for the Schrodinger equation:

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The wave function which describes the electronic structure for this molecule is the SUM of all 4 wave functions above.
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The coefficients (a,b,c,d) need not be equal.  Mathematically, this is how one resonance form can predominate over another in the resonance hybrid.
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For the above example, structures I, II, III are better than IV by virtue of the fact that they exhibit more bonds.  Structures I and III are better than II since they exhibit lower formal charge.  Finally, between I and III, I is the BEST because the formal charges are in the appropriate direction: oxygen, being more electronegative, gets the "-" formal charge.
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We would say that all four structures contribute to the resonance hybrid, but I predominates.  A bond order assessment may be difficult in this case, since it is not clear by how much structure I is better than II-III.  It is quite likely that the N-N bond order is somewhat less than a triple bond and the N-O bond order is somewhat greater than a single bond.

Example 4: Carbonate ion, CO32-
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Four Lewis structures for the carbonate ion are illustrated above.  I-III are equivalent by symmetry and must contribute equally to the resonance hybrid.  These are also significantly better than structure IV which has fewer bonds and greater formal charges.
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Question...  What is the C-O bond order in CO32-?  In as much as I-III dominate the resonance hybrid, a C-O bond order of 1.33 can be estimated.  Note that there are four C-O bonds drawn, and only three O atoms...  this averages out to 4/3 = 1.33.
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