# Bond order for carbonate ion for resonance

I saw in a textbook that for carbonate ion, there are 3 resonance forms and the bond order is 1 and 1/3. So in general, how should we calculate the bond order for resonance structures?

Is there any definite way to do this?

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There definitely is an easy way to do this.

One of the easiest examples that comes to mind is benzene. If we look at the structure:

we see that each of the carbon bonds are either single bonds to the adjacent carbon or double bonds to the carbon in the other direction. If we draw the other resonance structure these bonds shift by 1 atom to look like the following:

Thus, the overall structure can be obtained by looking at those two structure and averaging the bond order between them. For benzene one resonance form for each bond will be single and the other double (2 + 1)/2. The "2" on the bottom of the equation is the number of resonance structure being considered. Thus, for benzene the bond order is 1.5.

Applying this same method to the carbonate ion, we have 3 resonance structures with bond orders of 2, 1, 1 when considering the bond between carbon and a single oxygen. Since there are 3 structures the answer is (2+1+1)/3 = 1.33333 or 4/3.

Hope this helps!

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Indeed. I'll add that this only works for resonance structure that are equivalent by symmetry… since they have the same weight. You cannot, for example, calculate in any simple way a bond order for furan, even though you can easily write its resonance forms: they don't have the same weight. –  F'x Oct 5 '12 at 14:31
And given that resonance is a figment invented to make valence bond theory handle delocalization, there is likely no theoretical approach to determine the relative weight of furan's resonance structures. Comparison of experimental bond lengths for related molecules (for example, the cyclopentadienyl anion is symmetric) and for tetrahydrofuran and the the dihydrofuran isomers may get you an estimate. Using MO theory will only get you the total bond order for the molecule, since there are no localized bonds. –  Ben Norris Oct 6 '12 at 0:06

Only in simple cases, it is possible to make reliable estimates of the relative weight of resonance structures from the Lewis structure alone. If you want a somewhat quantitative yet simple approach to bond orders in delocalized systems, have a look at the Hückel method. It is a quantum-mechanical theory for determining the energies of $\pi$ orbitals, and it defines a method to determine a measure of the $\pi$ bond order between two atoms. If you want to go beyond that, you will have to look further into quantum chemistry and different schemes for bond localization and population analysis. In many cases there is no one definite answer, but rather, your results will depend heavily on the quantum-chemical calculations and assumptions for the bond-order analysis itself.

(There are probably also ways to tackle the problem from an experimental side, although I'm not all sure about this; I'm thinking about perhaps determining electron distributions through NMR chemical shifts, or bond strengths through vibrational spectroscopy.)

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