Is it the difference of energies of formation of the resonance hybrid and the average of the energy of formation of all the contributing structures? How would we even calculate the energy of a resonance contributer?

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    $\begingroup$ I think what you are asking is: how do we measure the energy of fictitious structures, which don't exist in real life but nevertheless are used to deal with the fact that our model doesn't properly delocalize electrons? $\endgroup$ – Zhe Aug 18 at 15:05
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    $\begingroup$ For contributing forms we are confined to calculations. For the rest we can imagine thermochemical cycle, the simplest of which should be that comparing benzene to what would be benzene with three localised double bounds. At least one answer exists here in Chemistry SE (by me) but a search should reveal many related Q & A. $\endgroup$ – Alchimista Aug 18 at 15:58
  • $\begingroup$ I think this article will be helpful: mjcce.org.mk/index.php/MJCCE/article/view/…. $\endgroup$ – Reihani Aug 18 at 16:04
  • $\begingroup$ @Zhe yes that is a nice way to put it $\endgroup$ – l1mbo Aug 18 at 16:47
  • $\begingroup$ @Reihani thanks for your help but the article only states an approximate formula $\endgroup$ – l1mbo Aug 18 at 16:48

Resonance energy is a fictitious value, it cannot be measured, it is always only estimated. The definition in the gold book[1] clearly states this:

The difference in potential energy between the actual molecular entity and the contributing structure of lowest potential energy. The resonance energy cannot be measured, but only estimated, since contributing structures are not observable molecular entities.

The arising question is how to obtain the energy of the hypothetical contributing structure. One way to do it is to use tabulated (averaged) values for 'normal' bonds to estimate the total energy of the hypothetical molecule.[2]

Another way to do it is to extrapolate from measured hydrogenation energies. This was famously done for benzene. For example, the hydrogenation energy of cyclohexene to cyclohexane is about $\pu{110 kJ mol-1}$. This is the energy to hydrogenate one double bond. In the hypothetical Kekulé structure of benzene you'd expect three of them, giving you a theoretical hydrogenation energy of about $\pu{330 kJ mol-1}$. The measured hydrogenation energy of benzene is about $\pu{200 kJ mol-1}$. This difference of $\pu{130 kJ mol-1}$ can now be taken as the stabilisation due to delocalisation, i.e. the resonance energy.[3]

There is no universal way of doing this, because none of the ways can be proven to be right; it's not real after all. Therefore you may find vastly different values for the resonance energies. It is better to think about resonance as a phenomenological, qualitative argument of mostly pedagogical value. If you are comparing values of hydrogenation (something that can be measured) against extrapolated values (or expectation values) then it is unnecessary to obscure this comparison by giving it another label.

  1. Resonance Energy in: IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. DOI 10.1351/goldbook.R05333

  2. You can find such values for example in this Chemistry LibreTexts article on Bond Energies.

  3. Values are loosely converted to SI units from the article on Chemistry LibreTexts Structure and Resonance Energy of Benzene: A First Look at Aromaticity.

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