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In order to determine the relative contributions of resonance structures, my textbook gives the following rules (in order):

  1. The more covalent bonds a structure has, the higher it scores.

  2. Structures in which all of the atoms have a complete valence shell of electrons (i.e., the noble gas structure) are especially relevant and make large contributions to the hybrid.

  3. Charge separation decreases the score.

  4. Resonance contributors with negative charge on highly electronegative atoms score higher than ones with negative charge on less or non electronegative atoms. Conversely, resonance contributors with positive charge on highly electronegative atoms score lower than ones with positive charge on non electronegative atoms.

How to determine the relative contribution of resonance structures when different rules give contradictory outcomes?

For example, let's consider the following resonance structures:

$$\ce{\overset{+}{C}H2-\underset{1}{O}-CH3}\longleftrightarrow \ce{CH2=\underset{2}{\overset{+}{O}}-CH3}$$

The following are my conclusions with respect to the above rules:

  1. Structure 2 scores higher than structure 1 as it has more number of covalent bonds.

  2. Structure 2 scores higher than structure 1 as all atoms have noble gas electronic configuration. In structure 1, the leftmost carbon atom has only six valence electrons.

  3. There is no charge separation in either of the two structures and so this rule cannot be used to determine the relative contribution.

  4. Structure 1 scores higher than structure 2 because in the first structure a carbon atom bears a positive charge whereas in the second an oxygen atom carries a positive charge. Since oxygen is more electronegative than carbon or carbon is more electropositive than oxygen, structure 1 scores higher.

Based on conclusions 1 and 2, we could say that structure 2 contributes more. But conclusion 4 contradicts the result given by points 1 and 2. So, how could we determine the relative contributions when the outcomes of the rules contradict each other?

Are some rules (out of the given 4) superior over the other? Or do we determine the overall score by the number of votes on either sides (similar to our community's voting system based on upvotes and downvotes :) ) i.e., structure 2 scores higher since it has two votes (points 1 and 2) supporting it and 1 vote (point 4) against it? If this is the case, what if there are equal number of votes? For example what if points 1 and 2 suggest a structure A scores higher than B whereas points 3 and 4 suggest structure B scores higher than A?

Kindly do not limit your answers to the above two resonating structures. I considered it just to explain the question.

I read the question - How to determine the least stable resonance structures out of a given set? and the answers to it. In fact, that question is based on a problem from the same book I follow. But still, I don't understand how to determine the relative contributions when some rules give contradictory outcomes.


Note: I understood resonance structures are hypothetical, i.e., they don't have an existence in the real world. The molecule is best represented by the hybrid of all the structures. As commented in my previous questions on resonance, I've already read the question/answer - What is resonance, and are resonance structures real? and I feel I don't have any misconceptions on the subject.

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  • $\begingroup$ Consider that in this case you analyse an ion. This makes consideration about electronegativity to be slippery. The leftmost carbon has only six electrons in the valence shell. Its charged goes along with. Also, in case, the energy of two limiting forms might be little. $\endgroup$ – Alchimista Jan 31 at 7:34
  • $\begingroup$ @Alchimista: Thanks for the comment. However, rule 4 is applicable only in the case of ions. I've seen the author explaining relative stabilities of ions in terms of whether positive "charge" is on an electronegative or an electropositive atom. $\endgroup$ – Guru Vishnu Jan 31 at 7:39
  • $\begingroup$ The reason I comment is that is somehow a delicate issue and one has to work for a nice answer. My comment was perhaps a convoluted way to say that major criteria are covalent bonds number and octets fulfillment. I think this is a duplicate of chemistry.stackexchange.com/questions/6638/…. Note that the accepted answer is right but it contains a wrong incipit. The fact that resonance structures taken individually do not represent any actual entity does not mean that we can't order them by energy, of course. $\endgroup$ – Alchimista Jan 31 at 8:08
  • $\begingroup$ @Alchimista: The linked question answers one of the aspect of the question based on the specific example I considered. However, I don't think it answers all the permutations of rules being satisfied or defied. So my question is not a duplicate of the linked. But it's "related" and thanks for the link. "Note that the accepted answer is right but it contains a wrong incipit." - Yes. I agree; "The fact that resonance [...] by energy, of course." - I understood this already. And finally, I think this is a good reason - "major criteria are covalent bonds number and octets fulfilment". $\endgroup$ – Guru Vishnu Jan 31 at 8:31
  • $\begingroup$ Your four textbook rules are not supposed to tell you if mesomeric structure the major contributor to hybrid, but, seems to me, are just an simplified way for beginners to "manually" tell which structures actually make sense, i.e. if you can't tell just by looking, then analyse with rules and maybe answer's gonna make some sense. $\endgroup$ – Mithoron Feb 1 at 0:05
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The Rules

Actually the rules for determining the relative stabilities (more accurately, contributions) of resonance structures do have their own priorities. Here is one version of them, with descending order of importance listed below (as is indicated by the bold words). The rules can be found in common organic chemistry textbooks (like [1], also supported by [3]).

  1. In any case, the more the octet rule is fulfilled (for appropriate atoms), the better.
  2. Resonance structures with charge separation are usually higher in energy than those in which charges can be neutralized, unless rule 1 is not obeyed.
  3. If charge is separated, then the best structure is consistent with the electronegativity of the atoms (e.g., a negative charge is best on the most electronegative atom).
  4. The more and stronger the bonds, the better. Adjacent atoms should not have the same sign of charges.

Examples

The first rule is undoubtfully the most important. The example of $\ce{CH2^+-O-CH3 <-> CH2=O^+-CH3}$ is already mentioned. Here I would like to provide an example to justify the importance of rule 1.

Consider the Lewis acids $\ce{BX3}$ where $\ce{X}=\ce{F},\ce{Cl},\ce{Br}$. We know that $\ce{BF3}$ is the least Lewis acidic despite the fact that $\ce{F}$ is the most electronegative. This fact can be explained by considering the resonance structures $\ce{X2B-X <-> X2B^-=X+}$. According to rule 1, the second resonance structure is more important, so the electron deficiency of $\ce{B}$ is determined by the orbital overlapping between $\ce{B}$ and $\ce{X}$. Therefore, since $\ce{F}$'s $2\mathrm p$ orbitals interact with $\ce{B}$'s best, $\ce{BF3}$ is the least Lewis acidic.

Another interesting example illustrating the relative importance of rule 3 and 4 comes from Grützmacher's work[2].

The phosphaethynolate anion $\ce{OCP-}$ may attack $\ce{TMSOTf}$ using $\ce{O}$ and $\ce{P}$. At 298K the product is $\ce{TMS-O-C\bond{3}P}$, and at 318K the product is $\ce{TMS-P=C=O}$. To account for this, let's analyze $\ce{OCP-}$'s resonance structures: $$\ce{P\bond{3}C-O- <-> O=C=P-}.$$ The latter has stronger bonds and the former has its negative charge on a more electronegative atom. According to rule 3, the former dominates (actually a ratio of former vs latter 40:52), hence at ambient temperature $\ce{O-}$ attacks more quickly to obtain the kinetic product, while $\ce{TMSPCO}$ is the thermodynamic product.

Theoretical Justifications

You can find theoretical justifications using Hückel Theory as always. I will not show this here because it may be to tedious to do the calculations. However, you can read this article for more information J. Chem. Educ. 2007, 84, 6, 1056.

Ref.

[1] Grossman, The Art of Writing Reasonable Organic Reaction Mechanisms, Springer, 2002.

[2] Grützmacher et al., Dalton Trans., 2014,43, 5920-5928.

[3] Humbel, J. Chem. Educ., 2007, 84, 6, 1056-1061.

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    $\begingroup$ This is mixing two different, though connected, subjects. Any consideration about the stability as per the question has to be carried out in vacuum as well. I appreciate listing of the rules in their order. I should have been more clear in my previous comment. Besides exceptions there is a strict order to follow. It is general enough that I don't even think this is worth a bounty. The only special aspect of the Question is that the two limiting forms are both possible and should both contribute with no too different extent to the description of the real actual molecule. So it is difficult to.. $\endgroup$ – Alchimista Feb 2 at 13:27
  • $\begingroup$ ... to do a quantitative assessment using rules not designed to have precision. $\endgroup$ – Alchimista Feb 2 at 13:31
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    $\begingroup$ It is in principle wrong to say that resonance structure have different energies; in that way most organic textbooks get it wrong. They only exist as a resonance hybrid, also only in the description in terms of Valence bond theory. $\endgroup$ – Martin - マーチン Feb 2 at 21:53

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