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

Question

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.

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^{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.}

Answer 1

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.