organic chemistry - What is Y-aromaticity? Is the trinitromethanide anion aromatic?

The wikipedia article on trinitromethane claims that:

There is some evidence that the anion (which obeys the $4n+2$ Hückel rule) is aromatic.

Unfortunately the citation is behind a paywall so I can't read it but my first obvious question is how can the trinitromethane anion obey Hückel's rule? Two of the requirements for the rule are that the molecule must be planar (or nearly planar) and must be cyclic and I fail to see how either of these conditions are satisfied since the anion is roughly trigonal pyramidal around the carbon and definitely not cyclic.

This appears to about Y-aromaticity. All the papers linked are behind paywalls for me so can someone please explain what Y-aromaticity is and how it applies to the example given. I found this previous answer which gives some discussion of Y-aromaticity in nitrate ions. If someone could provide a similar MO analysis of the trinitromethane anion this might be very interesting.

Answer

Introduction

It is fairly obvious that the statement given by Wikipedia cannot be entirely correct.

There is some evidence that the anion (which obeys the 4​n+2 Hückel rule) is aromatic.

The trinitromethane anion cannot obey the Hückel (4​n+2) rule because it is neither monocyclic nor planar. And assigning a number of π electrons is fuzzy at best, so the (4​n+2) part is also questionable. Hückel's rule is a very strict set, but an aromatic compound does not necessarily have to fulfil it. The easiest compound to understand this is naphtalene, which is clearly aromatic, but does not fulfil the criteria of Hückel's rule, i.e. it is not monocyclic. In extension to this, helicene is an aromatic compound that fails two of the given conditions. Another case is thiophene, which due to the included sulfur certainly does not entirely consist of trigonally hybridised (sp²) atoms (see Bent's rule).^[1]

But can the anion still be regarded as aromatic? In order to explain that, we need to look at the concept of Y-aromaticity.

What is Y-aromaticity?

The term and the concept is not without controversial discussion. It is an attempt to give the "traditional" concept of resonance energy an new, fancy and more catchy name. It is often used to explain the extraordinary stability of the guanidinium cation, which has tree equivalent resonance structures, i.e. the electronic ground state is heavily delocalised.
Conventional Lewis structures employ two electron two centre bonds only, which therefore cannot represent the highly delocalised electronic structures, e.g. of aromatic compounds. Hence the concept of resonance had to be introduced to account for such stabilising effects. Obviously the same holds true for any compounds, that exhibit excessively delocalised electronic structures.
The term Y-aromaticity has been used for compounds, that are Y-shaped, with a trigonal planar coordinated (carbon) centre. In addition to that the π orbitals hold six electrons.^[2] These compounds have a similar orbital picture and could therefore be grouped.

The electronic structure of Y-delocalised π systems

The π orbitals of a trigonal planar coordinated centre can be generalised by the following orbital picture, which was generated for the nitrate anion at the DF-BP86/def2-SVP level of theory.

What we can clearly see is, that there is one totally symmetric bonding orbital. Two degenerate (orthogonal) slightly bonding (or non-bonding) orbitals and another totally symmetric anti-bonding orbital.

The remarkable stabilisation comes from the lowest lying π orbital, which is delocalised over all atoms, just like in the more obvious cases like benzene. Additionally, such compounds often retain their planarity by undergoing substitution reactions, rather than addition reactions.

Pro and contra of Y-aromaticity

The concept itself allows the discussion of certain electronic properties in quite simple terms. It is related enough to the general concept of aromaticity so that it can easily be understood at the same level of teaching. Like aromaticity, it allows predictions - to a certain degree - about the reactivity of such compounds.

Peter Grund makes the following assessment, arguing in favour of the concept of acyclic aromaticity.^[3]

Despite recent trends, it would appear useful to designate systems as "aromatic" if they represent a delocalized system exhibiting peculiar chemical stability, in order to focus attention on such systems even when they are buried in complex structures. Since guanidine and its derivatives appear to possess really exceptional stability, and since their physical and chemical properties appear to be dominated by the tendency to retain the closed-shell, Y-delocalized 6 pi-electron configuration, we suggest that it is profitable to consider such substances as possessing a special type of "aromatic character," despite their acyclic nature.

For a general understanding of this feature it certainly does not hurt to keep it in the back of ones head.^[4]

However, the applicability of this concept is limited to a quite small subset of compound (the same holds true for Hückel's rule, too). It therefore seems to be quite a superfluous concept, since it is in a more general sense already covered by resonance stabilisation.
After all, electronic structures are often not well enough described with simple models and in some cases these simple models can lead to wrong assumptions. This is one of these cases, where one can only use this concept as long as its restrictions are well known.

Some people might argue, that the naming itself is the problem and it may lead to confusion. I can partly agree with that. That does not change the fact, that the description in resonance, valence bond and molecular orbital theory terms will produce this result. In general I think the term aromaticity is unfortunate right in the beginnings. The concept has changed and extended quite a few times already. I often see problems when the term "Hückel rule" is used synonymously with aromaticity.

There is no true theoretical and at the same time all general explanation for aromaticity. It is often determined on a case by case basis experimentally. This limitation also has to apply to any derivations of it.

Electronic structure of the trinitromethane anion (TNM^⊖)

Trinitromethane is a quite acidic substance, which can in part be attributed to the presence of the well delocalised π system. Cioslowski et. al. have investigated the anion and came to this conclusion. In their paper they also use the term Y-aromaticity.^[5]

Our calculations, however, show that at the HF/6-31G* level, the carbon atom is coplanar with the nitrogens while the oxygens of the nitro groups are rotated out of plane. The result is a structure with $D_3$ symmetry. The $\ce{C(CN)3^-}$ anion is likewise found to be planar, while the $\ce{CF3^-}$ ion exhibits a pyramidal geometry. In addition, we observe in $\ce{C(CN)3^-}$ a shortening of the carbon-carbon bond and a lengthening of the carbon-nitrogen bond relative to $\ce{CH(CN)3}$. We also find an analogous shortening of the carbon-nitrogen bond and lengthening of the nitrogen-oxygen bond in $\ce{C(NO2)3^-}$ relative to $\ce{CH(NO2)3}$. In contrast, the $\ce{C-F}$ bond length increases upon going from $\ce{CHF3}$ to $\ce{CF3^-}$. The planarity of the $\ce{C(NO2)3^-}$ and $\ce{C(CN)3^-}$ ions and the changes in bond lengths are obvious consequences of Y-aromaticity in these systems.

Obviously the bonding situation in the trinitromethane anion is a little more complicated than in guanidine, as the nitro group itself cannot be described by a single Lewis structure. The out of plane rotation of these groups further complicate things, but since the perpendicular $C_2$ axis is retained it is still somewhat possible to compare the resulting orbitals to a planar species. Therefore when you look at the orbitals you still find a remarkable resemblance to the picture above. For this purpose I have included the same schematic drawings next to the orbitals that resemble these best.

It is noteworthy, that because of the propeller structure there is no strict separation between σ and π orbitals, since the latter require a horizontal mirror plane, which is absent here.

But that is not all. Try counting the number of π electrons. This is far from trivial and it is in no case that makes sense six.^[6] Don't let your brain explode about that fact, we are clearly dealing with a borderline case at this point.

And we have not even started to talk about the possibility of bonds between the oxygens of the nitro group.^[7]

Take home message for TNM^⊖

The trinitromethane anion has a strongly delocalised electronic system. It is extraordinarily stable due to this. If you accept the concept of Y-aromaticity as valid, then it is still a borderline case, where additional considerations have to be taken into account.

Notes, References and further reading

1. Bent's Rule
   
   


2. The six π electrons are probably the reason for the statement in the Wikipedia article.



3. Gund, P. J. Chem. Educ. 1972, 49 (2), 100. DOI: 10.1021/ed049p100.


4. I have used this concept already various times to explain certain electronic structures. From a personal point of view I find it quite helpful.
   
   


5. Cioslowski, J.; Mixon, S. T.; Fleischmann, E. D. J. Am. Chem. Soc. 1991, 113 (13), 4751–4755. DOI: 10.1021/ja00013a007.


6. There are several possibilities, that can be considered to count electrons towards the number of π electrons.
   
   
   
   • The probably easiest way would be to flatten the molecule for this thought experiment, then count electrons perpendicular to the plane. This gives you two electrons for the central carbon (sp²), no electrons from the nitrogens (sp²) and two electrons each from the oxygens (sp). That gives you a total of 14 π electrons.
   
   
   • Maybe as simple as this, but somewhat the easy way out would be to disregard all contributions from the nitro groups, leaving only 2 π electrons.
   
   
   • Regard the nitro groups as π-backdonor. Since only one of the intrinsic π orbitals can effectively overlap with the central carbon, each of them would donate two electrons (maybe less, because backdonation). Plus two from the central carbon, makes up to eight electrons. This certainly is a very fuzzy approach.
   
   
   
   • Count four electrons per oxygen, which is kind of cheeky, but it could work. This would give 26 π electrons.
   
   
   • Write a Lewis structure and count only the double bonds (× 2), which gives a total of eight electrons.
   
   
   • I am almost certain, there are still more ways to count the electrons.
   
   
   
   


7. In [5] they analysed the anion with the quantum theory of atoms in molecules. They found bond critical points between the oxygen atoms. How these can be explained and what they mean is certainly a story for another time.

word choice - What is the difference between "meshi" and "don" for the food sometimes translated as "rice bowl" in English?

I'm a big fan of the Japanese fast food gyudon (cooked thinly sliced beef strips on top of a bowl of boiled white rice) and its variants such as butadon (the same but with pork).

But why do some chain restaurants call it "gyudon" and others "gyumeshi"? Are both spelled the same?

Also at my local Japanese restaurant at home in Australia they seem to sell this dish but never understand me when I ask for gyudon. Does it have other names or are there simply dishes which seem alike to ignorant foreigners like me?

Answer

The 丼 donburi in 牛丼 gyūdon specifically denotes a bowl of rice.
The 飯 meshi in 牛飯 gyūmeshi just means rice or even more generically meal.

Both describe the same thing:

ぎゅう‐どん【牛丼】
「牛飯（ぎゅうめし）」に同じ。

"See gyūmeshi."

ぎゅう‐めし【牛飯】
ネギなどと煮た牛肉を、汁とともにかけたどんぶり飯。牛丼（ぎゅうどん）。

"A rice meal with onions and fried beef [...]. Gyūdon."

I'm not sure which one is preferred in which situation, but personally I see more gyūdon in daily life (caveat: I don't eat it too often though). There are many specialized kinds of 丼 donburi, while 飯 meshi can be used for almost anything edible and is usually just used in the sense of "meal". It can also specifically denote rice though, as in 焼飯 yakimeshi - "fried rice", which is more often called チャーハン chāhan though.

meaning - What is the purpose of 中 in ダウンロード中?

When I am downloading something, this comes up. I guess it would mean that the download is in progress or something but it seems a little unexpected to have that there. Is it something that you'd say out loud for something else that is progressing or would it be exclusively for digital progressions?

resonance - Rationalizing the Planarity of Formamide

In formamide, the nitrogens appear to be $\ce{sp^3}$ hybridized, implying tetrahedral geometry. However, analysis shows that the molecule is actually very nearly planar with bond angles close to 120 degrees.

EDIT: as suggested by Martin and another poster, hybridization is a rough concept. So perhaps the hybridization of nitrogen upon further analysis should best be described as somewhere inbetween $\ce{sp^3}$ and $\ce{sp^2}$. This however would still necessitate planarity, correct? Pi bonds are formed through the above and below electron-pairing in p-orbitals; effective bonding is achieved when these p-orbitals are parallel with respect to each other.

I'm thinking this has to do with the partial double bond character in the molecule (also appears to be some ionic character to the molecule - likely due to electron-withdrawing effects of the nitrogen and the oxygen).

This is the standard answer. However, would intramolecular hydrogen bonding also play a role? Couldn't there be a hydrogen bond between the peripheral hydrogen on the nitrogen and the oxygen? Couldn't this also help with achieving the 120 degree bond angles?

Answer

Most of the amides are planar (due to steric reasons the restriction may be lifted) and so is also formamide.

The carbon is obviously $\ce{sp^2}$ hybridised (as this concept is very well applicable here), hence organising it's ligands in one plane with roughly $120^\circ$ angles. Naturally one would assume the nitrogen to be $\ce{sp^3}$ hybridised, which is the case for most amines. However, the inversion barrier for these molecules is (depending on the substituents) very low. $$\ce{[NH3]^{pyr-top} <=> [NH3]^{TS-plan} <=> [NH3]^{pyr-bot}}$$ For the nitrogen that means going from $\ce{sp^3}$ to $\ce{sp^2}$ and back again. You can now stabilise the intermediated structure with conjugation, and that is exactley the case here. In your chart, that refers to entry 2. This causes the nitrogen to most likely be of $\ce{sp^2}$ hybridisation and the lone pair of entry one would be in a $\ce{p}$ orbital.

The conjugation happens as stated in you chart by the overlap of that orbital with the antibonding $\pi^*~\ce{C-O}$ orbital. This causes the $\ce{N-C}$ bond order to increase, while the $\ce{C-O}$ BO has to decrease.

All those resonance structures are only descriptions of extreme states, the truth lies between them. The following scheme considers the most common ones and adds a third, that might explain delocalisation (in a non-traditional Lewis way) up to a certain visual point.

In molecular orbital theory you can form 3-centre orbitals from all molecules perpendicular to the molecular plain. If you choose this plane to be $xy$ then the contributing orbitals will be $\ce{p_{$z$}}$. The following scheme may support this claim, the dipicted orbitals were obtained by a BP86/cc-PVTZ calculation. (The HOMO is an in-plane lone pair of oxygen.)

While there is certainly no intra molecular hydrogen bond ($d(\ce{O-H}\approx 2.57$ same level), there will also most certainly be an attraction between the $\ce{C-O}$ and $\ce{N-H}$ bond helping to stabilize the planarity. But I will not go into detail about that, because it would involve breaking away from the very handy hybridisation concept.

words - Is Aggadah the same thing as Midrash?

(Inspired by a comment on this question.)

What characteristics define Aggadah and Midrash, and how are they related?

If the distinction is merely that Aggadah is a more general category of "legend" and Midrash is Aggadah as taught by a certain category of Aggadists (Tannaim/Amoraim), what is the practical difference in terms of how one approaches them from a theological or philosophical (or even historical) perspective?

how to - How do you vet a day school?

How do you go about investigating whether a particular day school is best for your kids? I am most interested in the behavior and attitude of the students and the professionalism of the teachers and staff. I realize that it's possible to get some sense of these by visiting, but the feel one gets from a single visit is skewed by the halo effect induced by the presence of the visitor. It seems that it would be difficult to get a good sense of these things by asking around because anyone who knows about the school is likely to present a biased perspective based on their own experience, and because frank talk on these topics veers uncomfortably close to lashon hara.

Answer

There are some objective questions that can be asked that may help.

BEHAVIOR/ATTITUDE OF STUDENTS

• How much of the school day/year is devoted to teaching of midot?


• 
  
  

  Does the school arrange activities outside of the school that would encourage good character like field trips to nursing homes for "Bikur Cholim"?

  
  


• 
  

  A subjective but perhaps more easily observed without getting into lashon harah areas: Look at the youth groups in your local shul: Is there any correlation between the kids who are respectful and those who are not and the schools they attend?

  
  

PROFESSIONALISM OF TEACHERS AND STAFF

• What kind of continuing education does the school provide?


• Do the school administrators attend professional conferences to stay on top of the latest methods in Jewish/secular education?



• Has the school brought in professional consultants in the development of it's curriculum or other programs?


• Also look at the board: What kind of professional development have they had? It's not uncommon in Jewsih schools to have the board try to micromanage the principal and other school adminsitrators. The board should not be discussing individual classroom situations and parent complaints. Hopefully they have vetted and hired a trusted administrator and should only be doing periodic evaluations, not trying to run the day to day operations of the school themselves. Overseeing the school financial stability should be their primary role. When you have parents on the baord with their own adgenda who are not educators, and allowing their own issues to supercede the big picture, the school's overall professional conduct suffers.

Hopefully there are a couple useful ideas in there.

particle は - ‥ができないと vs ‥はできないと

Every evening, we play the かたづけ怪獣 song, where they sing:

おかたづけができないと
あらあら、大変 (x3)
おかたづけ怪獣が出て来るぞ！

Now I've been grappling with this language long enough that ‥ができないと sounds natural in this context, while ‥はできないと sounds off, but I couldn't put my finger on why. My wife, a native speaker, pondered this for a moment and then theorized that は would be a simple statement of fact:

If you can't clean up, the cleanup monster will come!

While が implies that, while there may be lots of things you can't do, surely you can at least clean up:

If you can't even clean up, the cleanup monster will come!

I buy the first half of that explanation, but the second seems fuzzy. Is she right, and is there a more general rule here?

Answer

I think it's the opposite? が simply states the fact, while は would imply "at least". I'm a native speaker myself.

For example,

銀メダルが取れた
  -> I got the silver medal
銀メダルは取れた
  -> I got at least the silver medal (but not the gold medal)

銀メダルが取れないと帰れない

  -> If I don't get the silver medal, I can't return
銀メダルは取れないと帰れない
  -> If I don't even get the silver medal, I can't return