Aromaticity
Aromaticity is an important concept that explains the unusual stability of certain compounds in organic chemistry. Deeply understanding this concept led to entirely new synthetic pathways and a much richer appreciation of how biochemistry tends to leverage this. Additionally, we will see how chemistry is impacted by avoiding the instability brought by antiaromaticity. Note that, in general, we only apply the idea of aromaticity to ring systems.
1. Molecular Orbital Theory from the Perspective of Organic Chemistry
I want to immediately note that there are a variety of theories of chemical bonding that you have encountered at this point. The current state of the art for chemistry is a mathematical model known as quantum chemistry. Other models that are extant today are mathematically simpler models. For instance, we often employ valence shell electron pair repulsion theory (VSPR theory) to rapidly determine approximate bond angles. This theory states nothing more than that electrons occupy shared orbitals and that since they all share a negative charge they prefer to orient as far away from each other as possible. For atoms of low atomic number and relatively uncomplex compounds VSPR theory does a great job of predicting bond angles.
For instance, using VSPR theory to predict the bond angles around carbon for acetone we obtain 1200 for each angle. This is very close to the experimentally determined bond angles of approximately 121.50 between one of the noncentral carbon atoms and the oxygen atom. If use quantum theory to compute the bond angles it is in complete agreement within experimental precision. However, it takes many hours of computational time to run the simulation using quantum theory and we can get the VSPR approximation with a basic knowledge of cartesian geometry!
Molecular orbital theory (MO theory) is a more complex mathematical framework. It rests on the assumption that when atoms bond, they form molecular orbitals that proportionally combine the character of the atomic orbitals that went into them. You’ve been using MO theory every time you describe the hybridization of a carbon atom (in truth, you’re probably using both MO and VSPR theory when you think about a particular carbon atom!). MO theory also tells us that for every atomic orbital that went in, we get a molecular orbital out. I’m going elucidate an important point here: all practicing chemists understand MO and VSEPR theory are both fundamentally incorrect. However, when doing science, we often look to the SIMPLEST explanation with the MOST explanatory power. For instance, even when you do quantum calculations, we usually use VSEPR and MO theory to approximately orient atoms beforehand. Use of the full MO theory gives us bond lengths whereas VSEPR theory can only given approximate bond angles.
Let’s consider the quintessential MO theory example for organic chemistry: 1,3-butadiene. Below, we see the 4 possible molecular pi orbitals in order of increasing energy. The first orbital allows one electron to travel the length of the top of the molecule continuously while the bottom allows the other electron to travel the length of the bottom of the molecule continuously. The second orbital confines the electrons to smaller spaces. Now, electrons are not classical objects and occasionally, they can jump across a node through a process known quantum hopping, but they stay in the orbital of the same color. In general, confining electrons in smaller spaces increases their bonding energy and destabilizes a molecule. The proper kind of conjugation in a ring creates a system where the lowest energy electrons can travel entirely around the molecule.
The right two diagrams depict what are called nonbonding orbitals. On either end of the third diagram we have nonbonding orbitals which offer no molecular stabilization. The last diagram consists of only nonbonding orbitals. Every orbital in this diagram is out of phase with its neighbor and we call this situation antibonding. This offers no molecular stabilization at all. Even populating the third orbital results in molecular destabilization since this molecular orbital sets at a higher energy than any of the atomic orbitals that gave rise to it.
2. The Simplest Indicator: Huckel’s Rule
Let’s immediately lay out some of the framework for aromatic stabilization. Aromaticity only applies to cyclic compounds that have conjugated double bonds (alternating single and double bonds).
Huckel’s rule asks us to count the pi electrons in a given ring system. If that number is divisible by four then the system is likely antiaromatic. If that number has remainder 2 when divided by four then our system is likely aromatic. Consider the following two examples:
If we look at cyclobutadiene, we count 4 pi electrons. According to Huckel’s rule, this should be antiaromatic and this compound, indeed, is! We count 6 pi electrons in benzene and thus benzene should be aromatic and is!
Aromatic compounds are unusually stable and require high energy intermediates to undergo chemical reactions. They tend to persist in the environment and sometimes present environmental problems. PCBs (polychlorinated biphenyls) are an example a highly carcinogenic compound that persists in the ambient environment for a long time due to its aromatic stability.
Cyclobutane is a relatively stable liquid at room temperature. Cyclobutadiene, in contrast, is so unstable that it has never been isolated on its own (it immediately dimerizes in storage) and vaporizes at -1000C. It becomes particularly reactive at temperatures of 35 degrees above absolute zero.
3. Aromaticity on a Slightly Deeper Level: Three Dimensional Structure
Both antiaromaticity and aromaticity require that rings be planar. If the rings bend out of plane then the molecular orbitals can no long overlap. We can examine cyclooctatetra-1,3,5,7-ene
A huge proportion of organic chemistry is about being able to think of how three dimensional spatial arrangements of atoms lead to interesting or potentially unexpected results in properties and reactions if we hadn’t considered them. In organic chemistry we ALWAYS HAVE TO THINK THREE DIMENSIONALLY. Ring systems with 7 or more carbon atoms- even conjugated systems which might be inclined to lane flat often exhibit unexpected flexibility. Big ring systems are floppy! As a result, big ring systems are usually just nonaromatic, but we have to realize this is because the system is not planar. Ring systems with kinks in them also are unlikely to be aromatic.
You might think 1,2,4-cyclohexatriene is aromatic because you count six pi electrons and you see a structure that might be planar. The actual three dimensional geometry of the molecule given below on the right has weirdly kinked structure and this molecule is consequently nonaromatic.
If we use only Huckel’s rule, we assume that this molecule is antiaromatic and thus has lowered stability. This is not what is observed. Instead, this molecule bends out of plane and, as a result, produces a nonaromatic system.
Similarly, annulene (cyclodecapenta-1,3,5,7,9-ene) seems like it should be aromatic, however, it is not. Out of plane bending results in molecules that not additionally stabilized by aromatic resonance and readily undergo the normal chemical interactions of alkenes unlike benzene.
4. Stabilization vs. Destabilization and Frost Circles
Consider two reactions:
iodocyclopentane forms a carbocation
The second reaction looks particularly favorable because we form a secondary carbocation with resonance stabilization. The only issue here is that this reaction DOES NOT HAPPEN. We are in a position to explain this now. The first reaction happens readily, but the second is not observed. When Iodine leaves, I have vacant $pi$ orbitals that are conjugated to my double bonds. Cyclopentanes are planar and I now have 4 $pi$ electrons. This carbocation would be ANTIAROMATIC.
One useful shorthand method for determining aromaticity is a method called a frost circle. To construct a frost circle, you first verify your cyclic structure is fully conjugated, then you draw it with a vertex facing where a negative y-axis might run through your circle. Below, I have created 4 frost circles for the following compounds, cyclobutadiene, pyrrhole, benzene, and azepine.
All are fully conjugated systems (on paper, at least!). The green line represents the energy gained by aromatic stability. If orbitals at or above the line are populated then the molecule is destabilized instead of stabilized (it is antiaromatic). Now, we count up the free $\pi$ electrons in each system: 4, 6, 6, 8. Then we start filling orbitals from the lowest energy to the highest. Remember Hund’s rule- if two orbitals are of the same energy, we place 1 electron in each orbital before filling either of them. We also place electrons in orbitals with the same spin in two half-filled orbital. If we examine the diagrams below, we then see that cyclobutadiene is antiaromatic, pyrhhole is aromatic, benzene is aromatic, and azepine is antiaromatic. These are largely correct and reasonable conclusions. I do want to point out that once cyclic systems have 7 or more carbons they have added flexibility that may result in them being nonaromatic. This is exactly what we see in azepine. 8 or more carbon rings will always bend out of plane to avoid antiaromaticity, but 7 carbon rings are a case-by-case basis. Saying this azepine is antiaromatic based on a frost circle is a good first guess though!
