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I have been taught that the order of aromaticity is: benzene > thiophene > pyrrole > furan. However, I have been unable to deduce any logical explanation for that order. Also, I wish to compare pyridine's aromaticity with these, but my professor does not know about it.

According to me, all the rings are aromatic and satisfy the Huckel's rule of aromaticity with $6\pi$ resonating electrons and a planar ring. So, that point is useless for doing any comparison of aromaticity.

But, we note that $\ce{2p\pi-2p\pi}$ overlap is most favorable in conjugated systems. Hence, thiophene should be the least aromatic (since it has a $\ce{3p\pi-2p\pi}$ overlap instead).

I agree that benzene should be the most aromatic because both its resonating structures are equivalent and have no charge separation. Using exactly the same reasons, pyridine should be the second best aromatic ring (lesser than benzene because the N atom is an electron withdrawing group and is reducing the electron density in the ring)

That said, every resonating structure (except the uncharged one) for pyrrole and furan will create a formal positive charge on the hetero-atom. Since N is less electronegative than O, it will be slightly more stable than O with that positive charge. Hence, pyrrole will be more aromatic than furan.

Therefore, according to me, the aromaticity order should be: benzene > pyridine > pyrrole > furan > thiophene. But it is obviously wrong.

Hence, my question is: what is the order of aromaticity of benzene, thiophene, pyrrole, furan, and pyridine. And why?

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    $\begingroup$ It's not trivial to establish a quantitative degree of aromaticity, actually. Phil Baran writes benzene > pyridine > thiophene > pyrrole > furan, but I don't know where the values come from. Empirically, though, pyrrole and furan undergo dearomatisation fairly easily because they're very electron-rich; thiophene has more benzene-like reactivity because it's less electron-rich (sulfur 3p poorer overlap with carbon 2p). $\endgroup$ – orthocresol Mar 2 '18 at 12:49
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    $\begingroup$ This isn’t a full answer so I’m commenting it. Regarding thiophene, furan and pyrrole, in thiophene due to the lesser electronegativity of sulphur, the lone pair delocalises easily, and so aromatisation is better. I have no idea about how to include pyrridine among these. They(pyrridine and the other three) seem to be different systems so I’m having trouble comparing them. $\endgroup$ – Mr_Pea Mar 2 '18 at 13:28
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    $\begingroup$ I looked up Aromaticity percentages and found this: pubs.acs.org/doi/abs/10.1021/jp0657686. It says here that "In the present work concept, the ΔΔHH2 value of benzene defines the completely aromatic character (+100%), and the closed shell of the singlet cyclobutadiene represents maximum antiaromaticity (−100%)." So it's a reference scale, defined with respect to Benzene. $\endgroup$ – Abhigyan Chattopadhyay Mar 16 '18 at 5:45
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    $\begingroup$ Strictly speaking Hückel's rules do not really apply to these compounds except for benzene, as they are not derived for these cases. Also aromaticity is not a well enough defined concept to actually derive an order. You can evaluate their reactivity with respect to different mechanisms, but then you are comparing exactly that, and you are only deducing properties towards aromaticity. How could you quantify something that you can't really measure? $\endgroup$ – Martin - マーチン Mar 19 '18 at 3:26
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    $\begingroup$ @GaurangTandon That is somewhat more of a philosophical question. When you compare hydrogenation among those compounds, you do exactly that, you don't actually measure aromaticity. So with respect to aromaticity, these are all guesses; with respect to reactivity it is data, and that is in principle what you want to know. If you know which compound is "more aromatic", but it doesn't let you deduce which reactions it will undergo more than the other, then that is basically a pointless characteristic, designed to generalise. We already know that these approaches might lead to wrong conclusions. $\endgroup$ – Martin - マーチン Mar 19 '18 at 3:50
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The main criteria of aromaticity is resonant or delocalization energy. It is difference between energy contained in bonds if they were localized like in Kekule's formula for benzene and actual energy. For benzene if is about 150 kJ/mol. The more this energy the more stable molecule is.

The approaches for calculating this energy may differ. As for β-values mentioned in paper by @orthocresol it looks like it is Dewar's resonance energy per one π-electron calculated based on modified Hückel's MO method as mentioned in GSE article.

There is a table in this article with the same β-values: β-values

In English it is

Benzene                            0.065     Pentalene                     -0.018
Naphthalene                        0.055     Azulene                        0.023
Anthracene                         0.047     Fulvene                       -0.002
Tetracene                          0.042     Pyridine                       0.058
Cyclooctadecanonaene([18]annulene) 0.012     Pyrrole                        0.039
Cyclobutadiene                    -0.268     Furan                          0.007
Azete (Azacyclobutadiene)         -0.160     Thiophene                      0.032
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All the three molecules- furan,pyrrole and thiophene are aromatic in nature. There is a quite simple explanation for why thiophene is more aromatic than furan. If you draw the resonating structures of thiophene and furan, they seem almost identical. This is until the point when the lone pair of oxygen is about to return to the oxygen atom. In furan, the lone pair comes back on the oxygen atom and oxygen simultaneously shifts the existing pi-bond pair to the adjacent carbon atom. However, in thiophene, when the lone pair comes back to the sulphur atom, thiophene does not need to break any existing pi-bonds as it has an empty d-orbital to store the lone pair in. This results in an extra resonance structure for thiophene, thus increasing the extent of resonance and by extention its aromaticity.

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    $\begingroup$ Your answer implies that each resonance structure truly exists, which is incorrect. All that is actually there is the resonance hybrid alone- there is no interconversion between canonical structures -from review $\endgroup$ – William R. Ebenezer Apr 19 at 11:59
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    $\begingroup$ Unfortunately, this is fundamentally wrong on many levels. Resonance structures don't exist on their selves, and the are no unoccupied d orbitals for sulfur. $\endgroup$ – Martin - マーチン Apr 19 at 12:01
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all of the heteroatoms will give unshared electrons to the ring to complete the aromaticity,and the heteroatom that will give the unshared electrons easily will be more aromatic and this depends on the electroneagtivity therefore thiophene is more aromatic than pyrole and furan as tge sulphur has the least electronegativity

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protected by Martin - マーチン May 9 at 14:30

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