Huckel's rule for Aromaticity--what is n?

brady.fosse

1. The problem statement, all variables and given/known data

Probably a really stupid question. When using Huckel's rule to figure out if a cyclic compound is aromatic or not, and considering that it must have 4n + 2 pi electrons, how do I figure out what n is?

2. Relevant equations

4n + 2

3. The attempt at a solution

I'll just use Benzene as an example, but I have tried on many other compounds.
I have tried using the number of carbons in the ring (n is one for benzene but there are six carbons, so that doesn't work), the degree of unsaturation (which is 4 for benzene, not one), the number of hetero/electronegative atoms (obviously this doesn't work), and some other less impressive ways of thinking about it. I can't find an explanation anywhere in the textbook and am a bit confused about why they changed n from signifying 'number of carbons' to something else without telling anyone.

Someone told me n is the number of cyclic rings within a compound, which makes sense for benzene (1) and napthalene (2) but if that's the case then I don't know what to do with bigger aromatics such as octo/nano/decatriene--I'm not sure if those in particular are even aromatic due to my lack of understanding of this simple rule, but I did see some examples of bigger rings that had n values of two.

If anyone can shed any light on this at all I would appreciate it. I really can't advance with this material unless I grasp this. Thanks.

brady.fosse

oh...does the rule just mean that if the total number of pi electrons are a multiple of four plus two (n is whatever that multiplier is) then it qualifies as aromatic?

Borek

Yes, n is just any integer.

brady.fosse

thank you very much

neeraj93

True, n is just any integer, but it has to signify sumthing! i mean, come on, we're talking science, you can't just use any 'n' straightway without challenging its credibility.
Yes, it's true that there are hardly few books which mention what 'n' is. I don't think it's there even in Morrison and Boyd.
To answer the question, it's fundamentally based on the MOT: aromatic systems have 4n+2 electrons, where n is the number of pairs of degenarate bonding orbitals.
Consider Benzene as an example. we concern ourselves only with the pi-orbital system. Benzene has six atomic p-orbitals, which give six pi molecular orbitals (MO's): three bonding orbitals,say [tex]\psi[/tex]₁, [tex]\psi[/tex]₂, [tex]\psi[/tex]₃, and three antibonding, say, [tex]\psi[/tex]₄, [tex]\psi[/tex]₅, [tex]\psi[/tex]₆. the 6 p-electrons arrange themselves in the 3 bonding orbitals. [tex]\psi[/tex]₁ has no node, while [tex]\psi[/tex]₂ & [tex]\psi[/tex]₃ have one node each. Furthermore, The energy level of the orbitals increases with increasing number of nodes. Thus, [tex]\psi[/tex]₁ is at a lower energy level than [tex]\psi[/tex]₂ and [tex]\psi[/tex]₃, which share the same energy level, having one node each. [tex]\psi[/tex]₂ and [tex]\psi[/tex]₃ are said to be degenerate. Benzene, thus has one pair of degenerate bonding orbitals (i.e, n=1). For higher aromatic systems, the number of pairs of degenerate bonding orbitals increases. Napthlene has 10 atomic p-orbitals, thus, 10 MO's. The 5 bonding orbitals contain 2 pairs of degenerate orbitals and along with [tex]\psi[/tex]₁.
[tex]\psi[/tex]₁ can contain 2 electrons, while each degenerate pair has a capacity of 4 electrons. Thus, the rule: 4n+2, which is the configuration having all pi-bonding orbitals completely filled, associated with extra stability.

farooq

There are some conditions for application of Huckel's rule.One of the most important among them is that the molecule must have a planar structure. It must not contain any sp3 or dsp2 & other hybidised C atom which correspond to a three dimensinal structure. If the molecules do not obey this condition, then even if they have 4n+2 pi electrons, they will not looked upon as an aromatic compound.

the next speculum is that they must have a cyclic structure.

If the concerned molecule satisfies the above said conditions, we may apply the Huckel's rule that is it must contain 4n+2 pi electrons.(n=an integer, ie 0,1,2,3.....) .Each single bond correspond to 0 pi electrons ,each double bond correspond to 2 pi electrons,& each triple bond corresponds to 2*2=4 pi electrons.

If the concerned compound follows all these said conditions, it may be looked upon as an aromatic organic compound.

eg- Benzene(C6H6)
1)All carbon atoms in Benzeze is sp2 hybridised. So it has a planar structure.( 1st condition fulfilled)

2) it has a cyclis ring structure,(2nd condition fulfilled)

3) A benzene molecule contains 3 single & 3 double bond. Hence the total no. of pi electrons= 3*0+3*2=6
putting n=1,
hence 4n+2=6
Hence benzene follows 4n+2 rule.(3rd condition fulfilled)

all the conditions being fulfilled Benzene may be looked upon as an aromatic compound.