CCL: Correctly drawing aromatic compounds

Dear Aaron,

If I am understanding you correctly, you have a connectivity pattern or graph (in the mathematical sense) representing which atoms are bonded to which in an organic molecule, and you want to know how many of the bonds are double bonds?

It's easy.  I will assume your molecule consists of C, N, O, H only.  You have two equations.  Let E be the number of valence electrons that are involved in bonding.  Then:
E = 4C + 3N + 2O + H + (net charge).
Because every single bond uses two valence electrons and every double bond uses four,
E = 2 * (single bonds) + 4 * (double bonds).
Put these together and divide by 2 to get Equation (1):

Eq. (1)  (single bonds) + 2 * (double bonds) = [4C + 3N + 2O + H + (net charge) ] / 2.

Next, just count the total number of bonds in your drawing.  Obviously,

Eq. (2)  (single bonds) + (double bonds) = (total # of bonds).

Your unknowns here are (single bonds) and (double bonds).  Everything else is known from the drawing.

You have two equations in two unknowns.  Subtract Eq. (2) from Eq. (1) to get the # of double bonds.  I think the derivation and the two equations is clearest, but if you want me to do it for you, your final answer is:

(double bonds) = [4C + 3N + 2O + H + (net charge) ] / 2  - (total # of bonds).

Example: Anthracene is C14H10 and has 16 CC bonds and 10 CH bonds, giving
(total bonds) = 26.  The formula gives
(double bonds) = [4*14 + 10]/2 - (26) = 33  -  26 = 7.
There are several possible "resonance structures" for anthracene but all of them use exactly 7 C=C double bonds.

Obviously the formula will break down if there are unfilled shells, and it would have to be modified if there are triple bonds or 3rd row atoms.  I suppose if you have halogen atoms they are the same as "H" for the purposes of this calculation.

I hope this is helpful!

David Anick PhD MD
Harvard Medical School
---- Original message ----

Date: Wed, 23 Mar 2011 16:57:36 -0400
From: "Deskins, N Aaron nadeskins]-[WPI.EDU" <owner-chemistry |-at-| ccl.net>
Subject: CCL: Correctly drawing aromatic compounds
To: "Anick, David -id#3te-" <david.anick |-at-| rcn.com>
>
>Sent to CCL by: "Deskins, N Aaron" [nadeskins---WPI.EDU]
>Thank you all for your suggestions. Iâm looking into other software (ChemDraw) that may do a better job drawing some of these aromatics.
>
>But a more fundamental question is how do you predict the number of double bonds? I donât want to have to assume that a particular program is drawing the structure right, unless absolutely necessary. Much better is to determine the number of C=C bonds myself (as mentioned in my first email, I want to run some isodesmic reactions on these). Coronene and other small aromatics are easy because there are plenty of references on these structures. But Iâd like to look at other large compounds for which there is likely little data available. Someone must have some theory/method to determining the ideal number of double bonds in an aromatic structure.
>
>Any more ideas?
>
>N. Aaron Deskins
>Assistant Professor
>Chemical Engineering Department
>Worcester Polytechnic Institute
>http://users.wpi.edu/~nadeskins
>
>
>
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