# What does the charge distribution around a Stone-Wales defect look like?

I'm reading a book on carbon nanotubes (P.J.F. Harris, Carbon Nanotube Science, to be specific) at the moment and puzzling about Stone-Wales or 5775 defects. This is where two adjacent carbons undergo a 90-degree rotation about their mutual centroid and generate a defect consisting of two five membered rings and two seven membered rings, as I've illustrated below (This is only supposed to be qualitative, and is on a finite PAH fragment rather than a nanotube, but you should get the idea):

I note that tropylium ($\ce{[C7H7]^+}$) is aromatic as a cation, and the ever famous cyclopentadienide ($\ce{[C5H5]^-}$) is aromatic as an anion, so what I'm wondering is: do the 5 and 7-membered rings in a Stone-Wales defect pick up either formal or partial negative and positive charges to maintain aromaticity in a fashion consistent with the rest of the structure?

## P.S.

Big props to F'x, who attempted electronic structure calculations on the PAHs depicted, regrettably without SCF convergence.

• I've just noticed your use of equilibrium arrows - is this really an equilibrium? – CHM May 14 '12 at 17:06

FWIW, here are some Hückel calculations on the 5775 PAH.

I'm showing the first 7 energy levels. Each molecular graph presents the contribution of each atom to the electron density ($\mathrm{Abs}[c_i]^2$). This is not normalized. I do not use wavefunctions, only the coefficients multiplying them, assuming

$$\Psi_{\mathrm{mol}} = \sum_i^n c_i\psi_i$$

In this approximation (HMO), the first 7 energy levels will be occupied (14 pi electrons).

I will first give you pictures of each energy level, and then a linear combination of each. Take it for what it is, as there is much information lost in the process.

To me, this simply suggests that indeed, the system will behave as if composed of tropylium and cyclopentadienyl ions. But this is not publication quality calculation either =)

Here are compared the linear combination of the first 7 energy levels of the 5775 and 6666 systems. It is clear that electron distribution is not the same in both PAHs, which hints that my calculations are not so far fetched.

5775

6666