Subject: polyene spectra

From: Ulrike Salzner <[email-masked]>
Date: Mon, 04 Nov 2002 13:22:54 +0200

Thanks to everyone who replied. It looks like the oldest reference to 
the 1/n dependence of excitation energies in conjugated hydrocarbons is:
 H. Kuhn, A Quantum-mechanical Theory of Light Absorption of Organic 
Dyes And Similar Compounds, J. Chem. Phys. 1949, 17, 1198-1212.
I have not yet read the article because I need to find a library in 
Turkey that has the back issues of  J. Chem. Phys., but from the e-mails 
I gather that the relationship was derived for the particle in a box model.
Regards,
Ulrike Salzner

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From: Geoff Hutchison <[email-masked]>
Date: Mon, 4 Nov 2002 08:13:29 -0600

On Monday, November 4, 2002, at 05:22  AM, Ulrike Salzner wrote:

> Turkey that has the back issues of  J. Chem. Phys., but from the 
> e-mails I gather that the relationship was derived for the particle in 
> a box model.

It's a "nearly free electron" model. It scales ~1/N because N is the 
number of monomer units--so when you add length, you also add electrons. 
But a completely free electron model (particle in a box) would have zero 
bandgap.

So Kuhn applied a periodic potential, which recovers the Peierls 
distortion: the potential is lower at the double bonds and higher at the 
single bonds. The bandgap appears as the magnitude of the potential and 
you have an additional term.

I find that the 1/N fit is better at small lengths because the bond 
lengths are still changing slightly due to delocalization. In the 
polyacetylenes, which I haven't studied, Kertesz argued in an article in 
1998 in J. Chem. Phys. that there's something like a phase transition at 
longer lengths, changing bond lengths to a more delocalized form, but 
1/N keeps up.

--
-Geoff Hutchison	<[email-masked]>
Ratner/Marks Groups	(847) 491-3295
Northwestern Chemistry	http://www.chem.nwu.edu/