In
Hückel theory Hückel or Huckel may refer to:
* Erich Hückel (1896-1980), German physicist and chemist
** Debye–Hückel equation (named after Peter Debye and Erich Hückel), in chemistry, a method of calculating activity coefficients
** Hückel method (name ...
, a Dewar reactivity number, also known as Dewar number, is a measure of the reactivity in
aromatic system
In chemistry, aromaticity is a chemical property of cyclic ( ring-shaped), ''typically'' planar (flat) molecular structures with pi bonds in resonance (those containing delocalized electrons) that gives increased stability compared to satura ...
s. It is used to quantify the difference in energy between the π-system of the original molecule and the
intermediate having the incoming
electrophile
In chemistry, an electrophile is a chemical species that forms bonds with nucleophiles by accepting an electron pair. Because electrophiles accept electrons, they are Lewis acids. Most electrophiles are positively charged, have an atom that ca ...
or
nucleophile
In chemistry, a nucleophile is a chemical species that forms bonds by donating an electron pair. All molecules and ions with a free pair of electrons or at least one pi bond can act as nucleophiles. Because nucleophiles donate electrons, they a ...
attached. It can be used to study important transformations such as the
nitration
In organic chemistry, nitration is a general class of chemical processes for the introduction of a nitro group into an organic compound. The term also is applied incorrectly to the different process of forming nitrate esters between alcohols an ...
of conjugated systems from a
theoretical perspective.
The change in energy during the reaction can be derived by allowing the
orbitals nearby the site i of attack to interact with the incoming molecule. A
secular determinant
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix among its coefficients. The chara ...
can be formulated resulting in the equation:
where β is the Huckel interaction parameter and a
r and a
s are the coefficients of the highest energy molecular orbital at nearby sites r and s respectively. Dewar's reactivity number is then defined as
.
Clearly, the smaller the value of N
i, the less the destabilization energy in going towards the
transition state
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
and the more reactive the site. Thus, by computation of the molecular orbital coefficients it is possible to evaluate Dewar's number for all the sites and establish which one will be the most reactive. This has been shown to correlate well with experimental results.
The method is particularly efficient for
alternant hydrocarbon An alternant hydrocarbon is any conjugated hydrocarbon system which does not possess an odd-membered ring. For such systems it is possible to undertake a starring process, in which the carbon atoms are divided into two sets: all the carbons in one ...
s in which the coefficients of the non-bonding orbitals involved are very easy to calculate.
References
Molecular physics
Theoretical chemistry
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