Correlation between Fourier series expansion and Hückel orbital theory

Liu, Y., Liu, Y. and Drew, M. G. B. (2013) Correlation between Fourier series expansion and Hückel orbital theory. Journal of Mathematical Chemistry, 51 (2). pp. 503-531. ISSN 0259-8897 doi: 10.1007/s10910-012-0092-9

Abstract/Summary

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/31275
Item Type	Article
Refereed	Yes
Divisions	Life Sciences > School of Chemistry, Food and Pharmacy > Department of Chemistry
Publisher	Springer
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