This article is dedicated to Prof. Roald Hoffmann (Ithaca, New York), Prof. Friedrich Franz Seelig, Prof. Michael Hanack (Tübingen, Germany), and Dr. F.-W. E.
On the “Wolfsberg–Helmholz Conjecture” of “Extended-Hückel Theory”†
Article first published online: 22 NOV 2012
Copyright © 2012 Wiley Periodicals, Inc.
International Journal of Quantum Chemistry
Volume 113, Issue 10, pages 1568–1572, 15 May 2013
How to Cite
Koch, W. H. G. (2013), On the “Wolfsberg–Helmholz Conjecture” of “Extended-Hückel Theory”. Int. J. Quantum Chem., 113: 1568–1572. doi: 10.1002/qua.24362
- Issue published online: 2 APR 2013
- Article first published online: 22 NOV 2012
- Manuscript Accepted: 4 MAY 2012
- Manuscript Revised: 16 APR 2012
- Manuscript Received: 14 MAR 2012
- Mexican “Sistema Nacional de Investigadores (SNI)” of the “Consejo Nacional de Ciencia y Tecnología (CONACYT)”
- “Programa de Primas al Desempeño del Personal Académico de Tiempo Completo (PRIDE)” of “Universidad Nacional Autónoma de México (UNAM).”
- Rüdenberg's Integral Approximations;
- Roothaan's “Restricted Hartree–Fock” Theory;
- Implicit Multi-Center Integrations;
- non-empirical Extended-Hückel Theory
After having reviewed some pioneer integral approximations closely related to Rüdenberg's expansions of one- and two-electron orbital products, we apply the previously described “Implicit Multi-Center Integration” techniques on Roothaan's “restricted” Fock-matrix components over standard atomic orbital bases. The resulting compact forms are very similar to the well-known “Wolfsberg–Helmholz Conjecture” of “Extended-Hückel Theory,” which relates the various off-diagonal matrix elements of “restricted” Fock-type to their corresponding diagonal counterparts. In this way, a “nonempirical Extended-Hückel Theory” can be created. © 2012 Wiley Periodicals, Inc.