ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
We consider the Hückel approximation to the π-electron spectrum of molecules which are built by linking a number of identical fragments to a central atom in an identical manner. The Hückel matrix H of the composite molecule (or equivalently the adjacency matrix of the molecular graph) is simply related to the Hückel matrix h of the fragment and a vector \documentclass{article}\pagestyle{empty}\begin{document}$ vec{f} $\end{document} which encodes the bonding of a fragment to the central atom. The eigenvalues and eigenvectors of H are obtained from those of h. The orbitals of the composite molecule are of three types: (1) a molecular orbital of the fragment localized on one of the fragments, (2) a molecular orbital of the fragment spread over more than one fragment, and (3) orbitals spread over the entire molecule including the central atom. The orbital energies Λ of the first two types of orbitals are same as the orbital energies λ of the fragment. Energies of the third type of orbitals separate a subset of orbital energies of the fragment and, barring accidental degeneracy, they are distinct from all orbital energies of the fragment. It is only through the third type of orbitals that the composite molecule manifests itself as a new entity rather than an aggregate of noninteracting fragments. It is shown that the graph group of H fails to explain its degeneracy if any eigenvector of the subgraph, not orthogonal to the connection vector \documentclass{article}\pagestyle{empty}\begin{document}$ vec{f} $\end{document}, belongs to a degenerate manifold of h. This solves a long-standing puzzle regarding degeneracy in the Hückel spectrum of triphenylmethyl.
Additional Material:
5 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560350509
Permalink
