Journal ArticleDOI
On the graphical factorization of Hückel characteristic equations
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TLDR
In this article, it was shown that the method of McClelland for graphical factorization of Huckel matrices of conjugated systems can also be applied if the system has twofold symmetry but no plane of symmetry perpendicular to the molecular plane.Abstract:
It is pointed out that the method of McClelland [3] for the graphical factorization of Huckel matrices of conjugated systems can also be applied if the system has twofold symmetry but no plane of symmetry perpendicular to the molecular plane.read more
Citations
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The characteristic polynomial of a chemical graph
TL;DR: In this article, a list of uses of and the computational methods for the characteristic polynomial of a (chemical) graph is presented, and several computational methods are singled out for more detailed presentation.
Journal ArticleDOI
Electronic and structural properties of biazulene, terazulene, and polyazulene isomers
TL;DR: In this article, the dihedral angles between the azulene units at the bridging bond in biazulenes were determined by MM2 calculations, and they were predicted to be conductive only via the polaron mechanism.
Journal ArticleDOI
Splitting of n-fold rotationally symmetric graphs
TL;DR: In this article, the McClelland and D'Amato rules are special cases with n = 2 and n = 3, respectively, and they are derived from a unitary transformation on the adjacency matrix.
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Techniques in facile calculation of molecular orbital parameters and related conceptualizations—molecular orbital functional groups
TL;DR: The superhighway to greater understanding requires the development of techniques for facile methods (i.e., back of an envelope methods) of calculation and conceptualization of chemical phenomena as mentioned in this paper.
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Construction of planar graphs for IPR fullerenes using 5- and 6-fold rotational symmetry: some eigenspectral analysis
TL;DR: In this article, an algorithm has been developed for the construction of planar graphs for two series of IPR fullerenes of the general formula C50´+´10n and C60´´12n maintaining 5-and 6-fold rotational symmetry, respectively.
References
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Journal ArticleDOI
Graphical method for factorizing secular determinants of Hückel molecular orbital theory
TL;DR: In this paper, a graphical method for simplifying the solution of Huckel's secular equations for molecules with symmetrically-placed atoms is presented, where the solution can be expressed as follows:
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Quantum Mechanics of Mobile Electrons in Conjugated Bond Systems. III. Topological Matrix as Generatrix of Bond Orders
TL;DR: In this article, it was shown that in homonuclear conjugated systems the various bond orders and similar quantities can be written as matrix functions of the topological incidence matrix.
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Eigenvalues of graphs with twofold symmetry
TL;DR: In this article, it is shown that whenever a composite graph G has a twofold symmetry operation which defines two equivalent sets of vertices r and s, it is possible to construct two subspectral components G + and G -, whose eigenvalues, taken jointly, comprise the full spectrum of G. The following rules are given for constructing the components.