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:
Secular polynomials (SPs) have been constructed and studied for the adjacency matrices A(GaCh) and A(GbCh) corresponding to chemical graphs of alkanes in terms of atoms (GaCh) and in terms of bonds (GbCh). The three second-class Chebyshev polynomials Up(Q), Up - 1(Q), and Up - 2(Q), with respect to the variable Q proportional to the SP of an isolated CH2-like subgraph, have been shown to appear within both SPs P[A(GaCh)] and P[A(GbCh)] and to play the role of algebraic analogues of a (CH2)p-like subgraph. Common noncanonical algebraic expressions for both SPs reflecting the regular internal structure of alkanes have been constructed on this basis. Spectral properties of both graphs GaCh and GbCh have been shown to be determined by those of Up(Q), e.g., the band limits of spectra proved to be related to the orthogonality interval Q = [-1;1] for polynomials Up(Q). Since the adjacency matrices (AMs) A(GbCh), but not A(GaCh), are proportional to definite model Hamiltonian matrices, the obtained results serve to interpret the one-electron spectra of alkanes in terms of peculiarities of usual chemical structure. © 1996 John Wiley & Sons, Inc.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
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