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Characteristic polynomials of organic polymers and periodic structures
Author(s) -
Balasubramanian K.
Publication year - 1985
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540060620
Subject(s) - periodic boundary conditions , mathematics , frame (networking) , hexagonal crystal system , boundary (topology) , pure mathematics , boundary value problem , combinatorics , mathematical analysis , crystallography , computer science , chemistry , telecommunications
It is shown that the Frame's method (also, Le Verrier‐Faddeev's method) for characteristic polynomials of chemical graphs can be extended to periodic graphs and structures. The finite periodic structures are represented by cyclic structures in the Born‐von Kárman boundary condition which leads to complex matrices. In this article we demonstrate that our earlier computer program (based on Frame's method) can be extended to these periodic networks. The characteristic polynomials of several lattices such as polydiacetylenes, one‐dimensional triangular, square, and hexagonal lattices are obtained. These polynomials can be obtained with very little computer time using this method.