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Title of Journal: J Math Chem

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Abbravation: Journal of Mathematical Chemistry

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Kluwer Academic Publishers

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DOI

10.1007/bf01022459

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1572-8897

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Repeat Space Theory Applied to Carbon Nanotubes an

Authors: Shigeru Arimoto
Publish Date: 2006/03/18
Volume: 41, Issue: 3, Pages: 231-269
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Abstract

The present article is the first part of a series devoted to extending the Repeat Space Theory RST to apply to carbon nanotubes and related molecular networks Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST All of these four problems are solved affirmatively by using tools from the RST The Piecewise Monotone Lemmas PMLs are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons The solution of the fourth problem gives a generalized analytical formula of the pielectron energy band curves of nanotube a b with two new complex parameters c and d These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply Based on the above affirmative solutions of the problems a central theorem in the RST called the asymptotic linearity theorem ALT has been applied to nanotubes and monocyclic polyenes Analytical formulae derived in this application of the ALT illuminate in a new global context i the conductivity of nanotubes and ii the aromaticity of monocyclic polyenes moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s 4n+2 rule The present article forms a foundation of the forthcoming articles in this series

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  1. Optimal inputs and sensitivities for parameter estimation in bioreactors
  2. A Method for Clustering and Screening of Long-dimensional Chemical Data Based on Fingerprints and Similarity Measurements
  3. Modelling of carbon dioxide: methane separation using titanium dioxide nanotubes
  4. Decomposition of reaction networks: the initial phase of the permanganate/oxalic acid reaction
  5. Use of Harriman’s construction in determining molecular equilibrium states
  6. Closed form analytical approach for a second order non-linear ODE interpreting EPDM vulcanization with peroxides
  7. The architecture of Platonic polyhedral links
  8. Kinetic analysis of solid-state reactions: errors involved in the determination of the kinetic parameters calculated by one type of integral methods
  9. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges
  10. Surface tension and Laplace pressure in triangulated surface models for membranes without fixed boundary
  11. Proof of the Fukui conjecture via resolution of singularities and related methods. IV
  12. A family of four-step trigonometrically-fitted methods and its application to the schrödinger equation
  13. Repair of irradiated cells by Michaelis–Menten enzyme catalysis: the Lambert function for integrated rate equations in description of surviving fractions
  14. Kinetic analysis of the mechanism of plasminogen activation by streptokinase
  15. Padé optimization of noise-corrupted magnetic resonance spectroscopic time signals from fibroadenoma of the breast
  16. Global Forcing Number of Benzenoid Graphs
  17. A Novel Lu Index to QSPR Studies of Aldehydes and Ketones
  18. Mathematical aspects of the LCAO MO first order density function (5): centroid shifting of MO shape functions basis set, properties and applications
  19. On the fundamental conjecture of HDMR: a Fourier analysis approach
  20. Solving the adsorption integral equation with Langmuir-kernel and the influence of temperature on the stability of the solution
  21. On reciprocal reverse Wiener index
  22. On the chemical synthesis of new topological structures
  23. Information content of molecular graph and prediction of gas phase thermal entropy of organic compounds
  24. Monotone Chemical Reaction Networks
  25. Topology and electronic structure of nanotube junctions of tetrapod shape
  26. Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules
  27. Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics
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  29. The PI index of phenylenes
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  32. Kinetic Monte Carlo approach to Schottky defects in noble metal nanoclusters
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