Nihonkai Mathematical Journal

The squared chain length function of 5 or 6-membered straight-chains with the tetrahedral bond angle

Kazushi Komatsu

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Abstract

We provide straight-chains with the tetrahedral bond angle $\cos^{-1}(-1/3)$ as a mathematical model of $n$-membered straight-chain hydrocarbon molecules. We study the squared chain length function on the configuration space of the model and determine the critical points with planar configurations when $n = 5, 6$.

Note

The authors would like to express their sincere gratitude to the referee for useful comments. The authors would like to express their sincere gratitude to the editor for valuable help.

Article information

Source
Nihonkai Math. J., Volume 28, Number 2 (2017), 89-98.

Dates
Received: 27 August 2016
First available in Project Euclid: 26 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1524708083

Mathematical Reviews number (MathSciNet)
MR3794317

Zentralblatt MATH identifier
06873761

Subjects
Primary: 52C99: None of the above, but in this section
Secondary: 57M50: Geometric structures on low-dimensional manifolds 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

Keywords
configuration space molecular structure

Citation

Komatsu, Kazushi. The squared chain length function of 5 or 6-membered straight-chains with the tetrahedral bond angle. Nihonkai Math. J. 28 (2017), no. 2, 89--98. https://projecteuclid.org/euclid.nihmj/1524708083


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References

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  • S. Goto, K. Komatsu and J. Yagi, The configuration space of a model for 5-membered straight-chain hydrocarbon molecules parametrized by chain lengths, Nihonkai Math. J. 26 (2015), 37–45.
  • H. Kamiya, Weighted trace functions as examples of Morse functions, J. Fac. Sci. Shinshu Univ. 6 (1971), 85–96.