The squared chain length function of 5 or 6-membered straight-chains with the tetrahedral bond angle. (English) Zbl 1390.52027

Komatsu, Kazushi

Nihonkai Math. J. 28, No. 2, 89-98 (2017).

Summary: 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 \(n=5,6\).

MSC:

52C99	Discrete geometry
57M50	General geometric structures on low-dimensional manifolds
58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
92E10	Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

Keywords:

configuration space; molecular structure

References:

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[4]	H. Kamiya, Weighted trace functions as examples of Morse functions, J. Fac. Sci. Shinshu Univ. 6 (1971), 85-96. · Zbl 0322.58006