Strongly subspectral pairs in C50+10n and C60+12n fullerenes via a common generic graph

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DOI 10.1039/A902553G
Impact Factor 3.676
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Abstract

A convenient scheme has been developed for drawing the Schlegel digrams (graphs) of C50+10n and C60+12n (n=integer) fullerenes maintaining five-fold and six-fold rotational symmetry, respectively. It has been found that after symmetry-factorisation, 10+2n eigenvalues common to C50+10n and C60+12n fullerenes can be obtained from a generic graph and for this reason (C60, C72), (C70, C84), (C80, C96) ... , corresponding to n=1, 2, 3, ... respectively, are strongly subspectral pairs having 12, 14, 16, ... common eigenvalues respectively. Of the 10+2n common eigenvalues, n+3 can be expressed in the analytic form: λj= -1+2 cos[jπ/(n+4)], j=1, 2, ... n+3. The other n+7 common eigenvalues can be obtained from a weighted linear chain whose characteristic polynomial can be easily derived by means of a recently developed scheme; a sample calculation for n=1 has been shown. Results for a number of subspectral pairs have been tabulated.

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Physical Chemistry Chemical Physics

Physical Chemistry Chemical Physics
CiteScore: 5.5
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Physical Chemistry Chemical Physics (PCCP) is an international journal co-owned by 19 physical chemistry and physics societies from around the world. This journal publishes original, cutting-edge research in physical chemistry, chemical physics and biophysical chemistry. To be suitable for publication in PCCP, articles must include significant innovation and/or insight into physical chemistry; this is the most important criterion that reviewers and Editors will judge against when evaluating submissions. The journal has a broad scope and welcomes contributions spanning experiment, theory, computation and data science. Topical coverage includes spectroscopy, dynamics, kinetics, statistical mechanics, thermodynamics, electrochemistry, catalysis, surface science, quantum mechanics, quantum computing and machine learning. Interdisciplinary research areas such as polymers and soft matter, materials, nanoscience, energy, surfaces/interfaces, and biophysical chemistry are welcomed if they demonstrate significant innovation and/or insight into physical chemistry. Joined experimental/theoretical studies are particularly appreciated when complementary and based on up-to-date approaches.

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