Journal
JOURNAL OF COMPUTATIONAL CHEMISTRY
Volume 36, Issue 6, Pages 408-422Publisher
WILEY
DOI: 10.1002/jcc.23816
Keywords
persistent homology; filtration; fullerene; isomer; nanotube; stability; curvature
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Funding
- NSF [IIS-0953096, IIS-1302285, DMS-1160352]
- NIH [R01GM-090208]
- MSU Center for Mathematical Molecular Biosciences initiative
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [0953096] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1302285] Funding Source: National Science Foundation
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Persistent homology is a relatively new tool often used for qualitative analysis of intrinsic topological features in images and data originated from scientific and engineering applications. In this article, we report novel quantitative predictions of the energy and stability of fullerene molecules, the very first attempt in using persistent homology in this context. The ground-state structures of a series of small fullerene molecules are first investigated with the standard Vietoris-Rips complex. We decipher all the barcodes, including both short-lived local bars and long-lived global bars arising from topological invariants, and associate them with fullerene structural details. Using accumulated bar lengths, we build quantitative models to correlate local and global Betti-2 bars, respectively with the heat of formation and total curvature energies of fullerenes. It is found that the heat of formation energy is related to the local hexagonal cavities of small fullerenes, while the total curvature energies of fullerene isomers are associated with their sphericities, which are measured by the lengths of their long-lived Betti-2 bars. Excellent correlation coefficients (>0.94) between persistent homology predictions and those of quantum or curvature analysis have been observed. A correlation matrix based filtration is introduced to further verify our findings. (c) 2014 Wiley Periodicals, Inc.
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