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The Chemical Educator
ISSN: 1430-4171 (electronic version)
Abstract Volume 25
(2020) pp 50-57
One-Dimensional Cluster Analysis and its Application to
Chemistry
Cory C. Pye
Department of Chemistry, Saint Mary’s University, 923 Robie Street, Halifax, NS Canada B3H 3C3, cory.pye@smu.ca
Received December 18, 2019. Accepted February 5, 2020.
Published: 21 March 2020
Abstract. Clustering
of data is often observed in spectroscopy. The notion of clustering is made
mathematically rigorous by first fixing the number of clusters, defining the
cluster average, and then minimizing the sum of squared deviations between the
data and the cluster average to calculate the error. By analyzing some model
data, criteria for identifying the best number of clusters to use are
identified that correspond to intuitive notions. These are then applied to the
proton NMR spectra of ethyl ethanoate, the IR spectrum of carbon dioxide, and
the microwave spectra of CsI, CsBr, RbI, RbBr, and KI. For the NMR and IR
spectra presented, the primary features are identified. For the microwave
spectra presented, the cluster analysis (usually) allows for assignment of the
rotational and vibrational quantum numbers of the transitions, to separate
isotopologues, and to identify a putative printing error.
Key Words: Laboratories and Demonstrations; physical chemistry; analytical chemistry; computer-based learning; quantum chemistry; spectroscopy; cluster analysis
(*) Corresponding author. (E-mail: cory.pye@smu.ca)
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