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Open AccessCommunication

The Eigenproblem Translated for Alignment of Molecules

1
Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400641 Cluj, Romania
2
Chemistry Doctoral School, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Symmetry 2019, 11(8), 1027; https://doi.org/10.3390/sym11081027
Received: 12 July 2019 / Revised: 29 July 2019 / Accepted: 7 August 2019 / Published: 9 August 2019
(This article belongs to the Special Issue Applied Designs in Chemical Structures with High Symmetry)
Molecular conformation as a subproblem of the geometrical shaping of the molecules is essential for the expression of biological activity. It is well known that from the series of all possible sugars, those that are most naturally occurring and usable by living organisms as a source of energy—because they can be phosphorylated by hexokinase, the first enzyme in the glycolysis pathway—are D-sugars (from the Latin dextro). Furthermore, the most naturally occurring amino acids in living cells are L-sugars (from the Latin laevo). However, a problem arises in dealing with the comparison of their conformers. One alternative way to compare sugars is via their molecular alignment. Here, a solution to the eigenproblem of molecular alignment is communicated. The Cartesian system is rotated, and eventually translated and reflected until the molecule arrives in a position characterized by the highest absolute values of the eigenvalues observed on the Cartesian coordinates. The rotation alone can provide eight alternate positions relative to the reflexes of each coordinate. View Full-Text
Keywords: eigenproblem; eigenvalues; molecular alignment; orthogonal alignment eigenproblem; eigenvalues; molecular alignment; orthogonal alignment
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Jäntschi, L. The Eigenproblem Translated for Alignment of Molecules. Symmetry 2019, 11, 1027.

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