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    From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations

    80968B.pdf (259.9Kb)
    Access Status
    Open access
    Authors
    Glasser, Leslie
    Date
    2020
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Glasser, L. 2020. From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations. Journal of Applied Crystallography. 53: pp. 1101-1107.
    Source Title
    Journal of Applied Crystallography
    DOI
    10.1107/S1600576720007311
    ISSN
    0021-8898
    Faculty
    Faculty of Science and Engineering
    School
    School of Molecular and Life Sciences (MLS)
    URI
    http://hdl.handle.net/20.500.11937/80910
    Collection
    • Curtin Research Publications
    Abstract

    Values of molecular bond lengths, bond angles and (less frequently) bond torsion angles are readily available from databases, from crystallographic software, and/or from interactive molecular and crystal visualization programs such as Jmol. However, the methods used to calculate these values are less well known. In this paper, the computational methods are described in detail, and live Excel implementations, which permit readers to readily perform the calculations for their own molecular systems, are provided. The methods described apply to both fractional coordinates in crystal space and Cartesian coordinates in Euclidean space (space in which the geometric postulates of Euclid are valid) and are vector/matrix based. In their simplest computational form, they are applied as algebraic expansions which are summed. They are also available in matrix formulations, which are readily manipulated and calculated using the matrix functions of Excel. In particular, their general formulation as metric matrices is introduced. The methods in use are illustrated by a detailed example of the calculations. This contribution provides a significant practical application which can also act as motivation for the study of matrix mathematics with respect to its many uses in chemistry.

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