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

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...

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Bibliographic Details
Main Author: Glasser, Leslie
Format: Journal Article
Language:English
Published: INT UNION CRYSTALLOGRAPHY 2020
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/80910
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author Glasser, Leslie
author_facet Glasser, Leslie
author_sort Glasser, Leslie
building Curtin Institutional Repository
collection Online Access
description 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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spelling curtin-20.500.11937-809102020-10-21T03:57:48Z From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations Glasser, Leslie Science & Technology Physical Sciences Chemistry, Multidisciplinary Crystallography Chemistry metric matrices bond angles bond lengths torsion angles vectors CRYSTALLOGRAPHY GENERATION DATABASE 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. 2020 Journal Article http://hdl.handle.net/20.500.11937/80910 10.1107/S1600576720007311 English INT UNION CRYSTALLOGRAPHY fulltext
spellingShingle Science & Technology
Physical Sciences
Chemistry, Multidisciplinary
Crystallography
Chemistry
metric matrices
bond angles
bond lengths
torsion angles
vectors
CRYSTALLOGRAPHY
GENERATION
DATABASE
Glasser, Leslie
From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations
title From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations
title_full From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations
title_fullStr From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations
title_full_unstemmed From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations
title_short From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations
title_sort from atoms to bonds, angles and torsions: molecular metrics from crystal space, and two excel implementations
topic Science & Technology
Physical Sciences
Chemistry, Multidisciplinary
Crystallography
Chemistry
metric matrices
bond angles
bond lengths
torsion angles
vectors
CRYSTALLOGRAPHY
GENERATION
DATABASE
url http://hdl.handle.net/20.500.11937/80910