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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| Format: | Journal Article |
| Language: | English |
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INT UNION CRYSTALLOGRAPHY
2020
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| Online Access: | http://hdl.handle.net/20.500.11937/80910 |
| _version_ | 1848764288056950784 |
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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. |
| first_indexed | 2025-11-14T11:16:58Z |
| format | Journal Article |
| id | curtin-20.500.11937-80910 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:16:58Z |
| publishDate | 2020 |
| publisher | INT UNION CRYSTALLOGRAPHY |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |