| Summary: | 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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