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Embedding

Once upper and lower bounds are known for all interatomic distances in
the system, a matrix of actual distances chosen between those bounds
must be created in order to calculate coordinates. This is done for
each pair of atoms in the system with a uniform
distribution of random values. Since the initial upper and lower
bounds matrices are consistent with all possible conformations of
the molecule, interatomic distances chosen independently of each
other are, in general, inconsistent with any particular conformation.
The process of calculating coordinates from the resulting actual
distance matrix is called embedding. Briefly, the
distance matrix is converted to a metric matrix of distances centered
around their collective centroid, as described by
Crippen and Havel (1988).
If the three largest eigenvalues of this metric matrix are all positive,
their corresponding eigenvectors contain the x, y, and z
coordinates of all the atoms. If the three largest eigenvalues are not
positive, the chosen distances are too inconsistent to be embedded.
The MMDG statement declares a symbol $EMBEDDED
of type string that is
set to “TRUE" if the embedding was successful and otherwise to
“FALSE".

*Xplor-NIH 2023-11-10*