## Building the Bounds Matrix

The distance bounds matrix for each molecule contains lower bounds for each atom--atom distance in the lower triangle and the upper bounds for each distance in the upper triangle. These bounds are assigned using a rules-based approach [Blaney1994] where 1--2, 1--3, and some 1--4 distances are set using the force field's bond length, bond angle, and torsion parameters respectively. Bounds for some higher order distances (typically associated with rings) are also set. Any remaining distance bounds are set to conservative defaults: with a minimum above the sum of van der Waals radii and a large maximum.
Once the bounds matrix is constructed, it is refined using a triangle bounds smoothing algorithm that iteratively shrinks the individual bounds until they are as tight as possible.[Crippen1981]