**Figure 1**
Stereochemical restraints in a dipeptide. This figure shows the bonds, bond angles and torsion angles for the dipeptide Ala-Ser. Black lines indicate bonds, red arcs indicate bond angles and blue arcs indicate torsion angles. The values of the bond lengths and bond angles are, to the precision required for most macromolecular-refinement problems, independent of the environment of the molecule and can be estimated reliably from small-molecule crystal structures. The values of most torsion angles are influenced by their environment and, although small-molecule structures can provide limits on the values of these angles, they cannot be determined uniquely without information specific to this crystal. It is instructive to note that this example molecule contains 12 atoms and requires 36 degrees of freedom to define their positions (12 atoms times three coordinates for each atom). The molecule contains 11 bonds, 14 bond angles and five torsion angles, which together define 30 degrees of freedom. The unaccounted-for degrees of freedom are the six parameters that define the location and orientation of the entire dipeptide. This result is general; the sum of the number of bonds, the number of bond angles, the number of torsion angles and six will always be three times the number of atoms. Other stereochemical restraints, such as chiral volume and planarity, are redundant. For example, the statement that the carbonyl C atom and the atoms that bond to it form a planar group is equivalent to saying that the three bond angles around the carbonyl C atom sum to 360°. These types of restraints are added to refinement packages to compensate for their (incorrect) assumption that deviations from ideality for bond angles are independent of each other. |