Although X-PLOR provides improper angles to maintain planarity
of groups of atoms, the specification of these energy terms is
sometimes cumbersome, especially when many atoms are involved.
The restraints planarity statement allows
one to define an effective energy term that penalizes
out-of-plane conformations of the selected atoms. This feature
should be used for relatively few groups, as it involves a certain
amount of overhead. The planarity restraints energy term is defined as

(7.5)

where the first sum is carried out over all defined groups
of planar atoms, the second sum is carried out for all atoms
within each group, and is the orthogonal distance of from
the least-squares plane defined by all atoms of the group
(Schomaker et al., 1959). Note
that the energy term must be activated through the flags
statement (Section 4.5).