Improper Rotation
Sn
The Improper Rotation element involves
a
360/n degree rotation, followed by a reflection
through a mirror plane perpendicular to the rotation axis. The molecule
that results from this rotation-reflection is indistinguishable from the
original. Thus the Sn symmetry element is composed of
a Cn/2 followed by a s. However,
a molecule with an Sn element might contain neither a Cn
nor a s (although it will have Cn/2's
coincident with the Sn's). Molecules which contain an
improper axis of rotation are achiral. An S1 is equivalent
to a mirror plane, and an S2 is equivalent to an inversion center;
these operations prohibit chirality.
Methane, CH4, contains the S4
symmetry element. Rotation of 90° about the axis, followed
by a reflection through a mirror plane perpendicular to that axis gives
a molecule indistinguishable from the original. Note that methane
does not have a C4 rotation axis (although it does have C2's
coincident with the S4's). While methane does have mirror
planes, none are perpendicular to the S4 element.
