What does the symmetry operator Sn represent?

The symmetry operator Sn represents an improper rotation operation, which is a combination of a rotation followed by a reflection across a plane perpendicular to the axis of rotation. Specifically, Sn denotes a rotation by an angle of 360°/n followed by a reflection through a plane that includes the axis of rotation.

In this context, n refers to the order of the axis of rotation; for example, S3 indicates a rotation by 120 degrees (360°/3) followed by a reflection. This operator is crucial in the study of molecular symmetry as it helps classify and analyze the symmetry elements present in molecules.

Pure rotation, a vertical mirror image, and the identity operation do not incorporate the necessary combination of rotation and reflection that defines Sn. Therefore, the definition of Sn as an improper rotation followed by reflection accurately captures its significance in symmetry analysis.