Symmetry Notes

What does the identity of an object imply about its symmetry?

Everything has an identity, meaning it has symmetry and remains unchanged.

What is a symmetry operation?

An action that leaves an object looking the same after it has been carried out.

What is a symmetry element?

A set of points through which the symmetry operation is performed, such as an axis for rotation or a plane for reflection.

What does C_n represent in symmetry operations?

The rotation index or order, corresponding to a rotation of (360/n) degrees.

What is represented by sigma in symmetry operations?

Reflection.

What does inversion represent in symmetry operations?

Inversion is represented by i, where everything passes through a single point and returns to its original state.

What does S_n stand for?

Improper rotation, which involves a rotation combined with a reflection across a plane of symmetry.

What is the hierarchy of symmetry operations?

Identity, rotation, reflection, inversion, improper rotation.

How many rotations does water have and what is its order?

Water has 1 rotation of 180 degrees, making its order C₂.

What order does ammonia have in terms of rotation?

Ammonia has two rotations of 120 degrees and 240 degrees, making its order C₃.

What is the principal axis in symmetry operations?

The axis with the highest order (highest number of n), around which rotations are based.

What does sigma v represent?

A vertical plane of reflection.

What determines the hierarchy of reflections?

Planes that bisect atoms have the highest hierarchy, followed by planes through the principal axis, and lastly dihedral reflection planes.

What is the center of inversion?

The symmetry element for inversion, which is a single point.

What is required for improper rotations to occur?

The plane of symmetry must be perpendicular to the rotation axis.

What do point group symbols represent?

A shorthand representation of all the symmetry operations of a molecule.