Symmetry Operations & Groups (9/11)

Describe the two classes of C rotations in a benzene molecule.

intersect 2 atoms, axes that bisect 2 atoms

What is the Greek letter to represent reflections?

sigma

What is the symmetry element for reflections?

mirror planes

What is the symmetry operation for mirror planes?

reflections

What is the n for C rotations for square planar molecules?

n=4

What is the difference between reflections with a subscript of v and a subscript of d?

v = vertical; across bonds

d = dihedral, across interactions between bonds

Describe a center of inversion.

xyz → -x-y-z

What is the main requirement to look for when determining if something has a center of inversion?

atoms are in exact pairs (except for central atom)

What is an improper axis of rotation?

rotation like C and then a reflection

A mirror plane is always ___ to the axis of rotation

perpendicular

Describe the improper axis of rotation of trigonal bipyramidal molecules.

S3 - C3 (rotate 120 degrees) and reflect

Why can’t you have an even number of reflections?

They would just cancel each other

What is the difference between asymmetry and disymmetry?

asymmetric: only E

disymmetric: no S (could have others)

If there is a principal axis of rotation for symmetry and a dihedral reflection, what symmetry operation does it also have?

improper axis of rotation

S4 implies a Cn with n=

2

S2 = what symmetry operation?

i, an inversion (C2 xy → -x-y) (reflection z→-z)

S1 = what symmetry operation?

sigma, just a reflection

Requirements for groups in molecular symmetry: product of two elements must ___

also be an element

Requirements for groups in molecular symmetry: one element must commute with all others and leave ___

unchanged

Requirements for groups in molecular symmetry: ___ law of math applies

associative (a*b) + c = a + (b*c)

Requirements for groups in molecular symmetry: every element must have a ___ which is also an element

reciprocal

What is commuting?

When the order of two operations doesn’t matter

What is a point group?

Complete set of symmetry operations on a molecule