Worksheet: Point Groups

In this worksheet, we will practice finding the point group of a molecule by listing its inversion, reflection, rotation, and rotoinversion symmetries.

Q1:

By identifying all symmetry elements in ammonia (NH)3, assign the point group of the molecule.

  • ADh
  • BDh
  • CCv
  • DTd

Q2:

What is the point group of water?

  • A𝐶v
  • B𝐷
  • C𝐶2v
  • D𝑇d
  • E𝐶

Q3:

A molecule has the following symmetries only: 𝐸, 𝐶, and 2𝜎v. What is the point group of the molecule?

  • A𝐶v
  • B𝐶v
  • C𝐷
  • D𝐶
  • E𝑇d

Q4:

A molecule is linear, without a center of inversion. What is its point group?

  • A𝐷h
  • B𝐶v
  • C𝐶i
  • D𝐶
  • E𝑂h

Q5:

What is the point group of NH3?

  • A𝑇d
  • B𝐶
  • C𝐶v
  • D𝐷
  • E𝐶v

Q6:

A molecule has the following symmetries only: 𝐸, 𝐶, 𝐶, and 3𝜎v. What is the point group of this molecule?

  • A𝐶v
  • B𝑇d
  • C𝐶v
  • D𝐷
  • E𝐶

Q7:

What is the point group of HCl?

  • A𝐶i
  • B𝐶v
  • C𝑂h
  • D𝐷h
  • E𝐶

Q8:

Which of the following has C4v symmetry?

  • APCl6
  • BHO2
  • CBrF5
  • DW(CO)6
  • EBH3

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