CHE216
Assessed Coursework 2
Submit your answers as a separate file
Deadline Friday 11 April 16:00 h
Very Important: please ensure you appreciate the following before attempting this assessment.
This assessment is a primarily a test ofyou understanding of the topic (your ability to answer the questions is secondary to your understanding). Thus, in answering this question you must provide a detailed description ofyour method.
That is, you must explain: (a) what you are doing, and (b), why you are doing it, at every stage in answering this question.
Getting the answer right is worth less than half of the marks for this exercise. Convincing your examiner that you understand what you are doing to get the correct answer is worth most of the marks.
Question 1 30 marks
Consider a unit vector pointing along the z-direction.
By considering how this vector transforms under symmetry operations, show that the irreducible representations ofthis vector are:
A1 under C2v.
A1 under C3v.
A2” under D3h,
Au under C2h
A2u under D4h
Please note that you are told the answers. So, in this question all marks are for how well you explain your proofthat the answer is right.
Question 2 30 marks
Consider a basis of x,y,z displacement unit vectors on all atoms of the ammonia molecule.
(a) Show that three hydrogen atoms do not contribute to the character of the representative matrix of the for the C3 symmetry operation.
(b) Use the example of the C3 to show that the representative matrices for the symmetry C3 operation ofC3v cannot be reduced (block diagonalised) to 3 1x1 matrices, but instead must each give a 1x1 matrix for z with a character of 1 and a 2x2 matrix for x,y. with a character of -1.
Question 3 30 marks
Consider a basis of x,y,z displacement unit vectors on all atoms of the ammonia molecule.
(a) Use this basis to determine:
(i) The reducible representation for the motions of ammonia in 3D space.
(ii) The irreducible representation for the motions of ammonia in 3D space.
(iii) The irreducible representation for the vibrational motions ofthe ammonia molecule.
(iv) The irreducible representation for the IR-active and Raman Active modes of ammonia.
(b) Make sketches showing how the atoms move in allA1 vibrational modes of ammonia.
Question 4 10 marks
Consider a basis of x,y,z displacement unit vectors on all atoms of the benzene molecule.
Use this basis to determine: The irreducible representation for the IR-active modes of ammonia.
Hint: this question is only for 10 marks, but it might seem more difficult, or at lease more work, than is required in Question 3. However, you can take shortcuts and simplifications to vastly reduce the work required to answer this question. Your answer should though contain a description and justifications for using those short cuts.