Three-Dimensional Molecular Symmetry Operations - QS Study

For transformations in Three-Dimensional Molecular Symmetry Operations, find matrix equations that represent the following operations.

  1. Anticlockwise rotation about the x-axis.
  2. Anticlockwise rotation about the y-axis.
  3. Reflection in the xy-plane.
  4. Reflection in the yz-plane.
  5. Reflection in the zx-plane.
  6. Inversion through the origin.

Solution

a20

 

We have already looked at the solution for the rotation around the z axis in above figure, Now anticlockwise rotation about the x axis by an angle θ is.

a21

 

and anticlockwise rotation about the y-axis by an angle θ is,

a22

 

Reflection in the xy plane only changes the z coordinate to —z

a23

 

and reflection in the yz plane only changes the x coordinate to —x

a24

 

and the final reflection, in the zx plane only changes they coordinate to —y

a25

 

Inversion through the origin will change all three coordinates to their negative values

a25