1) Ethylene has a D2h point group.
a. List every symmetry operation for ethylene.
b. Write a transformation matrix for each operation and describe the effect that each
operation has on the molecule’s coordinates in (x,y,z)
Thank you!
That is essentially impossible on this forum. I suggest you Google the subject.
How comes no answer for this????
To determine the symmetry operations for a molecule, we can use group theory and character tables. For ethylene, which has a D2h point group, we need to refer to the D2h character table to find the symmetry operations.
a. List of symmetry operations for ethylene:
1. Identity (E)
2. C2 rotation about the z-axis (C2(z))
3. C2 rotation about the x-axis (C2(x))
4. Reflection through the xy-plane (σ(xy))
5. Reflection through the xz-plane (σ(xz))
6. Reflection through the yz-plane (σ(yz))
7. Inversion through the origin (i)
8. Reflection through C2 axis (σv)
b. Transformation matrix and effect for each operation:
1. Identity (E):
Transformation matrix:
E = 1 0 0
0 1 0
0 0 1
Effect: This operation does not change the molecule's coordinates.
2. C2 rotation about the z-axis (C2(z)):
Transformation matrix:
C2(z) = -1 0 0
0 -1 0
0 0 1
Effect: This operation rotates the molecule 180 degrees around the z-axis.
3. C2 rotation about the x-axis (C2(x)):
Transformation matrix:
C2(x) = 1 0 0
0 -1 0
0 0 -1
Effect: This operation inverts the y and z coordinates while leaving the x coordinate unchanged.
4. Reflection through the xy-plane (σ(xy)):
Transformation matrix:
σ(xy) = 1 0 0
0 1 0
0 0 -1
Effect: This operation changes the sign of the z coordinate.
5. Reflection through the xz-plane (σ(xz)):
Transformation matrix:
σ(xz) = 1 0 0
0 -1 0
0 0 1
Effect: This operation inverts the y coordinate while leaving the x and z coordinates unchanged.
6. Reflection through the yz-plane (σ(yz)):
Transformation matrix:
σ(yz) = -1 0 0
0 1 0
0 0 1
Effect: This operation inverts the x coordinate while leaving the y and z coordinates unchanged.
7. Inversion through the origin (i):
Transformation matrix:
i = -1 0 0
0 -1 0
0 0 -1
Effect: This operation inverts all the coordinates of the molecule.
8. Reflection through C2 axis (σv):
Transformation matrix:
σv = -1 0 0
0 1 0
0 0 1
Effect: This operation inverts the x coordinate while leaving the y and z coordinates unchanged.
These are the symmetry operations, their transformation matrices, and the effects they have on the coordinates of ethylene in the D2h point group.