Question

The CO ligands in the molecule Ni(CO)4 could have two possible geometries – a tetrahedral arrangement of carbon monoxides around the central nickel atom, or a square planar geometry in which all of the atoms are in the same plane and all of the C-Ni-C angles are 90º. For each geometry, determine the following:

(a) What is its point group?

(b) Write the reducible representation for the C-O stretching vibrational modes. (Hint: For the square planar form, C2' and sv pass through CO ligands, whereas C2" and sd are between them.)

(c) Use the reduction formula to determine the irreducible representations for the C-O stretching vibrational modes.

(d) Which of the C-O stretching vibrational modes are allowed in the infrared spectrum, and how many absorptions could potentially be observed?

(e) Which modes are allowed in the Raman spectrum, and how many emissions could potentially be observed?

For the square planar geometry:

(e) Write the reducible representation for all of the atomic motions for Ni(CO)4.

(f) Use the reduction formula and the character table to determine the irreducible representations for the vibrational modes only.

(g) Which of the vibrational modes are allowed in the infrared spectrum, and how many absorptions could potentially be observed?

(h) Which modes are allowed in the Raman spectrum, and how many emissions could potentially be observed?

Please help I have no idea how to do this!

Answer 1

(a) The point group could be determined by finding out the associated symmetry elements. Please symmetry point group tree in the attachments. In case of Ni(CO)4 tetrahedral case, the molecule belongs to high symmetry that is tetrahedral. It has 4 equivalent C3 axis, 3 equivalent C2 axis and three S4 axes apart from six equivalent mirror planes. So, it belongs to Td point group.

In the case of square planar, the molecule has one C4 axis and four equivalent C2 axis and all these C2 axes are perpendicular to principal axis i.e. C4. So going to the symmetry table it belongs to D group. Again it has four vertical mirror planes along the C2 axis and one horizontal mirror plane. However, since the vertical mirror planes are perpendicular to the horizontal mirror plane; so the point group is D4h.