Question

Polly Ester has synthesized a new compound, ML3. Elemental analysis confirms that the molecule contains one central atom, M, with three atoms, L's, attached to the central atom. Polly has postulated three possible 3-coordinate structures for the molecule with point groups D3H, C2V and C3V. Polly then records the IR and Ramen specta of the molecule and finds three M-L stretches in both the IR and Ramen spectra, with each IR and Ramen band being coincident ( bands occur at same energy in both IR and Ramen).

Preform a vibrational analysis on each of the three structures and prove which of the three structures is the correct one.

Answer 1

The point, lines and planes to which symmetry operations are carried out known as the symmetry elements.Symmetry operations are performed on the object which is superimposable, indisguishable from the original configuration. Symmetry elements include C_n which is on the proper axis rotation by 360/n, is the reflection, i is inversion and S_n is improper axis rotation.

Each rotation brings an indistguishable from the original configuration.

If the mirror plane contains the rotational axis then the point group is called C_2v or C_3v group.

Adding a (plane prependicular to the principal axis)to D_n group generates D_nh group.

As per our case, ML₃ is a linear molecule and it also contain center of inversion and molecule does not contain symmetry.It is a non symmetrical molecule.

Vibrational analysis is the study of interaction of energy with matter. For the representations of vibration only we have to subtract rotational and translation modes from the total representations.

Translational mode is basically a mode in which all the atoms are moving in the same direction equivalent to moving the molecule.

Rotational mode is mode in which the atoms rotate the molecule and change the orientation of the molecule. There are 2 rotational modes for linear molecule.

For linear molecule total modes can be calculated by 3n-6 so total modes are 3 X 4 -6 = 6. In this 2 are rotational modes so we subtract it only remain 4.

If there is non symmetrical molecule and it contains center of inversion it contains 4 indentity so the refer molecule contains D3H point group structure.