Plane triangular molecule The molecule BCl3 (boron trichloride) is plane and symmetrical. In equlibrium, the Cl atoms are at the vertices of an equilateral triangle with the B atom at the centroid.

Show that the molecule has six vibrational modes of which five are in the plane of the molecule; show also that the out-of-plane mode and one of the in-plane modes have axial symmetry;

and show finally that the remaining four in-plane modes are in doubly degenerate pairs. Deduce that the BCl3 molecule has a total of four distinct vibrational frequencies.