Question

Do a complete symmetry analysis on a general molecule of type AX5 having trigonal bipyramidal geometry. a) TO what point group does it belong? b) Use contributions per unshifted atom to determine the reducible representation to which all the degrees of freedom for the molecule belong. c) Write the above reducible representation as a direct sum of the irreducible representations of the group. d) What are the symmetries of the translational degrees of freedom for the molecule. e)What are the symmetries of the rotational degrees of freedom. f) What are the symmetries of the vibrational modes for the molecule g)Which modes are due to bond stretching? angular deformation modes? out of plane bending modes?

Answer 1

(a) Molecule having trigonal bipyramidal geometry of the type AX₅ has the point group D_3h

(d) any has always 3 translational degrees of freedom.

(e) For a non linear molecule, 3 rotationla degrees of freedom are possible as all the axis will result in a change in position of the atoms.

(f) For a molecule having 'n ' atoms total degrees of freedom = 3n

Hence, vibrational degrees of freedom = 3n - 3 - 3 = 3n - 6

for given molecule total number of atoms = 6

Therefore, no. of vibrational degrees of freedom = 3(6) - 6 = 12

(g) Out of plane bending modes