Question

Tools Fill & Sign Comment 3. (a) What are the symmetry operations for the molecule AB where the B atoms lie at the corners of a square and the A atom is at the center and is not coplanar with the B atoms. (b) Find the multiplication table. (c) List the subgroups. Which subgroups are self-conjugate? (d) List the classes. (e) Find the multiplication table for the factor group for the self-conjugate subgroup(s) of (c).

Answer 1

Answer 3 a) A molecule with AB₄ formula in which B atoms lie at the corner of square and A atom at the center belongs to tetrahedral symmetry group. The symmetry elements through which the symmetry operations could be performed include E (identity), 4C₃ (four C₃ axis of rotation) 3C₂ (Three C₂ axis of rotation) 3S₄ (three improper axis of rotation or rotation-reflection axis) and 6$\sigma$_d (six dihedral plane of symmetry).  

Ans 3b) Multiplication table is given below

Multiplication table for Td symmetry TO E SC3 3C2 654 60 Cubic Function Quadratic function x2 + y2 + z2 xyz A1 1 1 A2 1 1 E 2 -1 Ti 30 T2 3 0 1 1 2 -1 -1 1 -1 0 1 -1 1 -1 0 -1 1 Linear function rotation - - - (Rx R. Rz) (x, y, z) (2z2-x2-y?. x2 - y2) - [x(22-y), y(z2-x2), z(x2-y)] |(x,y,z) (x(z2+y2), y(z2+x), z(x2+y21 (xv. xz, yz)