with these Selected character Tables may be picked for helping in calculation,

Q4. Construct 3x3 matrices for three vectors representing sigma bonding only. What are possible hybrid orbitals in central metal ion (A13+) in AICI3? (15 marks) Note: Construct matrices, determine character of each matrix, reducible representations, determine contribution of each irreducible representation and hybridization in the metal ion. Direct answer will be accepted with partial marking. a; az Annexure C2 E C2 0,(xz) (yz) 1 1 1 - 1 A A2 B B2 1 1 1 1 1 1 1 - 1 Z R, X, RY *?, y2, 22 xz 1 - 1 1 y, R yz C3 E 2C 30, Z x2 + y2,22 A A2 E 1 1 1 2 1 1 0 - R. (x, y)(Rx, Ry) (x2 - y2, XY)(xz, yz) E 2C 3 C on 25, 30, 1 1 1 1 1 1 D3h AL Az E' 1 1 -1 1 1 -1 x2 + y2, 22 R, (x, y) |(x2 - y2, xy) 2 -1 0 2 -1 0 1 1 1 -1 -1 -1 A," AZ" E" 1 1 -1 -1 -1 1 Z 2 -1 0 -2 1 0 (RR) (xz, yz) Dan E 2C. C2 202 20," i 284 on 2, 2, 1 Ang 1 - 1 1 1 A24 B1a R 1 - 1 1 -1 1 1 - 1 1 1 1 1 x2 + y, 22 x - y (xz, yz) 1 1 2 0 B24 EG Ai A2u (Rx, R) 1 1 1 1 2 1 1 1 1 2 1 1 -1 -1 0 1 1 - 1 -1 0 1 1 1 1 2 1 1 1 1 -2 1 -1 -1 1 0 -1 1 1 -1 0 1 -1 0 1 1 -1 1 0 z 1 -1 1 -1 0 1 B24 1 1 1 1 0 -1 -1 - 1 2 Eu (x, y) D4 E 2C4 C2(=C42) 2C; 20" 1 x2 + y2, 22 1 1 1 1 2, R, A A2 B B2 E 1 -2 - 1 0 1 0 x? y? (xz, yz) 0 (x, y)(RX, R,) Cov E 2C6 203 C2 30, 30 1 Z x2 + y, z? 1 1 1 1 - 1 R, A. A2 B B2 E Ez 2 2 2 0 0 1 0 (x, y)(Rx, RY) 0 (.xz, yz) (x2 - y2, xy) 1 DO E 200 2C; C2 302' 30" i 25; 25. Oh 304 30, *2 + y?, z? 1 A19 1 1 1 -1 1 1 1 R, 1 1 1 1 1 1 1 - 1 1 1 1 1 1 1 -1 1 - 1 1 1 - 1 - 1 2 2 A29 B19 B29 E19 E29 Aiu 2 -1 -1 (RX, R) (x2, yz) (x2 y?, xy) 1 -1 1 -1 0 0 1 1 - 1 1 0 0 1 2 0 0 1 1 1 - 1 0 0 Biu 1 -1 1 B2- Elu 1 1 2 2 1 1 2 - 2 1 1 1 1 - 1 (x, y) 2 2 0 1 E2u