7. Using the D2d character table, a. Determine the order of the group. b. Verify that the E irreducible representation is orthogonal to each of the other irreducible representations. c. For each of the irreducible representations, verify that the sum of the squares of the characters equals the order of the group. d. Reduce the following representations to their component irreducible representations: D2d E 2.S4 20 a 6. 0. 2 2 2 6. 4 2 8. Reduce the following representations to irreducible representations: C3v E 2C3 30, 6 2 -1 -1 On E 8C, 6C, 6C, 3C, i 65, 85, 30, 604 6 0 2 0 0 4 9. For the following molecules, determine the number of IR-active C-O stretching vibrations: b. c. Fe(CO)5 a. CI Fe- . Fe CO Fe CI CO