Without the use of a character table, answer each of the following about the IF_5 molecule: Make a complete list of all the possible symmetry operations in the molecule. determinee the molecular point group. determinee the inverse of each symmetry operation. determinee which symmetry operations belong to the same class. determinee the characters for each of the matrices representing the three p-orbitals, p_x p_x and p_y. determinee the characters for each of the matrices representing the three rotational axes, R_x, R_y, and R_z. determinee the characters for each of the matrices representing the five d-orbitals h. determinee all of the IRRs for the point group and assign the appropriate Mulliken symbol to each IRR. Using the rules for IRRs, generate the complete character table for this point group. determinee the molecular point group for the tricapped trigonal prismatic ReH_9^2- ion, whose structure is shown below. Use the bond vector basis set, determinee the symmetries IRR's) of the nine Re-H- single bonds in this ion. determinee the molecular structure of boric acid, H_2BO_2 and identify its molecular point group. Use the degrees of freedom basis set to generate a reducible presentation and then factor this reducible representation into its IRRs using the great orthogonality theorem. Cyanogen, (CN) is a linear molecule belonging to the D_infinity_n point group. Use the 3N degrees of freedom basis set to generate a reducible representation and then factor this reducible representation into itsIRRs using the great orthogonality theorem. Detemine the number of IR-active modes and the number of Raman-active modes for each of the following molecules and identify the symmetries of each mode: NH_3 PF_5 Al_2Cl_6 SF_4 BrF_3