Apply the projection operator method to derive the group orbital SALCs for BF3 on the ba...

Apply the projection operator method to derive the group orbital SALCs for BF₃ on the basis of the irreducible representations given in Figure 5.31 for sets of 2s, 2p_x, 2p_y, and 2p_z orbitals, respectively. Employ a set of three identical orbitals where all have the same bias (i.e . , the group orbitals with symmetry in Figure 5.31 ) as a starting point. For each determination, provide a table like that in Section 5.4.4 to tabulate wave function coefficients, their squares, and how these values simultaneously satisfy the normalization requirement and confirm that each atomic orbital contributes equally to each set of group orbitals.