Chapter 5, Problem 5.27P

Apply the projection operator method to derive the group orbital SALCs for ${\text{BF}}_{\text{3}}$ on the basisof the irreducible representations given in Figure 5.31 for sets of $\text{2s2},{\text{p}}_{\text{x}},{\text{p}}_{\text{y}}$ orbitals,respectively. Employ a set of three identical orbitals’ where all have the same bias (i.e., the group orbitalswith ${\text{A}}_{\text{1}},{\text{A}}_2^{\text{'}}$ , and ${\text{A}}_2^{\text{'}}$ symmetry in Figure 5.31) as a starting point. For eachdetermination, 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 andconfirm that each atomic orbital contributes equally to each set of group orbitals.