3. In the Hückel theory treatment of butadiene, C4H6, symmetry can be used to simplify the secular determinant by utilizing symmetry-adapted linear combinations (SALC's) of atomic orbitals, as demonstrated in Lessons 7A and 7B. As is customary for applications of the Hückel method, the basis, C 2 |0i) = |2pz,i), is the set of p-orbitals responsible for the π-bonds, S¿¡ = §¡¡, and α i=j i Hij = (þi|Ĥ|$;) = }_t=j±1 0 otherwise -ک- (a) One can define two sets of two symmetry-adapted orbitals for this problem, defined by Ψ1 = Φι + Φα 1 $4 $3 Ф2 = Ф2 + Ф3 = 43-02-03 ΨΑ = Φ1 - ΦΑ (Aμ symmetry) (Bg symmetry) These basis functions are not normalized, though the atomic orbitals, i, are orthonormal within the Hückel theory assumptions. What is the constant that normalizes each of these symmetry-adapted functions? (b) Using these definitions for the basis set functions, determine the elements of the secular determinant for butadiene in terms of a and ẞ. On the submission quiz, you will be asked some questions about the format and elements found in the determinant.