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.

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.