In the Hckel 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 some of the video tutorials for Lesson 6D. Recall that in Hckel method, the overlap and Hamiltonian integrals were defined as (note: 10i) = 12pzi)) (1 i=j I Sij = {4:16;) = 8ij = {0 17"} = - (a i =j Hij = ($i|A|0j) = {B i =j #1 lo otherwise (a) One can define two sets of two symmetry-adapted orbitals for this problem, defined by , = + 4 2 = 2 + 3 (Ay symmetry) V3 = 02-03 = - 4 (B, symmetry) These basis functions are not normalized, though the atomic orbitals, a, are orthonormal within the Hckel theory assumptions. What is the constant that normalizes each of these symmetry-adapted functions (you will be asked to report one of them, chosen at random, on the submission quiz). = (b) Using these definitions for the basis set functions, determine the elements of the secular determinant for butadiene in terms of a and B. On the submission quiz, you will be asked some questions about the format and elements found in the determinant