Question 2 (6pts, sub-points noted below) The pi bonding in benzene can be modelled using a simple Hückel model.
a. (2) Write down the Hamiltonian matrix H in terms of the basis {|pj>, j=1,2..6} where {|pj> are the 2pz orbitals localized on the jth carbon atom. State the assumptions you made to generate these matrix elements and express them in terms of ? and ? discussed in class
b.(1) Explain why setting the determinant of the matrix: |H â EI] = 0, is equivalent to finding the eigenvalues and eigenfunctions of the Hamiltonian in the atomic basis.
c. (1) Use the website: https://www.stolaf.edu/depts/chemistry/courses/toolkits/247/js/huckel/ to determine the eigenvalues (E1,.., â¦E6) for the pi molecular orbitals of benzene in terms of ?alpha and ?beta
d. (2) Use this website to determine the energy levels of the linear polyene with the same number of C atoms. Compare the âdelocalization energyâ of benzene (cyclic) with this linear polyene
Question 2 (6pts, sub-points noted below) The pi bonding in benzene can be modelled using a simple Hückel model.
a. (2) Write down the Hamiltonian matrix H in terms of the basis {|pj>, j=1,2..6} where {|pj> are the 2pz orbitals localized on the jth carbon atom. State the assumptions you made to generate these matrix elements and express them in terms of ? and ? discussed in class
b.(1) Explain why setting the determinant of the matrix: |H â EI] = 0, is equivalent to finding the eigenvalues and eigenfunctions of the Hamiltonian in the atomic basis.
c. (1) Use the website: https://www.stolaf.edu/depts/chemistry/courses/toolkits/247/js/huckel/ to determine the eigenvalues (E1,.., â¦E6) for the pi molecular orbitals of benzene in terms of ?alpha and ?beta
d. (2) Use this website to determine the energy levels of the linear polyene with the same number of C atoms. Compare the âdelocalization energyâ of benzene (cyclic) with this linear polyene
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