Q 2(a) [70 Marks] The secular equations for describing the overlap of the four unhybridised p orb...
Q 2(a) [70 Marks] The secular equations for describing the overlap of the four unhybridised p orbitals in butadiene (shown above) lead to a matrix of the form H11- ES ES12 H13- ES13H14-ES14 H21- ES21 H22- ES22 H23 - ES23 H24- ES24 H31- ES31 H32 - ES32 H33 - ES33 H34- ES34 41 - ES41 H42 - ES42 H43- ES43 H44- ES44 where Hy is the Hamiltonian integral for orbitals i and j and Sj is the overlap integral for orbitals i and j. This matrix can be simplified using the approximations of Hückel molecular orbital (MO) theory, which involves two constants α and β () Explain the approximations of Hückel MO theory in terms of Hij and Sj, and define a and B (ii) Re-write the above matrix applying these assumptions (ii) Write the equivalent Hückel MO theory matrix for cyclo-butadiene (iv)Briefly explain (without performing any calculations) how this matrix is used to determine the energies and coefficients of the MOs 30 Marks] Q 2(b) The energies of the π MOs obtained from Hückel MO theory for n atoms are given by where k is the energy level (k 1,2, ..., n) (i) Draw an energy diagram that indicates the Tt orbitals in butadiene that are occupied with electrons. Label the HOMO and LUMO (ii) Calculate the HOMO-LUMO gap of butadiene in kJ/mol if β-_250 kJ/mol
Q 2(a) [70 Marks] The secular equations for describing the overlap of the four unhybridised p orbitals in butadiene (shown above) lead to a matrix of the form H11- ES ES12 H13- ES13H14-ES14 H21- ES21 H22- ES22 H23 - ES23 H24- ES24 H31- ES31 H32 - ES32 H33 - ES33 H34- ES34 41 - ES41 H42 - ES42 H43- ES43 H44- ES44 where Hy is the Hamiltonian integral for orbitals i and j and Sj is the overlap integral for orbitals i and j. This matrix can be simplified using the approximations of Hückel molecular orbital (MO) theory, which involves two constants α and β () Explain the approximations of Hückel MO theory in terms of Hij and Sj, and define a and B (ii) Re-write the above matrix applying these assumptions (ii) Write the equivalent Hückel MO theory matrix for cyclo-butadiene (iv)Briefly explain (without performing any calculations) how this matrix is used to determine the energies and coefficients of the MOs 30 Marks] Q 2(b) The energies of the π MOs obtained from Hückel MO theory for n atoms are given by where k is the energy level (k 1,2, ..., n) (i) Draw an energy diagram that indicates the Tt orbitals in butadiene that are occupied with electrons. Label the HOMO and LUMO (ii) Calculate the HOMO-LUMO gap of butadiene in kJ/mol if β-_250 kJ/mol