Set up and solve the hiickel secular equations for

Question

Part -1:

1. Set up and solve the Hiickel secular equations for the Π electrons of CO₃^-2. Express the energies in terms of the Coulomb integrals α_o and α_c and the resonance integral β. Determine the delocalization energy of the ion.

2. For monocyclic conjugated polyenes (such as cyclobutadiene and benzene) with each of N carbon atoms contributing an electron in a 2p orbital, simple Hiickel theory gives the following expression for the energies E_k of the resulting it molecular orbitals:

E_k = α+2βcos 2kΠ/N k=0,±1,...±N/2 for N even

                                 k=0,±1,...±(N-1)12 for N odd

(a) Calculate the energies of the Π molecular orbitals of benzene and cyclooctatetraene (5). Comment on the presence or absence of degenerate energy levels.

(b) Calculate and compare the delocalization energies of benzene (using the expression above) and hexatriene. What do you conclude from your results?

(c) Calculate and compare the delocalization energies of cyclooctatetraene and octatetraene. Are your conclusions for this pair of molecules the same as for the pair of molecules investigated in part (b)?

Part -2:

1. Consider the following four diatomic molecules 02+, 02, 02-, 022-.

a. Sketch the molecular orbital energy level diagram for each molecule. Make sure to indicate the occupation and symmetry label of each level.

b. Calculate the bond order for each molecule and list the four molecules in order of decreasing bond length.

2. The dissociation energy is the energy needed to separate a molecule into its constituent atoms. Use molecular orbital theory to explain why the dissociation energy of N2 is greater than N2+, but the dissociation energy of 02 is less than 02k.

3. The ionization energy of the H 1s electron is 13.6 eV, and the ionization energy of a Cl 3p electron is 13.1 eV. Let the molecular orbitals zp+ and zp_ denote the lowest a-type bonding and antibonding molecular orbitals formed between the H 1s and Cl 3p, with energies E+ and K, respectively. If the value of the resonance integral is fi = -1.2 eV and the overlap S is assumed to be zero, calculate the MO coefficients in zp+ and zp_, and their associated ener¬gies E+ and K.

4. Atkins and de Paula, Problem 10E.1 (the one involving CO32-).

5. Atkins and de Paula, Problem 10E.2 (the one involving benzene and cyclooctatetraene).